ASTROCLK Astronomical Clock and Celestial Tracking Program Page 69 CELESTIAL NAVIGATION The close relationship between navigation and astronomy as well as the development of accurate time keeping is no accident, as related elsewhere in this text. In this age of constellations of artificial navigation satellites (NAVSTAR Global Positioning System) and precision inertial guidance or navigation systems (INS), it is easy to forget how difficult navigation was when the only "instrument" available may have been keen eyesight or a simple compass. The captain of a modern ship or aircraft only needs to glance at a digital readout to know his position within a few meters. It has not always been so, and indeed the occasional human or instrument failures which result in disaster remind us that navigational skills (and common sense) still need to be kept handy when traveling long distances. Navigation, which might be defined as the skills required to determine how to move from Point A to Point B, may be divided into two reasonably distinct classes: visual and calculated. Visual navigation is a skill we each practice every time we move about; it involves those actions and reactions necessary to move from our present location to a second location, whether across the room or across town, which is always in view or via intermediate way points always in view. Regardless of the conditions or obstacles we encounter, we automatically make any adjustments in our course required to keep us heading toward our objective. The outcome is usually certain and we seldom think much about the processes involved. Even longer distance travel by automobile is primarily visual navigation, with occasional reference to a map to remind us of the landmarks to watch for; although some practice at map reading may be helpful, few calculations are required. True long distance travel, whether by land, sea, or more recently in the air, requires navigation. The goal is to attain a known destination which is not in view through conditions which may be unknown or which may constantly be changing. Once again, those of us who are merely passengers think little of the processes involved. Unfortunately in a few cases, those charged with our safety sometimes assume that Nature will unfailingly cooperate and that they have correctly supplied all required information to instruments which are (and will continue to be) working perfectly. Airline pilots, ship captains, and weekend sailors may occasionally fallen victim to these dangerous assumptions with deadly results. To be successful, any scheme of navigation must include certain essential ingredients: the correct (UT) time, where you are now, where you want to go, and how to measure or calculate your progress towards that destination. The text which follows describes two ingredients which are in common use today (if only as backup skills in the event of electronic failure), "Navigation by Dead Reckoning" and "Calculation of Position by Sight Reduction". ASTROCLK uses both of these methods to provide navigational information and calculations. The equations required for these calculations are given in the Nautical Almanac 1989 (see ASTROCLK Astronomical Clock and Celestial Tracking Program Page 70 BIBLIOGRAPHY). Beginning in 1989, the Nautical Almanac has included a new section which describes the "Formulae and method ... for use with an electronic calculator or microcomputer for the determination of position at sea". I have adapted this material for use in ASTROCLK. One final comment regarding ASTROCLK's navigation functions is in order. So as to minimize the code and memory required to perform these tasks, ASTROCLK utilizes common subroutines to perform many of the calculations and display functions. These are used for navigation and otherwise. In particular, navigational positions may be shown to a precision of 0.01 seconds of arc and such accuracy is far beyond even the most sophisticated satellite navigation equipment today, never mind ASTROCLK. There are many possible sources of error, both human and electronic, in the data used for dead reckoning and celestial navigation, any one of which could contribute a position difference of some minutes of arc or more. I have made every effort to achieve reasonable accuracy, but the user should keep possible error factors in mind when using the navigation functions. Setting UT TIME ZONE OFFSET Prior to the inclusion of the Navigation Mode (Version 8943 and higher), ASTROCLK always assumed that the computer's internal clock was set correctly to the local time and based all other time calculations upon that assumption. Navigation, however, presumes that the computer may be moving from place to place and that the longitude (and therefore the local time and time zone) may be changing. Under these circumstances, what ASTROCLK really needs to know is Universal Time, UT1, and for our purposes UT = UT1 = UTC to sufficient accuracy in most cases except extremely precise navigation and astronomical measurements. One way to accomplish that end is to simply set the computer's clock to UT and be done with it; most users, myself included, would object to that inconvenience especially when using the computer outside of ASTROCLK. The alternative is to introduce a constant which tells ASTROCLK how to calculate UT from the setting of the computer's clock. I have chosen to use the second method and to call the constant "UT TIME ZONE OFFSET". When operated in this mode, the computer clock remains set to "home" local time; UT time is always available by applying the UT TIME ZONE OFFSET, and the correct local time is obtained directly from the current longitude (either calculated or manually entered). However, since local time is always calculated, no ZONE CORRECTION is permitted in the Navigation Mode and any ZONE CORRECTION in effect will be cleared when the UT TIME ZONE OFFSET is set. For users accustomed to the "old" versions of ASTROCLK (Versions 8935 and earlier) and who are not concerned with the navigation features, program operation is essentially unchanged and the ZONE CORRECTION is permitted if the UT TIME ZONE OFFSET is left disabled (the default condition). Several advantages result from the use of the UT TIME ZONE OFFSET. Most importantly, ASTROCLK can always calculate UT time, and therefore all of the celestial time and position information ASTROCLK Astronomical Clock and Celestial Tracking Program Page 71 regardless of the actual location of the user. Once properly set, the user may "move" his computer from place to place and the time will remain correct. Unlike operation in the normal real time mode, the user may select another location using F6 and the correct local time (as determined by the longitude) will be displayed. By selecting a starting point (a navigational "fix") and entering the true course and speed, the user may place himself upon a moving vessel, calculate the current position by dead reckoning (see following section), and maintain real time coordinates for planetary or celestial bodies based upon the current estimated position. Finally, the user may accurately calculate his current geographic position using two or three star sights, ASTROCLK's version of classical celestial navigation. At the same time, several minor penalties must be paid for these additional capabilities. First, as noted above, the ZONE CORRECTION is not permitted. This may represent an inconvenience for users in local time zones different from that calculated by ASTROCLK. Second, for users with slower computers not equipped with a math coprocessor, additional time is required for calculations in all modes and performance for those computers is slightly degraded. Performance degradation of AT and 386 computers, whether or not equipped with a math coprocessor, is not significant. Last of all, additional RAM memory is required for ASTROCLK to accomodate these features. [See the section PROGRAM OPERATION, Required ASTROCLK Files, for additional discussion.] When ASTROCLK is first started, the UT TIME ZONE OFFSET is disabled and program operation is essentially unchanged from prior versions. The UT TIME ZONE OFFSET may be enabled or disabled at any time by pressing Function Key F10 (NAVIGATION) and then F10 again. If currently disabled, the main ASTROCLK NAVIGATION menu will appear in the main window the first time F10 is selected: ASTROCLK NAVIGATION INFORMATION Navigation functions available are: F1 = Show current NAVIGATION DATA F5 = Select USNO Navigation Stars Before using other NAVIGATION functions, you must use F10 to set the time offset between your computer clock and UT Time. F10 = Set Computer UT Time Zone Offset Select function or press RETURN to cancel: Note that except for displaying current NAVIGATION DATA and selecting USNO Navigational Stars, no other navigation functions are available until the UT TIME ZONE OFFSET has been set. If the UT TIME ZONE OFFSET is enabled, other functions will be available ASTROCLK Astronomical Clock and Celestial Tracking Program Page 72 for selection (see below). Pressing F10 the second time, to set the UT TIME ZONE OFFSET, will display the following: ASTROCLK NAVIGATION INFORMATION In order to calculate positions and times correctly, ASTROCLK must know the time zone offset from UT Time to which your computer is now set. If LOCAL and UT times are both correctly displayed press '*'; otherwise enter the time offset in hours. Press RETURN to skip or F10 to disable UT OFFSET and NAVIGATION. The current UT OFFSET is: (disabled) Enter UT TIME ZONE OFFSET (hours): The display reproduced above shows that the UT TIME ZONE OFFSET is now disabled; if the UT TIME ZONE OFFSET were active, the actual offset in hours would be displayed instead of "(disabled)". If the local and UT times displayed in the small windows on the right side of the screen are correct and no ZONE CORRECTION is in effect, simply enter '*' (without the apostophes) and ASTROCLK will calculate the offset. Otherwise, enter the correct offset in hours followed by RETURN. Decimal fractions of an hour are permitted. If the UT TIME ZONE OFFSET is now active (a number such as "-7.00" is displayed instead of "(disabled)") and you wish to disable the function, press F10 again. If you wish to retain the present value, press RETURN. The required value for UT TIME ZONE OFFSET will be positive for East longitudes and negative for West longitudes. For example, the correct value is -8.00 for Pacific Standard Time or -7.00 for Pacific Daylight Time and -5.00 for Eastern Standard Time or -4.00 for Eastern Daylight Time. CAUTION: If your time zone is non-standard (that is, if you must normally use a ZONE CORRECTION to obtain the correct local and UT time displays), you must enter the value that corresponds to your time zone as calculated based upon your longitude and subtract an hour if daylight time is in effect. Any ZONE CORRECTION in effect will be cleared. Verify that local time and UT time are both correct when ASTROCLK resumes normal operation and repeat the process if necessary. For locations with "standard" time zones, there will be no apparent difference so long as the current longitude remains in the original time zone. All standard time zones extend 7-1/2 degrees on either side of the 15 degree meridians. Once set, the UT TIME ZONE OFFSET is saved in file ASTROCLK.INI and will continue in effect until disabled. You may verify the operation of the UT TIME ZONE OFFSET by using Function Key F6. First, press "1" to select Local Time in the main display window, then press F6. If you live in the Western United States, enter "USNO" as the location and Eastern Standard or Daylight Time will be shown, as determined by the ASTROCLK Astronomical Clock and Celestial Tracking Program Page 73 current setting of the DAYLIGHT FLAG. If you live in the Eastern United States, enter "RPV" as the location and Pacific Standard or Daylight Time will be shown. Press F6 again and restore your correct local name and coordinates and observe that the display returns to your correct local time. UTC Time will not change as you change location. Even if you do not plan to use the other navigation features of ASTROCLK, you may find it helpful to set the UT TIME ZONE OFFSET. Once properly set, you may change ASTROCLK's local coordinates using Function Key F6 to any desired location, display the correct local time for that location, and view planetary or celestial coordinates as they appear at that location for the current time. For example, you may determine where a particular object would appear in the sky (or if it is below the visible horizon) at a given instant for Los Angeles, Chicago, New York, London, and so forth. This may be done in real time, or the clocks may be stopped and set to any desired time and/or date. Navigation by Dead Reckoning The oldest and perhaps the most basic method of navigation is called Dead Reckoning. The name derives from the fact that you assume you are proceeding along the course you have "reckoned", come what may. In theory it is quite simple: if you know where you started and your course and speed, you may calculate your present position; similarly, if you know where you are and where you want to go, you may calculate the course, speed and time necessary to get there. To improve accuracy, you may also take into account the effects of wind, currents and other factors as they occur. Provided all these things are known to sufficient accuracy and are correctly included in your calculations, easy to say but more difficult in practice, you will know your present position and will likely reach your destination. It is a considerable credit to the navigators of old that, long before the development of the nautical chronometer, they were able to sail for days and sometimes weeks relying entirely upon dead reckoning and still come reasonably close to their intended destination. Captain William Bligh, of "Mutiny on the Bounty" fame (or notoriety, if you prefer), may never qualify as Mr. Nice Guy but he nevertheless performed what must rank as one of the most amazing feats of navigation ever recorded. This in 1789 by sailing a small boat on open seas nearly four thousand miles from the point where he and 18 others were set adrift from the Bounty all the way across the South Pacific to Timor in the East Indies, arriving some six and a half weeks later. Even with ASTROCLK along, I'm not sure I'd like to try to duplicate that trick! Less spectacular but equally impressive feats were almost a matter of routine for the master navigators of that age and earlier. ASTROCLK takes a somewhat simple minded approach to navigation by dead reckoning. Four items of information are required to specify the last "fix" or position from which future movements are calculated: longitude, latutude, time, and date. ASTROCLK Astronomical Clock and Celestial Tracking Program Page 74 The longitude and latitude may either be obtained from star sights (as described in the following section) or be taken from charts or other sources. CAUTION: West longitude and South latitude are negative; not all sources use the same sign conventions, particularly with respect to longitude. To avoid confusion with respect to time zones, all navigational times and dates are UT (Universal Time), still referred to by most navigators as GMT or Greenwich Mean Time; even NASA retains the older designation. Once these data are entered, the current position is then calculated by taking the true course and speed (in knots, nautical miles per hour) and calculating the direction and distance traveled in the time elapsed since the last position. If the last position is accurate and if, as is less likely, the course and speed correctly take into account all those effects such as wind and current, the calculated position will be accurate. Even when the current course and speed are less well known, dead reckoning can provide a useful confirmation for other methods of position determination. ASTROCLK uses true bearings rather than magnetic bearings since the magnetic declination, the difference between true North and magnetic North as shown by a compass, varies considerably and changes very slowly with time. The direction of the declination is given as "East" or "West", meaning that true North is in the specified direction from magnetic North. Magnetic declination should not be confused with astronomical declination. In the United States, the magnetic declination ranges from about 20 degrees West in the extreme Northeast to 22 degrees East in the extreme Northwest. The line of zero magnetic declination, where the true and magnetic bearings are the same, passes near Chicago, Illinois and Tallahasse, Florida. Local magnetic anomalies can also cause significant changes in the magnetic declination. Most large ships and aircraft use satellite or inertial navigation systems which provide true bearings but smaller craft (and the air traffic control system) use magnetic bearings. Knowing the local magnetic declination is therefore important in navigation and can also be helpful for the alignment of telescopes when the North star is not visible (i.e. during daylight hours). When traveling long distances, life is not quite so simple if the navigator wishes to minimize the distance covered. The bearing or "true course" to a distant destination, that course plotted directly on a conventional map or chart, does not represent the ideal course. Depending upon the projection used in the preparation of the chart, the minimum distance and best course are not necessarily represented by a straight line. For distances under several hundred miles, the difference is usually trivial and can be ignored. However, for distances of hundreds of miles or more which involve significant differences in longitude, the navigator should plot his "great circle" course. A few minutes spent with a globe and a piece of string stretched taut between two locations will suffice to demonstrate that a great circle route can be considerably shorter than what appears to be the most direct route on a flat map. The polar route used by aircraft from the Western United States to Europe is an example of a frequently used great circle route. It is important to note ASTROCLK Astronomical Clock and Celestial Tracking Program Page 75 that, unlike lines of equal latitude, the meridians (lines of equal longitude) are already great circle routes; therefore, voyages which are primarily North-South gain little or no benefit from plotting a great circle route. Exactly following a typical great circle route involves constant changes in course, since the route follows an arc rather than a straight line when plotted on a standard projection chart. In practice, therefore, navigators usually select a series of way points along the desired route and follow a set course between each point. The more way points selected, the better the approximation to the great circle route -- and the greater the chance for human error. It has been suggested that Korean Air Flight 007 may have met disaster because of an entry error on a way point, most likely a digit transposition in the longitude coordinate, thereby crossing restricted Russian airspace rather than being well out over the Pacific ocean and thus setting the stage for what followed. Although ASTROCLK calculates the distance already traveled from the last navigation fix and the current position using dead reckoning (current speed times elapsed time in the direction specified by the current course), the distance to a selected destination (or way point) is computed using the great circle arc from the current position to that destination. To a first order approximation, each degree of that arc is sixty nautical miles. (The conversion is exact by definition along the equator but becomes slightly less accurate as the latitude increases due to the flattening of the Earth at the poles. ASTROCLK takes this factor into account in its distance-to-destination calculations.) The displayed distance to the destination is therefore always the current great circle distance from the current position; whether or not the destination lies along the present course is of no consequence to the calculations, and that fact must be kept in mind when using the data for navigation. If the current speed is entered as zero, ASTROCLK may be used to calculate the great circle distance from the current navigation point to the selected destination. The distance is shown in nautical miles and kilometers. Also shown is the "chart course" from the navigation point to the destination. By deliberately picking an off-course destination, you may take advantage of this method and watch for the point of closest approach as you pass by. By setting the speed to zero, which forces the current position to remain at the navigation fix or geographic location, ASTROCLK may also be used to calculate the great circle distance between any two points on the globe. Point-to-point navigation by either true or magnetic bearings, as opposed to great circle routes, is most accurate in the mid latitudes and over moderate distances. As the route approaches polar regions and as the distances become longer, inaccuracies become more and more significant; these inaccuracies are almost entirely due to the coordinate system used to project the surface of a sphere onto a flat surface. Since ASTROCLK and most navigators use that same coordinate system, some care must be used in these cases. The problem is easily illustrated by an example: plot a straight line course of 45 degrees (Northeast) on a typical Mercator or cylindrical projection of the world. Sooner ASTROCLK Astronomical Clock and Celestial Tracking Program Page 76 or later you will arrive at the top edge of the map, and that entire upper edge represents the North Pole. Therefore, ANY northerly course will eventually wind up at the North Pole; the same applies with respect to the South Pole for southerly courses. Transferring the plot to a globe will trace a gradually curving course toward the pole. If the course were 80 degrees rather than 45 degrees, it would trace a spiral route toward the pole through successive revolutions around the globe. Of course, no navigator would ever steer 80 degrees in hope of eventually reaching the North Pole, but ASTROCLK must know how to handle such a case in the event that a course is entered and left alone for some days or even months. Having reached the Pole, regardless of the circuitous route, the program must select a reasonable and consistent method of processing continuing travel. The most obvious choice is to assume that, having reached the Pole, the voyage should continue on the opposite side of the globe with a course 180 degrees different from the initial course. Using this method, an initial course of 0 degrees (North) will result in polar circumnavigation of the globe, just as expected; reaching the North Pole, the course becomes 180 degrees and continues to the South Pole where the process is reversed. This is the algorithm which ASTROCLK uses over long distances but it can yield results which appear rather peculiar taken out of context. When first started, the navigation functions of ASTROCLK are disabled. Before attempting to enable these functions, the UT TIME ZONE OFFSET must be set as described above. If the navigation functions are enabled, they may be disabled at any time by using Function Key F6 to enter new local coordinates. This disables navigation without clearing the data; the navigation data may be re-enabled with Function Key F10 followed by F2 and then pressing RETURN to select the old data. Once the UT TIME ZONE OFFSET has been set, pressing Function Key F10 displays the full Navigation Menu: ASTROCLK NAVIGATION INFORMATION Navigation functions available are: F1 = Show current NAVIGATION DATA F2 = Set current NAVIGATION DATA F3 = Set current DESTINATION DATA F4 = Set current STAR SIGHT DATA F5 = Select USNO Navigation Stars F10 = Set Computer UT Time Zone Offset Select function or press RETURN to cancel: Pressing Function Key F1 will display the Navigation Data now stored, whether or not navigation is active. A typical display contains the following data: ASTROCLK NAVIGATION INFORMATION ASTROCLK Astronomical Clock and Celestial Tracking Program Page 77 The current NAVIGATIONAL DATA are: Nav LONGITUDE: -15.000000 Nav LATITUDE: 32.000000 Nav POSITION TIME: 20.0 UT Nav POSITION DATE: 16-06-1989 Nav COURSE (true): 325.000000 Nav SPEED (knots): 20.00 DISTANCE Traveled: 10.00 nm = 18.53 km ELAPSED TIME: 0.5000 hrs Press RETURN to resume ASTROCLK: When you have finished reviewing the data, press RETURN to resume normal operation. You may use Function Key F7 to select the preferred format of displaying angles and time. Pressing Function Key F2 will display the current navigational data as above except that the prompt at the bottom of the window is changed to: Press SPACE to enter NEW Navigation Data, or press RETURN to ACCEPT, or F10 to CANCEL: Press RETURN to accept the data as shown, press Function Key F10 to cancel data entry and return to normal operation, or press the SPACE BAR to enter new or changed data. If you press RETURN, you will be prompted for each of the six required items and the current value of that item will be shown. Nav LONGITUDE: -15.000000 Nav LATITUDE: 32.000000 Nav POSITION TIME: 20.0 UT Nav POSITION DATE: 16-06-1989 Nav COURSE (true): 325.000000 Nav SPEED (knots): 20.00 If the current value of an item is correct, press RETURN for that item. If you wish to change the item, enter the new value followed by RETURN. The input format is very flexible, and the longitude, latitude and course may be entered in degrees, degrees and minutes, or degrees and minutes and seconds. Any item may have a fractional decimal part. Use the comma as a separator. If you wish to use the local coordinates and the current time as the navigation fix, enter "*" (without the quotation marks) followed by RETURN in response to the prompt for LONGITUDE. In this case, only the COURSE and SPEED will remain to be entered. When all items have been processed, the original display will be repeated with any new or changed values shown and the same prompt: Press SPACE to enter NEW Navigation Data, or press RETURN to ACCEPT, or F10 to CANCEL: Press RETURN to accept the values shown and enable navigation or press SPACE BAR if some values must be corrected. This process may be repeated as many times as necessary and at any time. Once ASTROCLK Astronomical Clock and Celestial Tracking Program Page 78 the navigation functions have been enabled, the local coordinates window will display the current calculated position based upon the data just entered above using dead reckoning. If a non-zero speed has been entered, the local coordinates window will display the title "Calculated Position" instead of a location name, and that position will be calculated in real time when the clocks are on. The local time will be adjusted according to the current longitude and all celestial and planetary positions and other data will be calculated dynamically. Once the navigation data has been entered, the main display window may be set to the Navigation Mode by pressing the "N" key. A typical navigation data display contains the following data: ASTROCLK NAVIGATION INFORMATION Data relative to: NAVIGATION DATA LONGITUDE: -15 00'00.00" LATITUDE: 32 00'00.00" DISTANCE: 280.00 nm = 519.49 km ELAPSED TIME: 14:00:00 Current COURSE: 325 00'00.00" (No DESTINATION DATA entered) In this example, Function Key F7 has been used to set the angle and time formats as shown. Note that the distance traveled is based solely upon the elapsed time multiplied by the current speed and does not necessarily bear any relationship to the distance between the navigational position or fix and the current position. Note also that if the current speed has been set to zero, the DISTANCE and COURSE data will not be displayed. Even when actual navigation is not intended, ASTROCLK may be used to measure great circle distances between the current navigation point (or local coordinates) and any other geographic location by setting the speed equal to zero. In this case, certain items which do not apply, such as distance traveled, are eliminated from the displays. One final step is required to fully set up a navigation or distance measuring situation: entering a "destination". The destination may be the intended destination, a way point along the projected course, or simply a point of interest. Two methods are available for entering the destination data: Function Keys F10 and SHIFT-F6; both methods accomplish the same purpose but by slightly different techniques. To manually enter the destination data, press F10 and then F3. The current destination information, if any, will be displayed: ASTROCLK NAVIGATION INFORMATION Current DESTINATION DATA: NAME: Way Point A LONGITUDE: -15 14'57.84" LATITUDE: 32 20'57.47" You will be prompted in turn to enter new or changed information: ASTROCLK Astronomical Clock and Celestial Tracking Program Page 79 Enter NAME (SPACE to cancel): Enter LONGITUDE (W = negative): Enter LATITUDE (S = negative): To clear all destination information, enter SPACE followed by RETURN instead of a name or designation. Press RETURN to leave an item unchanged. Note that West longitudes and South latitudes are entered as negative numbers. The input format is very flexible, and the longitude and latitude may be entered in degrees, degrees and minutes, or degrees and minutes and seconds. Any item may have a fractional decimal part. Use the comma as a separator. Function Key SHIFT-F6 may also be used to enter destination data, especially when that data is available in a "city file" on disk. For example, file USWEST.VOR is available which includes complete data for the 287 VOR's (VHF Omni-Directional Range, a radio navigation aid for aircraft) in the 11 western states. A navigator might wish to prepare a special file of navigation points for use in an upcoming trip. Operation of SHIFT-F6 is identical to that used to set the local coordinates with Function Key F6. Once destination data has been entered, pressing the "N" key to enable the Navigation Mode will automatically include the calculation of your present position compared to that destination: ASTROCLK NAVIGATION INFORMATION Data relative to: NAVIGATION DATA LONGITUDE: -15 00'00.00" LATITUDE: 32 00'00.00" DISTANCE: 280.00 nm = 519.49 km ELAPSED TIME: 14:00:00 Current COURSE: 325 00'00.00" Data relative to: WAY POINT A LONGITUDE: -15 14'57.84" LATITUDE: 32 20'57.47" DISTANCE: 253.54 nm = 470.40 km TIME TO DEST: 12:40:37 Chart COURSE: 140 04'26.57" In this example, we have obviously sailed well past Way Point A by some 254 nautical miles (great circle distance), and the course back to that point as plotted on a conventional chart is approximately 140 degrees. At the present speed, it would require about 12 hours and 40 minutes to return to Way Point A IF we follow the great circle route. For longer distances, the great circle route and the chart course will NOT be the same, as discussed above. For short and moderate distances, the two courses will be approximately the same. When the speed has been set to zero (using Function Key F2), information which does not apply in that case is deleted from the navigation mode display: ASTROCLK Astronomical Clock and Celestial Tracking Program Page 80 ASTROCLK NAVIGATION INFORMATION Data relative to: NAVIGATION DATA LONGITUDE: -120 34'00.00" LATITUDE: 38 09'00.00" ELAPSED TIME: 0:34:15 Data relative to: Crazy Woman, WY CZI LONGITUDE: -106 26'06.00" LATITUDE: 43 59'54.00" DISTANCE: 727.77 nm = 1350.24 km = 838.03 mi Chart COURSE: 67 31'04.73" In this example, the destination has been set to the aircraft VOR at Crazy Woman, Wyoming (VOR code "CZI"), and the navigation fix is for Calaveras County, California. Using SHIFT-F6, you may select different destinations from the current city file and obtain a display of the coordinates, distance and chart course relative to the navigation fix. Note the addition of the distance in statute miles ("mi") in this version of the display. Celestial Navigation with Star Sights To be effective, any method of navigation requires that the initial position be known as precisely as possible. Departing a location whose coordinates are known provides that initial data but within a relatively short time, depending upon the speed of travel, a navigator needs to determine a new position both to check the accuracy of his dead reckoning calculations as well as to serve as a new basis for position calculations. Failure to do so can have unfortunate results. One of the most accurate methods of establishing a position, or "fix", has been to take sights of the Sun, Moon, planets or selected bright stars, and use that information to compute a position. This technique is known as celestial navigation. To do this, a triangle known as the "celestial triangle" or "navigational triangle" is formed between the observer, the North or South Celestial Pole, and the selected star or other celestial object. These three points are projected onto a sphere and the solution of the angles of the resulting celestial triangle using spherical trigonometry provides the position information the navigator seeks. A number of different methods have been used over past centuries to obtain the solution to the celestial triangle. Early methods were very cumbersome and difficult to solve accurately. In the nineteenth century a technique called the Altitude- Intercept Method was developed by the Frenchman Marc St. Hilaire using two trigonometric equations (known as the Cosine-Haversine formulas) to solve the problem. Although this new method was a considerable improvement over earlier methods, it was still quite a chore to manually calculate a position. About 1930 a Japanese, Ogura, developed a simplified solution based upon sight reduction ASTROCLK Astronomical Clock and Celestial Tracking Program Page 81 tables. These tables gave the position of the Sun and selected stars and planets at regular intervals throughout the year. By recording the altitude of two or preferably three celestial objects whose positions were tablulated, along with the time of each measurement and the vessel's course and speed, the navigator could determine his position at a specific time and calculate his present estimated position. The Nautical Almanac, jointly published every year by the U. S. Naval Observatory and H. M. Nautical Almanac Office, gives similar, improved tables today that form the basis for manual calculation of a position by sight reduction. Data are given for the Sun, Moon, Venus, Mars, and Saturn for each hour of each day, and the positions of the 57 USNO navigational stars for each three day period (since the rate of change of stellar positions is relatively slow). The method involves little more than noting the date and time, looking up numbers in the tables, and then performing various interpolations, additions, and subtractions. Simple as that may sound, the calculations must be performed correctly and with sufficient precision in order to obtain a reliable position. With the advent of electronic calculators and, more recently, portable computers, attention has again been focused on St. Hilaire's original Cosine-Haversine formulas developed in 1875. Using the formulas directly instead of tables derived from them makes electronic calculation relatively straightforward once the formulas themselves have been properly entered. ASTROCLK uses this method with observations of any of the 57 USNO Standard Navigational Stars, as described in the Nautical Almanac 1989. (However "straightforward" the data entry process may be, a brief look at ASTROCLK's inner workings will reveal that setting up all the information needed to use the formulas is a non-trivial task!) Regardless of which of these methods is employed, sight reduction tables or formulas, everything depends upon taking accurate star sights and knowing the correct time. Taking a sextant sight on a moving vessel requires considerable skill and practice as well as an accurate instrument. ASTROCLK and a good short wave radio can provide the time to sufficient accuracy almost anywhere in the world. The resulting position calculations are more accurate than the typical star sights by an average navigator. Star sights are typically made using a marine sextant or a bubble sextant. One of the important differences between these two instruments is the method by which the horizon is determined. The marine sextant uses the apparent horizon (which must therefore be visible at the time of measurement) and the resulting star altitudes must be corrected for "horizon dip", the lowering of the apparent horizon as the elevation of the observer increases. The bubble sextant, on the other hand, uses an artificial (true) horizon formed by a bubble in a liquid, much like the common carpenter's level, and needs no horizon correction. Depending upon the type of instrument being used, the elevation must be set to the actual elevation of the observer's ASTROCLK Astronomical Clock and Celestial Tracking Program Page 82 eye above mean sea level (marine sextant) or to zero (bubble sextant) using ALT-F6. ASTROCLK then makes the appropriate correction for horizon dip using a standard formula. Failure to set the elevation to the correct value can cause appreciable position errors. Some care should be used in the selection of the stars to be used for celestial navigation. Since objects near the zenith (directly overhead) are difficult to observe with a marine sextant, they should be avoided; similarly, errors due to refraction increase near the horizon. It is therefore recommended that the selected stars be at observed altitudes of from about 15 degrees to 80 degrees. Before the actual navigation calculations can be made, an estimated position or navigational fix must be entered and the celestial star sights must be taken. Using Function Key F7, set the display format to your preference (i.e. the same format as your sextant or navigational instrument uses). Then press Function Key F10 followed by F2 (a combination referred to as "Navigation Function Key F2") to enter the navigational fix data. The longitude and latitude of the navigational fix need only be entered to an accuracy of several degrees; a less accurate estimate simply means a few more calculations for ASTROCLK to achieve the desired accuracy. UT Time, UT Date, course and speed complete the required items. If you are in a fixed position, enter zero for course and speed. (See the Dead Reckoning section above for a more detailed description of setting the navigational fix.) Taking an accurate star sight typically requires from five to fifteen minutes. Record the UT Time when the sight is taken along with the observed altitude. While you may wish to check the azimuth of the star, ASTROCLK does not require that information for its calculations. Star sights may be made before or after the time of the estimated position. HINT: If you set the estimated position as the current coordinates using Function Key F6, you may then use ASTROCLK to help select suitable stars for your location and time; select a USNO Standard Navigational Star using Function Key F5 followed by F1 and check the Target Tracking Display to see that it is observable. ASTROCLK internally "plots" each of your star sights to determine a Line of Position (LOP) starting with the given altitudes and times, and processes the internal star database along with the course and speed to determine the various required functions. The initial estimated position and calculated position for each star sight should lie approximately along the Line of Position. ASTROCLK then generates a calculated position from these data and compares this calculated position with the initial estimated position. If these differ appreciably, it substitutes the new calculated position for the estimated position and repeats the process until the difference in positions reaches a minimum. The result is the final calculated position. To begin ASTROCLK's celestial navigation calculations, press Function Keys F10 and then F4. The program reminds you that you must take either two or three star sights and have previously ASTROCLK Astronomical Clock and Celestial Tracking Program Page 83 entered your estimated position: ASTROCLK NAVIGATION INFORMATION Celestial Navigation requires observed data for two or three USNO Navigational Stars. For this data to be valid, you must first have entered your last Navigation Fix using Navigation Function Key F2. Press RETURN to begin data entry or press any other key to cancel: Press RETURN if you are ready to enter the star sight data or press any other key to cancel and resume normal program operation. After pressing RETURN, ASTROCLK requests that you enter the instrument INDEX ERROR to be used in correcting the altitude measurements: Altitude measurements made with a sextant or other instrument often have an associated INDEX ERROR which must be removed from each measurement prior to performing calculations. Enter the INDEX ERROR (minutes) for your instrument or press RETURN to enter zero. The Index Error will be SUBTRACTED. Enter Index Error: Enter the index error in minutes of arc or press RETURN to enter an index error of zero. Once you have entered an index error value, ASTROCLK retains that value until the program is halted. Note that the index error entered will be subtracted from your altitude measurements. ASTROCLK now requests that you select the USNO Standard Navigational Star for the first star sight: Select USNO Standard Navigational Star Enter STAR NAME or STAR NUMBER: You may enter either the star name, using upper or lower case and sufficient letters to unambiguously identify the star, or the star number, 1 to 57. Use "DENEB ", with a trailing space, to select Deneb rather than Denebola. If you select star #49, for example, the program will look up the star, display its full name, and prompt you for the UT TIME of the star sight and the observed altitude: USNO Star #49 - a Lyrae - Vega Enter UT TIME for Star Sight #1: ASTROCLK Astronomical Clock and Celestial Tracking Program Page 84 Enter Observed Altitude [Ho]: ASTROCLK interprets any time entered as UT TIME, without adding a trailing "U". The time may be before or after the time entered for the navigation fix, but in practice the star sights should be made at approximately the same time as the estimated fix in order to minimize the dead reckoning errors if you are on a moving vessel. The observed altitude is the reading directly from the instrument; ASTROCLK will apply the horizon dip, index error and refraction corrections automatically. Repeat the last steps for the second (and third) star sight, as prompted. If you are entering only two star sights, press RETURN when requested for the USNO star number for the third sight. ASTROCLK uses the least squares method of calculating the position described in the Nautical Almanac 1989. However, ASTROCLK uses its own internal algorithms to calculate altutides and azimuths rather than those given in the NA; the results are essentially the same using either method. While two "perfect" sights are sufficient to do the calculations, three sights are preferred to minimize potential errors. After a brief delay, the results of the calculations are displayed: The sextant altitudes have been corrected to: Ho ALTITUDE 1: 20 02'31.94" Ho ALTITUDE 2: 29 28'28.19" Ho ALTITUDE 3: 43 55'22.80" The Celestial Navigation calculations have estimated the Navigational Fix Position as: Nav LONGITUDE: -15 14'58.27" Nav LATITUDE: 32 20'59.27" Press RETURN to ACCEPT the calculated posi- tion or any other key to discard: The first section of data are the corrected values for the observed altitudes. If data for only two sights have been entered, no data will be shown for a third sight. The second section of data are the results of the sight reduction calculations: the calculated longitude and latitude. If you wish to accept the new position, press RETURN; the new position will then appear in the local coordinates window and ASTROCLK will resume normal operation. Use Navigation Function Key F2 to set the new position as the current navigation fix. Selecting USNO Navigational Stars Before star sights can be used with ASTROCLK's celestial navigation functions, the two or three USNO Navigational Stars must be selected. While the skilled star gazer or navigator will immediately recognize the USNO stars, the casual observer may have more difficulty. Navigation Function F5 scans all 57 USNO stars, calculates the horizon coordinates (Altitude and Azimuth), then displays the first 20 which may be found above 15 degrees ASTROCLK Astronomical Clock and Celestial Tracking Program Page 85 and below 80 degrees referred to the actual horizon. (Be sure that the ELEVATION is correctly set!) All calculations are based upon the current local coordinates and time. In order to display this list, select Navigation Function F5. A brief delay (longer for computers not equipped with a math coprocessor!) will follow and then ASTROCLK will display the selected stars. The first 20 stars which are suitable will be displayed. Since the USNO stars are well distributed around the celestial sphere, from 15 to 20 stars are usually acceptable at a given time and place. USNO STARS: 15 < ALTITUDE < 80 # ALT AZ MAG # ALT AZ MAG 3 67.1 5.1 2.2 | 47 21.7 318.4 2.2 4 38.0 174.7 2.0 | 49 22.3 302.7 0.0 6 65.6 108.5 2.0 | 51 22.5 265.6 0.8 8 43.1 120.6 2.5 | 53 46.2 302.5 1.3 9 53.8 50.0 1.8 | 54 45.9 246.7 2.4 10 31.8 90.7 0.9 | 56 23.2 200.8 1.2 12 34.9 54.0 0.1 | 57 63.9 229.5 2.5 13 16.2 93.2 1.6 14 27.1 72.2 1.6 40 20.7 350.1 2.1 Press RETURN to continue ... The example above indicates that 17 USNO stars were considered suitable for navigation purposes using the current local coordinates and the current time. The following information is displayed for each star: USNO number, Apparent Altitude (ALT, degrees), Azimuth (AZ, degrees in the sense NESW), and standard visual magnitude (MAG). The Altitude has been corrected for refraction and horizon dip and therefore corresponds to the apparent position in horizon coordinates where the star may be found. Note that a star is brightest when its magnitude is smallest; negative magnitudes are brightest of all. Since the calculations are based upon the current location and time, the navigator may use the current calculated position or set an anticipated location and time (using F6 and F3) before taking star sights and select "suitable" stars in advance. If the current position is reasonably close to the expected position, only the time need be set; this avoids disabling and then re- enabling navigation mode when F6 is used. The non-navigator may also find the display useful: by setting the SPEED to zero (as discussed above), you may see an immediate display of the current positions of the visible USNO navigational stars (which also, by no coincidence, are the brightest stars) visible at the current position and time. Star gazers not yet accustomed to using horizon coordinates, altitude and azimuth, may find the information helpful in orienting their view of the night sky and in locating these stars. ASTROCLK Astronomical Clock and Celestial Tracking Program Page 86 Celestial Navigation Example It is often helpful to examine a worked out problem to see how entries are made and calculations performed. The following example illustrates how ASTROCLK can compute a position using celestial navigation and is based upon the example on pages 282 and 283 of the Nautical Almanac 1989. The original objective, of course, was to verify ASTROCLK's accuracy using known data. 1. Using Function Key F3, set the time and date to 20:00:00 UTC ("20U") on 16 June 1989 ("16,6,1989"). Note the "U" to signify Universal Time. 2. Using Function Key F7, set the display format for degrees to "ddd.dddddd" in order to agree with the format displayed in the Nautical Almanac. (The display format makes no difference to ASTROCLK.) 3. Using Function Key ALT-F6, set the Elevation to 0. Leave all other local conditions at their default values. In practice, the elevation should be be set to zero if the instrument provides an accurate artificial horizon; otherwise, set the elevation (height of the observer's eye above mean sea level) so as to compensate for the dip of the apparent horizon. The pressure and temperature should be set to the current conditions, if known. 4. Using Function Key F10 followed by F2, set the navigation fix to the coordinates, time, date, course, and speed required. The following display should appear if all information has been entered correctly: ASTROCLK NAVIGATION INFORMATION The current NAVIGATIONAL DATA are: Nav LONGITUDE: -15.000000 Nav LATITUDE: 32.000000 Nav POSITION TIME: 20.0 UT Nav POSITION DATE: 16-06-1989 Nav COURSE (true): 325.000000 Nav SPEED (knots): 20.00 DISTANCE Traveled: 0.00 nm = 0.00 km ELAPSED TIME: 0.0000 hrs Note that because the navigational fix time and date are the same as the time and date set in Step 1, the calculated distance traveled and the elapsed time are both zero. 5. Using Function Key F10 followed by F3, set the destination name and coordinates. Use the following values: Name: NA-1989 Longitude: -15.2494 Latitude: 32.3493 ASTROCLK Astronomical Clock and Celestial Tracking Program Page 87 These values are the final position estimate calculated in the Nautical Almanac and will be used to compare ASTROCLK's position calculation. The destination information is not required for ASTROCLK to perform the celestial navigation calculations and it is included here only for purposes of comparison. 6. Using Function Key F10 followed by F4, enter the star sight information as follows: Index Error: 0 Star #1: 49 (or "Vega") UT Time: 20:00 Altitude: 20.08481 Star #2: 21 (or "Pollux") UT Time: 19:50 Altitude: 29.50204 Star #3: 33 (or "Spica") UT Time: 19:40 Altitude: 43.93917 Either the USNO Star Number or its proper name (sufficient letters to unambiguously identify it, upper or lower case) may be used without the quotation marks. The time entry does not require the "U" to signify UTC. The altitude is shown entered in degrees and decimal fraction, but may be entered in any of the usual formats. Note that if you were using an actual sextant, an index error would normally be entered and automatically subtracted from the measured altitudes. Once entered, the index error is retained by ASTROCLK until the program is next restarted, on the assumption that all altitude measurements will be performed with the same instrument. The Nautical Almanac example does not include any index error, hence no error is entered here. 7. When the data have all been entered, the following display will appear to enable you to check your data: ASTROCLK NAVIGATION INFORMATION The sextant altitudes have been corrected to: Ho ALTITUDE 1: 20.042198 Ho ALTITUDE 2: 29.474503 Ho ALTITUDE 3: 43.923001 The Celestial Navigation calculations have estimated the Navigational Fix Position as: Nav LONGITUDE: -15.249526 Nav LATITUDE: 32.349772 ASTROCLK Astronomical Clock and Celestial Tracking Program Page 88 Press RETURN to ACCEPT the calculated posi- tion or any other key to discard: The data input in Step 6 have been "rigged" to yield the observed altitudes (Ho) in the display above. Comparison of these corrected data with that published in the Nautical Almanac will show a difference of no more than 0.000003 degrees, a trivial amount. The reason for rigging the data is that the Nautical Almanac uses fully corrected data while ASTROCLK automatically corrects the sextant altitude for refraction. The input data have been adjusted so that the observed altitudes agree after that refraction correction. The second set of data are the position coordinates which ASTROCLK has calculated from the input data. Press RETURN to accept this position, or press any other key to discard the calculation; either choice will return to ASTROCLK. Accepting the data will change the local coordinates window to the new longitude and latitude. 8. Now press "N" to change to Navigation Mode. The following display will appear: ASTROCLK NAVIGATION INFORMATION Data relative to: NAVIGATION DATA LONGITUDE: -15.249526 LATITUDE: 32.349772 DISTANCE: 0.00 nm = 0.00 km ELAPSED TIME: 0.0000 hrs Current COURSE: 325.000000 Data relative to: NA-1989 LONGITUDE: -15.249400 LATITUDE: 32.349300 DISTANCE: 0.03 nm = 0.05 km TIME TO DEST: 0.0014 hrs Chart COURSE: 165.108506 The first portion of the display shows the data relative to the last navigation fix (which is the data ASTROCLK has just calculated in Step 7) and is obvious. The distance and time are both zero because ASTROCLK is set to the time of the navigation fix. The course is as set in Step 4. The second portion of the display shows the data relative to the "destination", set to the results of the calculation in the Nautical Almanac; note that the longitude and latitude are exact. The distance is therefore the great circle distance bewteen the fix ASTROCLK has just calculated and the Nautical Almanac result, shown in nautical miles (nm) and kilometers (km). In this case, ASTROCLK produced a result within less than 200 feet of the Nautical Almanac. Note that the initial position estimate entered in Step 4 is ASTROCLK Astronomical Clock and Celestial Tracking Program Page 89 quite close to the end result, following the example in the Nautical Almanac. In fact, the estimated longitude and latitude may be off by five or ten degrees in either direction with little effect on the final result except to increase the computation time on computers not equipped with a math coprocessor. When using these celestial navigation functions, it is important to note that the accuracy of ASTROCLK's calculations is actually far better than can likely be achieved in practice. Not only is it all but impossible to read a sextant or similar instrument to the accuracy and precision used in the example, but changing atmospheric conditions especially near the horizon (which are difficult to measure from the Earth's surface without a fully equipped observatory) can cause the refraction to vary by as much as several arc seconds from the calculated value. The purpose here is to provide a method which introduces little or no additional error in the celestial navigation calculations. This example demonstrates that ASTROCLK's apparent geocentric equatorial star positions are typically within one arc second of the values published in the Astronomical Almanac and the Nautical Almanac as well as those generated by USNO's Interactive Computer Ephemeris and Floppy Almanac, and that the resulting navigational calculations are essentially exact. For comparison with current state of the art navigation and position determination equipment, manufacturers are claiming an accuracy of better than 50 feet with military versions of the NavStar Global Positioning System (GPS) receivers. Commercial versions of the GPS receiver, which cannot decode some of the special signals on NavStar (which are required for maximum accuracy), are expected to achieve accuracies on the order of 300 feet or less. In practice, ASTROCLK's navigation calculations can all be made with the clocks running; the current calculated position is displayed in real time and all celestial and planetary data are similarly calculated. However in the case of this example from the Nautical Almanac, because the date of June of 1989 is now long past, the resulting calculated position after many months at 20 knots is not correct. By setting the computer clock and date to some time shortly after the time of the last star sight (use Function Key ALT-F4 to enable the SIMULATION mode, or use Function Key F9 to return to DOS and then use the TIME and DATE commands), the "real" situation can be simulated and the actual running position will be displayed in the local coordinates window, labeled "Calculated Position". At that point, you may select a star or planet in the usual manner, display its coordinates, and they will be referenced to the current calculated position in real time. ASTROCLK Astronomical Clock and Celestial Tracking Program Page 90 SIDEREAL TIME AND EQUATORIAL COORDINATES The concept of sidereal time is perhaps a bit difficult for the layman to grasp. Even the idea that time is not absolute may be a little unsettling to some and confusing to others. However, visualizing a "celestial sphere" with the Sun (heliocentric) or the Earth (geocentric) at the center and with the stars, planets, and other astronomical objects on its surface is relatively straightforward. Using this approach, the stars remain in more or less fixed positions on the sphere (although the planets continuously change their positions) and the sphere appears to rotate around us. Thus, stars appear to rotate about the celestial pole in a counter-clockwise direction in the Northern Hemisphere. Given this constantly changing scenario, astronomers had to develop a coordinate system which would allow them to unambiguously locate each celestial object. Although there are several coordinate systems in use depending upon the application, the most common is called Equatorial Coordinates and uses Right Ascension and Declination, roughly analogous to geographical longitude and latitude, respectively, to locate an object. This is the coordinate system used in catalogs of star positions. The problem, and the reason for sidereal time, is that the Earth is rotating about its axis as it orbits the Sun. As a result of this, when viewed at the same time each night the stars appear to change their position by a small amount. After a full year, they are back in their original positions. If we divide the 360 degrees around the celestial sphere into 24 hours (much the same as our earthly time zones) and call the resulting coordinate Right Ascension, we have described what is sometimes called "star time" but is more properly termed Mean Sidereal Time. (Declination, the second coordinate, specifies the number of degrees above or below the celestial equator.) Because of the Earth's rotation, sidereal time runs just a bit faster than regular (mean solar) time; the difference is about 4 minutes per day. If you are sufficiently patient, you can watch one of ASTROCLK's sidereal clocks and see it skip a second about every six minutes. Further, variations in the orbit and rotation of the Earth and other considerations cause true sidereal time not to be constant and astronomers therefore usually use mean (or average) sidereal time. The difference between solar and sidereal time is best illustrated by an example. Remembering that the Earth makes one complete orbit around the Sun in about 365 days, it follows that the Earth moves through approximately one degree each day (360/365). Since solar time is measured from noon to noon, the Earth must therefore rotate through approximately 361 degrees each day in order for a given point on the Earth's surface to again be directly facing the Sun. But the sidereal day is the time elapsed for the Earth to make exactly one revolution of 360 degrees. That one degree difference distinguishes the two methods of time measurement and means that the solar day is about 4 minutes longer than the sidereal day (3 minutes 56.6 seconds mean solar time, actually). Both solar and sidereal time use the same units: days, ASTROCLK Astronomical Clock and Celestial Tracking Program Page 91 hours, minutes, and seconds; care must be taken that the type of time being used is specified in order to avoid errors. The mean sidereal times in ASTROCLK are calculated to a precision of 0.0001 seconds and have been checked against the Astronomical Almanac for accuracy and are exact. All times displayed in the small windows on the right of the screen have been rounded to the nearest second. Near the vernal equinox each year (March 20th in 1988), sidereal time is exactly 12 hours different from mean solar time. Similarly, sidereal time equals mean solar time near the autumnal equinox in September. The current sidereal time corresponds to the right ascension that is on your meridian (the "line" running from the North celestial pole to the South celestial pole and passing directly overhead) at that instant. Therefore, if you know a star's right ascension, you know that the star may be found somewhere on the line from the North Pole through a point directly above you when that right ascension equals the sidereal time. Where the star will appear on that line is determined by its declination; +90 degrees corresponds to the North Pole, zero to the celestial equator, and -90 degrees to the South Pole. If you hold your fist out at arms' length with the thumb folded out of sight, its width corresponds to about 10 degrees of arc (declination), or 40 minutes of time (right ascension) near the celestial equator. As you move toward the poles, the lines of right ascension come closer together, just as a section of orange is narrower at each end. Another useful guide is that the stars most easily visible at a given time will have right ascensions within a couple of hours of the current sidereal time. Some stars, called circumpolar stars, will always be visible if their declination is greater than your latitude. If you stand at one of the poles, naturally, all the stars you can see are circumpolar. When you are far away from clocks, books, and program ASTROCLK, you can estimate sidereal time or right ascension using the two pointer stars of the Big Dipper; the right ascension of both stars is very close to 11 hours. Using the meridian connecting those two stars and the North celestial pole as a starting point, you can imagine a "clock" in the heavens to tell you the sidereal time and to estimate the right ascension of a star. That's the good news; the bad news is that this simple sounding analogy is complicated by the fact that the celestial clock must be divided into 24 hours instead of 12 hours, and that the hour numbers go around in the opposite direction from a "normal" clock, or counter-clockwise. Even so, it's worth giving it a try just to familiarize yourself with the concept and to practice locating a few well known stars. See the following section for the Equatorial Coordinates of a number of bright stars selected by USNO as Standard Navigational Stars. ASTROCLK Astronomical Clock and Celestial Tracking Program Page 92 USNO COMPUTER EPHEMERIS PROGRAMS Beginning in the mid-1980's, the U. S. Naval Observatory (USNO) supplemented its printed almanacs and ephemerides with a disk-based program called the Floppy Almanac and designed to execute on IBM-compatible personal computers (among others). The Floppy Almanac was produced for years through 1999. While not all Floppy Almanac data were equal in accuracy to that contained in the Astonomical Almanac and other similar publications, the Floppy Almanac provided more than sufficient accuracy for most purposes and made reliable astronomical data available to the vast majority of would-be users. USNO produced a custom Floppy Almanac for each calendar year (400 days, actually, with an small overlap from year to year). Starting with 1988, all Floppy Almanac versions used a common set of data files and by adding the custom Floppy Almanac program for each year the user could produce astronomical data for the years 1988 through 1999. One of the more useful features of ASTROCLK (from my perspective, at least) is to automatically execute the Floppy Almanac. When Function Key ALT-F9 is pressed, ASTROCLK examines the current date, writes a default data file of initial values, and then executes the proper version of the Floppy Almanac. The only significant problem with the Floppy Almanac has been that each user must acquire a different version of the program for each calendar year, plus or minus a few days. To address this problem, USNO in early 1989 released a new program, the Interactive Computer Ephemeris or ICE. ICE uses a common program to process data for a 250 year period, from December 21, 1800, through June 7, 2049. A set of highly compressed ephemeris data files (EPH01.DAT through EPH24.DAT), each covering approximately 4000 days, allows the program to cover this extended time span. For the approximate period 1980 through 1999, only the data files EPH18.DAT and EPH19.DAT are required. This added capability and convenience has its price, however. Each data file (except the first and the last) requires approximately 37K bytes of disk storage and the complete package requires approximately 1.1M bytes of disk storage. The Floppy Almanac for a given year, by comparison, easily fits on a single 360K byte floppy disk. Each time it is executed, ICE must select and then decompress the appropriate ephemeris data file. Particularly when executed on a computer without a math coprocessor, ICE therefore runs more slowly than FA. ICE and FA appear to have essentially the same accuracy. In view of these factors, some users may may decide to continue using the Floppy Almanac in preference to the Interactive Computer Ephemeris. I have no information as to whether or not USNO will continue to make the Floppy Almanac available; I presently have FA versions for 1988 through 1992 and these are available via my bulletin board system. As of Version 8915, ASTROCLK allows the user to select which USNO program will be executed via ALT-F9, or ALT-F9 may be disabled if neither program is available. This selection is made using ALT-F10. See the section SETTING PROGRAM OPTIONS for ASTROCLK Astronomical Clock and Celestial Tracking Program Page 93 additional information on using ALT-F10 to select the desired USNO program and to set the proper drive and path names. Both USNO programs operate in essentially the same manner. Users familiar with the Floppy Almanac will have no difficulty using ICE. The program name has changed, of course, and the compressed ephemeris data files are a new fetaure. The star catalog file names are unchanged and appear to be identical to those supplied with the Floppy Almanac although the file dates and times are different. The default parameter files, FA.DFT and ICE.DFT, are slightly different; because of the time span covered, the date parameter in the first line now requires the full year for ICE. ASTROCLK correctly formats a default parameter file for either program. Each time ALT-F9 is invoked, the default parameter file, ICE.DFT or FA.DFT, is written with the current ASTROCLK date and time, the current local geographical coordinates, and the local time zone referred to UTC; the parameters "Time Step" and "Num of Positions" are each set to +1.00. The USNO program is therefore ready to use immediately upon entry. The following is a typical ICE.DFT file as written by ASTROCLK (FA.DFT is the same except the Starting Date would read "890328" rather than "19890328"): Starting Date = 19890328.005806 Latitude = 38.150000 Longitude = -120.566667 Time Step = 1.0000 Num of Pos'ns = 1.0 Time Zone = -8.0 Use F1 after starting the program to adjust these parameters if desired. See the User's Guide for each program for more information on operation and features. Upon exit from ICE or FA (using F10), ASTROCLK automatically resumes normal operation. Operation of ASTROCLK with the USNO programs has been tested with ICE Beta (test) version 0.50 and with FA versions 2.11.88 and 2.11.89. If ICE has been selected (using ALT-F10), pressing ALT-F9 will automatically execute the ephemeris provided the current date falls within ICE's time span and the proper ICE data files are available. ICE may be used for any date from December 21, 1800 through June 7, 2049 inclusive. An error message is displayed if the date falls outside these limits and ICE will not be executed. The ICE ephemeris data files, EPH01.DAT through EPH24.DAT, cover approximately 4000 days each; EPH18.DAT and EPH19.DAT are sufficient for dates from about 1980 through 2000. If FA has been selected (using ALT-F10), pressing ALT-F9 will automatically execute the Floppy Almanac if the current ASTROCLK date falls within the years 1988 through 1999. An error message is displayed if the date falls outside these limits and FA will not be executed. (NOTE: ASTROCLK allows the use of FA88 for the last 15 days of December, 1987 and of FA99 for the first 15 days of January, 2000.) The proper Floppy Almanac program (FA88.EXE through FA99.EXE) must be present in the ASTROCLK directory or the Floppy Almanac drive and path must have been set ASTROCLK Astronomical Clock and Celestial Tracking Program Page 94 using ALT-F10, SETTING PROGRAM OPTIONS. ASTROCLK assumes that neither ICE nor FA is present when it is first started. Use ALT-F10 to first select the USNO ephemeris program you desire, then to set the drive and/or path where the program and its data files may be found. If the drive and/or path for the selected ephemeris program is not set or is set incorrectly, the ephemeris may fail to execute or it may warn the user that it has used its internal default files. The default selection for ASTROCLK is that both USNO programs are disabled and ALT-F9 will have no effect. NOTE: ASTROCLK remains in memory while ICE or FA is executing; systems with less than 640K of main memory or which have large Terminate and Stay Resident (TSR) programs active may have insufficient memory for this feature. Also for this reason, ICE and FA cannot be executed from ASTROCLK when using the QuickBASIC interpreter rather than the complied program. ASTROCLK Astronomical Clock and Celestial Tracking Program Page 95 USNO STANDARD NAVIGATIONAL STARS The U. S. Naval Observatory (USNO) has designated 57 stars as Standard Navigational Stars and publishes their coordinates (along with those of other important stars) in a number of their publications including the Almanac for Computers. For convenience, I have added Polaris to the USNO list as number zero. Throughout this text, the phrase "Standard Navigational Stars" will mean the 57 USNO stars plus Polaris. The stars are listed by Standard Navigational Star Number, Bayer Designation, Proper or Common Name, Right Ascension (RA, hours), and Declination (DEC, degrees). The Bayer designation consists of two parts: a Greek letter, such as Alpha, to designate the particular star in a constellation and usually in descending order of brightness; and the name of the constellation in the Latin genitive (possessive) case, such as Ursae Minoris and meaning "of Ursa Minor". The names of the 88 constellations are always given in Latin regardless of the origin of the name. Most of the common names for stars are inherited from Arabic (the scientists and mathematicians in North Africa being the conduit for much of our knowledge of ancient astronomy and astronomers), with a few from Greek and other languages. For an explanation and a listing of constellation names, see the following section CONSTELLATIONS AND NAMES. The actual star data has been extracted from the USNO Floppy Almanac 1988, Version 2.11.88, file STAR1.CAT, and is for Epoch J2000.0. Not shown in the table below but included within the program are constants for adjusting the data for proper motion. The data represent the "mean place" of the star, described by USNO in the Almanac for Computers 1988 as "a fundamental reference point with no simple geometric or observational significance. The apparent place of a star is the geocentric position, referred to the true equinox and equator of date, at which the star is observed. Thus, the apparent place is the position needed for navigation, calibration of telescope setting circles, computation of transit time, etc." Star catalogs with earlier epochs, such as B1950.0, use "mean catalog place" which has a slightly different meaning. # Bayer Designation and Name RA DEC ---------------------------------------------------------------- 0 Alpha Ursae Minoris, Polaris 2.530195556 89.264088889 1 Alpha Andromedae, Alpheratz .139795833 29.090438889 2 Alpha Phoenicis, Ankaa .438063889 -42.306058333 3 Alpha Cassiopeiae, Schedar .675125000 56.537350000 4 Beta Ceti, Diphda/Deneb Kaitos .726492222 -17.986616667 5 Alpha Eridani, Achernar 1.628570000 -57.236716667 6 Alpha Arietis, Hamal 2.119556389 23.462405556 7 Theta1 Eridani, Acamar 2.971026667 -40.304713889 8 Alpha Ceti, Menkar 3.037992500 4.089702778 9 Alpha Persei,Mirfak 3.405379167 49.861205556 10 Alpha Tauri, Aldebaran 4.598676944 16.509275000 11 Beta Orionis, Rigel 5.242296667 -8.201661111 ASTROCLK Astronomical Clock and Celestial Tracking Program Page 96 # Bayer Designation and Name RA DEC ---------------------------------------------------------------- 12 Alpha Aurigae, Capella 5.278153611 45.998027778 13 Gamma Orionis, Bellatrix 5.418849167 6.349650000 14 Beta Tauri, Elnath 5.438197500 28.607408333 15 Epsilon Orionis, Alnilam 5.603558056 -1.201950000 16 Alpha Orionis, Betelgeuse 5.919529722 7.407041667 17 Alpha Carinae, Canopus 6.399199722 -52.695694444 18 Alpha Canis Majoris, Sirius 6.752464167 -16.716108333 19 Epsilon Canis Majoris, Adhara 6.977096667 -28.972083333 20 Alpha Canis Minoris, Procyon 7.655031389 5.225016667 21 Beta Geminorum, Pollux 7.755262778 28.026183333 22 Epsilon Carinae, Avior 8.375231389 -59.509586111 23 Lambda Velae, Suhail 9.133271111 -43.432605556 24 Beta Carinae, Miaplacidus 9.219988056 -69.717208333 25 Alpha Hydrae, Alphard 9.459790833 -8.658652778 26 Alpha Leonis, Regulus 10.139531944 11.967191667 27 Alpha Ursae Majoris, Dubhe 11.062129444 61.750894444 28 Beta Leonis, Denebola 11.817661111 14.572041667 29 Gamma Corvi, Gienah 12.263435000 -17.541936111 30 Alpha1 Crucis, Acrux 12.443297500 -63.099050000 31 Gamma Crucis, Gacrux 12.519424722 -57.113194444 32 Epsilon Ursae Majoris, Alioth 12.900485556 55.959852778 33 Alpha Virginis, Spica 13.419885278 -11.161308333 34 Eta Ursae Majoris, Alkaid 13.792342778 49.313319444 35 Beta Centauri, Hadar 14.063724444 -60.372997222 36 Theta Centauri, Menkent 14.111375278 -36.370008333 37 Alpha Bootis, Arcturus 14.261021389 19.182419444 38 Alpha Centauri A, Rigil Kentaurus 14.659968056 -60.835400000 39 Alpha2 Librae, Zubenelgenubi 14.847975833 -16.041783333 40 Beta Ursae Minoris, Kochab * 14.845096111 74.155494444 41 Alpha Coronae Borealis, Alphecca 15.578132222 26.714705556 42 Alpha Scorpii A, Antares 16.490121944 -26.431986111 43 Alpha Triangulii, Atria 16.811074722 -69.027727778 44 Eta Ophiuchi, Sabik 17.172966944 -15.724919440 45 Lambda Scorpii, Shaula 17.560148333 -37.103811111 46 Alpha Ophiuchi, Rasalhague 17.582243333 12.560038889 47 Gamma Draconis, Eltanin 17.943435278 51.488947222 48 Epsilon Sagittarii, Kaus Aust. 18.402868611 -34.384647222 49 Alpha Lyrae, Vega 18.615647778 38.783658333 50 Sigma Saggittarii, Nunki 18.921090000 -26.296730556 51 Alpha Aquilae, Altair 19.846389444 8.868341667 52 Alpha Pavonis, Peacock 20.427458889 -56.735105556 53 Alpha Cygni, Deneb 20.690532500 45.280363889 54 Epsilon Pegasi, Enif 21.736434444 9.874977778 55 Alpha Gruis, Al Na'ir 22.137222222 -46.960997222 56 Alpha Piscis Austrini, Formalhaut 22.960848611 -29.622250000 57 Alpha Pegasi, Markab 23.079349444 15.205250000 * The Right Ascension for Beta Ursae Minoris, #40, appears in error but is correct. The USNO J1988.5 list was in strict descending order of SHA (Sidereal Hour Angle, directly related to RA) but proper motion and precession changes to J2000.0 have changed the RA. To avoid possible confusion, I have retained the original USNO order and numbering (Almanac for Computers, 1988). ASTROCLK Astronomical Clock and Celestial Tracking Program Page 97 CONSTELLATIONS AND NAMES One of my early "novice" problems when trying to identify a star or constellation was to learn the names of the various constellations and their standard 3-letter IAU abbreviations. Some were easy to guess but others were less obvious and it was some time before I discovered a reference with the proper information. There are still a few that I have not yet memorized. I have divided the list which follows into three sections, Northern, Zodiacal, and Southern. The Northern and Southern designations correspond roughly to the location of the constellations with respect to the celestial equator. The twelve constellations of the zodiac, of course, are closely linked with astrology, a "science" once considered a part of astronomy, and span a band of approximately eight degrees on either side of the ecliptic following the course of the Sun through the heavens. The names marked with an asterisk are those known to the Egyptian astronomer Ptolemy and, for the most part, the ancient Greeks; many of these names have survived essentially unchanged for two thousand years and more although all 88 constellations are now known by the Latin version of their names, whatever the origin. To the ancients, and continuing almost to modern times, the constellations were more or less casual groups of stars usually clustered around one of the brighter stars easily visible to the naked eye. Descriptions of the ancient Greek constellations are found in the poetry of Homer (9th century B.C.) and Aratus (3rd century B.C.). Ptolemy (2nd century A.D.) cataloged about 1022 stars, divided into 48 different constellations, that could be seen from Alexandria. His chief work, the Almagest, remained the definitive authority until the European voyages of discovery in the sixteenth century brought navigators into Southern latitudes. The first star atlas, published by Johann Bayer in 1603, employed a method of identification still in use today and added 12 new Southern constellations. During the three hundred plus years which have followed Bayer, more constellations have been added to the list, old constellations have been split into several new groupings, and new names have been adopted or proposed. Some of these changes stuck, some did not. Since about 1750, no changes to the constellation names have been accepted except that since about the mid-1800's Ptolemy's constellation Argo Navis (Argo the Ship) has usually been divided into three parts representing the keel (Carina), the stern (Puppis), and the sails (Vela). The compass (Pyxis) is also sometimes considered part of the original Argo Navis. With the advent of the telescope, many more stars were visible and the practice of naming and cataloging stars according to the constellation in which they appeared continued. Unfortunately, the boundaries of the constellations were not well defined and there was occasional confusion. The boundary problems were codified in 1930 when the International Astronomical Union (IAU) agreed upon precise definitions. The new divisions were drawn along lines of right ascension and declination for Epoch 1875.0 and were made to zigzag in order to retain the ancient ASTROCLK Astronomical Clock and Celestial Tracking Program Page 98 figures. One result of this new precision, however, was that a few stars previously known as part of one constellation became part of another. For example, one of the four stars of the Great Square of Pegasus became part of the constellation Andromeda and is now known as Alpha Andromedae. Because of precession since 1875, the boundary lines are no longer nicely aligned with the coordinate scales. Only a few stars have a common or proper name such as Polaris or Arcturus. The remaining stars, those few out of the uncounted billions that have names or numbers at all, were named by the individuals who cataloged them. Since there are many different catalogs, stars often have multiple names, another source of possible confusion and errors. One catalog often includes a star or other objects with coordinates very slightly different from a comparable object in another catalog, probably the same object but not always. More confusion! Many different methods have been used to name or number stars, but one of the most common is still the Bayer designation. Each star in a constellation was assigned a Greek letter, usually starting with the brightest (alpha), and the name of the constellation was appended. The Greek letter may be followed by a superscript to distinguish multiple stars. The constellation name is used in the Latin genitive (possessive) case, meaning "of" or "belonging to". Thus the first and brightest star of the constellation Andromeda is Alpha Andromedae, and in Ursa Minor we have Alpha Ursae Minoris (Polaris), and so forth. In most references, however, both the Greek letter and the constellation name are abbreviated. The first three lists show the standard IAU abbreviation, Latin constellation name, Latin genitive name, and common English translation for the three groups of constellations. The final list gives the standard abbreviations for the letters of the Greek alphabet. Using these lists, the abbreviated Bayer designation of a star can easily be "decoded"; for example, OMI CVN is Omicron Canum Venaticorum. NORTHERN CONSTELLATIONS (28) AND *Andromeda Andromedae Andromeda AQL *Aquila Aquilae Eagle AUR *Auriga Aurigae Charioteer BOO *Bootes Bootis Herdsman CAM Camelopardis Cameloparids Giraffe CVN Canes Venatici Canum Venaticorum Hunting Dogs CAS *Cassiopeia Cassiopeia Cassiopeia CEP *Cephus Cephi Cephus COM Coma Berenices Comae Berenices Berenice's Hair CRB *Corona Borealis Coronae Borealis Northern Crown CYG *Cygnus Cygni Swan DEL *Delphinus Delphini Dolphin DRA *Draco Draconis Dragon EQU *Equuleus Equulei Little Horse/Colt HER *Hercules Herculis Hercules LAC Lacerta Lacertae Lizard LMI Leo Minor Leonis Minoris Little Lion ASTROCLK Astronomical Clock and Celestial Tracking Program Page 99 LYN Lynx Lyncis Lynx LYR *Lyra Lyrae Harp OPH *Ophiuchus Ophiuchi Ophiuchus PEG *Pegasus Pegasi Pegasus PER *Perseus Persei Perseus SGE *Sagitta Sagittae Arrow SER *Serpens Serpentis Serpent TRI *Triangulum Trianguli Triangle UMA *Ursa Major Ursae Majoris Big Bear UMI *Ursa Minor Ursae Minoris Little Bear VUL *Vulpecula Vulpeculae Little Fox CONSTELLATIONS OF THE ZODIAC (12) AQR *Aquarius Aquarii Water Bearer ARI *Aries Arietis Ram CNC *Cancer Cancri Crab CAP *Capricornus Capricorni Goat GEM *Gemini Geminorum Twins LEO *Leo Leonis Lion LIB *Libra Librae Scales PSC *Pisces Piscium Fish SGR *Sagittarius Sagittarii Archer SCO *Scorpius Scorpii Scorpion TAU *Taurus Tauri Bull VIR *Virgo Virginis Virgin SOUTHERN CONSTELLATIONS (48) ANT Antlia Antilae Pump APS Apus Apodis Bird of Paradise ARA *Ara Arae Altar CAE Caelum Caeli Chisel CMA *Canis Major Canis Majoris Big Dog CMI *Canis Minor Canis Minoris Little Dog CAR Carina Carinae Ship's Keel CEN *Centaurus Centauri Centaur CET *Cetus Ceti Whale CHA Chamaeleon Chamaeleonis Chameleon CIR Circinus Circini Compass COL Columba Columbae Dove CRA *Corona Australis Coronae Australis Southern Crown CRV *Corvus Corvi Crow CRT *Crater Crateris Cup CRU Crux Crucis Southern Cross DOR Dorado Doradus Swordfish ERI *Eridanus Eridani River Eridanus FOR Fornax Fornacis Furnace GRU Grus Gruis Crane HOR Horologium Horologii Clock HYA *Hydra Hydrae Water Snake HYI Hydrus Hydri Water Snake IND Indus Indi Indian LEP *Lepus Leporis Hare LUP *Lupus Lupi Wolf ASTROCLK Astronomical Clock and Celestial Tracking Program Page 100 MEN *Mensa Mensae Table MIC Microscopium Microscopii Microscope MON Monoceros Monocerotis Unicorn MUS Musca Muscae Fly NOR Norma Normae Level OCT Octans Octantis Octant ORI *Orion Onionis Orion PAV Pavo Pavonis Peacock PHE Phoenix Phoenicis Phoenix PIC Pictor Pictoris Easel PSA Piscis Austrinus Picis Austrini Southern Fish PUP Puppis Puppis Ship's Stern PYX Pyxis Pyxidis Ship's Compass RET Reticulum Reticulii Net SCL Sculptor Sculptoris Sculptor SCT Scutum Scuti Shield SEX Sextans Sextantis Sextant TEL Telescopium Telescopii Telescope TRA Triangulum Australe Trianguli Australis Southern Triangle TUC Tucana Tucanae Toucan VEL Vela Velorum Ship's Sails VOL Volans Volantis Flying Fish GREEK LETTER ABBREVIATIONS ALP Alpha NU Nu BET Beta XI Xi GAM Gamma OMI Omicron DEL Delta PI Pi EPS Epsilon RHO Rho ZET Zeta SIG Sigma ETA Eta TAU Tau THE Theta UPS Upsilon IOT Iota PHI Phi KAP Kappa CHI Chi LAM Lambda PSI Psi MU Mu OME Omega ASTROCLK Astronomical Clock and Celestial Tracking Program Page 101 USING EXTERNAL STAR CATALOGS ASTROCLK stores all the data for the 57 USNO Standard Navigational Stars plus Polaris internally. USNO has prepared a catalog, STAR1.CAT, of 1536 bright stars (the first 57 of which are the Standard Navigational Stars) in conjunction with their Floppy Almanacs. This catalog is from the Fifth Fundamental Catalog, FK5, with one star (Eta Ophiuchi) added. A second USNO catalog, MESSIER.CAT, contains data for the 109 standard Messier objects; M40 has always been "missing" but an entry with null data occupies its place in the catalog. All catalog data is for Epoch J2000.0. These two USNO catalogs have been converted to an ASCII format (using the USNO program CATALOG) and combined to form ASTROCLK.CAT with a total of 1645 stars and objects included. The catalog is fairly large, requiring approximately 160K of disk space. For those users short of space and who might wish to omit the catalog from their disk, ASTROCLK will issue a warning message if a search is requested and ASTROCLK.CAT cannot be found; press RETURN to resume normal operation. The Messier catalog is also available separately in ASCII format as MESSIER.CAT. ASTROCLK can perform two types of catalog searches: search for USNO Name or Number or, search for star closest to specified RA/DEC or ALT/AZ position as selected by Function Key F5 followed by F3, F4, and F5 respectively. Each entry in the catalog is assigned a "catalog number" corresponding to its position in the file. If you wish to examine the whole file, you may print it with your favorite print utility (adding sequential line numbers, if desired) or look at it with your favorite editor. The names assigned by USNO follow standard IAU conventions but may take a bit of getting used to for the novice user. USNO allows up to three different 8-character names for each star. In the following explanation each type of name is followed by an example in parenthesis. The first name is either the Bayer Designation (BET AND or ALP2 LIB) if one has been assigned to that star, or the Messier Number (M 23). The second name, if any, is the common name usually associated with the star (Polaris) or the NGC number for the Messier object (NGC 1976). The third name is the DM Number (Bonner Durchmusterang Catalogue) for the star (-15 3996) or the common name for the Messier object (Orion). Note that a SPACE is required between two part names. Many stars, particularly those toward the end of the STAR1.CAT catalog, have only the DM Number as a name and a printout of the catalog is almost essential if these stars are to be used with ASTROCLK. Any name field may be left blank and names have been truncated to 8 characters if necessary. Press F3 to search by name or number. After the requested name or number has been entered, ASTROCLK will capitalize the name and adjust the spacing if necessary to that required by the catalog. ASTROCLK then locates the catalog file (ASTROCLK.CAT unless another catalog has been designated using ALT-F10). If a catalog number has been entered, ASTROCLK reads the corresponding ASTROCLK Astronomical Clock and Celestial Tracking Program Page 102 data immediately; when a name is entered, a search of the catalog is required. Floppy disk based computer systems may notice a considerable delay for stars located near the end of the catalog and for searches which require testing the whole catalog. For floppy disk systems and slower hard disk systems, a considerable improvement in search time can be obtained if you have sufficient memory and use a "RAM DISK" to store the catalog and specify the new drive and name using Function Key ALT-F10. Searches by ALT/AZ or RA/DEC also search the entire catalog; F4 is used for RA/DEC (Right Ascension and Declination), and F5 for ALT/AZ (Altitude and Azimuth). Pressing F4 gives the follwing prompt (F5 is the same except ALTITUDE and AZIMUTH will be requested): SET TARGET COORDINATES Search external STAR CATALOG for nearest star using Right Ascension & Declination: Enter RIGHT ASCENSION (hours): Enter DECLINATION (degrees): Show nearby star list [Y/n]: Enter the coordinates as requested. Searches can be made in two modes: find the 10 stars nearest to the coordinates given, or find the single star nearest to the coordinates given. The search mode is determined by the third prompt: "Y" (or RETURN) will find 10 stars and display a list of those stars; "N" will find the nearest star and immediately switch to the Target Tracking Display. Searches for a single star are somewhat quicker than searches for 10 stars, due to the additional sorting required. The following is a typical list of 10 stars (the degree symbol has been omitted): CAT # Diff RtAscension Declination Mag 49 0.04 18:36:56.33 38 47'01.16" 0.0 536 4.33 18:19:51.70 36 03'52.43" 4.3 1050 5.30 18:15:38.79 42 09'33.61" 5.6 208 6.00 18:50:04.80 33 21'45.65" 3.5 390 6.23 18:55:20.11 43 56'46.00" 4.0 894 6.57 19:07:18.12 36 06'00.61" 5.3 1593 6.63 18:53:36.00 33 02'00.00" 0.0 1475 7.49 18:33:47.66 46 13'09.02" 6.7 193 7.52 18:58:56.61 32 41'22.42" 3.2 585 7.73 19:16:22.10 38 08'01.46" 4.4 Press RETURN for #49 or enter CAT #: The first column gives the catalog number for each star. The stars on the list are displayed in order of increasing angular separation (in degrees) from the requested coordinates, given in the second column. Only stars with a declination within 10 degrees of that given will be displayed. The remaining columns are the Right Ascension, Declination, and Magnitude. This display was prepared using the standard catalog, ASTROCLK.CAT, which ASTROCLK Astronomical Clock and Celestial Tracking Program Page 103 includes the 109 Messier objects at the end of the file and have magnitudes of 0.0. Note star #1593 in the sample above; this is a Messier object rather than a true star. Note also that all searches are made using the "raw" catalog data, in this case J2000.0 Mean Place. The first 57 stars in ASTROCLK.CAT are the standard USNO Navigational Stars, identical to the ASTROCLK internal star database. Press RETURN to select the first star in the list, #49 (Vega) in the sample, or enter the catalog number of another star (which does not necessarily have to appear on the list). The data for the selected star will be displayed in the Target Tracking Display. The message "SEARCHING ..." is displayed at the upper right and the on-screen clocks are stopped during searchs. Once started, a search may be cancelled by pressing SPACE BAR. When the requested star has been selected, its catalog number (prefixed by the letter "C" to indicate "Catalog") and all valid names are displayed in the Tracking Display title, the star data is read from the file, and the coordinates are displayed as with internal star data. If a requested star cannot be found, ASTROCLK displays a warning message; press RETURN to resume normal operation. For those interested in the technical details, ASTROCLK expects the standard USNO ASCII catalog format of 96 characters plus CR/LF per record as described in The Floppy Almanac User's Guide, 2nd Edition, Appendix A. Provided the exact format is maintained, the user may edit the catalog file or prepare a new one. The following field definitions are extracted from that appendix: Field Field Position Format Contents Units ---------------------------------------------------------------- 1- 8 A8 Name1, left justified ----- 9-16 A8 Name2, left justified ----- 17-24 A8 Name3, left justified ----- 25-38 F14.10 J2000.0 Right Ascension hours 39-52 F14.10 J2000.0 Declination degrees 53-62 F10.4 J2000.0 Proper Motion in RA sec/J Cent* 63-72 F10.4 J2000.0 Proper Motion in DEC arcsec/J Cent* 73-80 F8.4 Parallax arcsec 81-88 F8.4 Radial Velocity km/sec 89-96 F8.4 Visual Magnitude (or flux) mag, Jy 97-98 CR/LF Carriage Return + Line Feed * Proper motion is given in seconds (RA) or arcseconds (DEC) per Julian Century of 36525 days. ASTROCLK Astronomical Clock and Celestial Tracking Program Page 104 PRECESSION AND STELLAR MOTION The Earth's pole of rotation is tilted approximately 23 degrees 27 minutes from the plane of the ecliptic, that plane which describes the Earth's orbit about the Sun. Rather than constantly pointing to some fixed point in the heavens, however, the gravitational influence of the Moon, Sun, and to a far lesser extent the planets, cause the Earth to "wobble" slightly and the pole describes a small circle with a period of about 25,770 years. This phenomena is known as lunisolar precession. A number of other phenomena, such as nutation, also contribute to a lesser extent to changes in the orientation of the Earth relative to the plane of the ecliptic. One of the by-products of precession is that Polaris, whose proper name is Alpha Ursae Minoris, has not always been the pole star. In ancient times Beta Ursae Minoris, (whose Arabic name Kochab derives from the words "pole star", about 1,200 B.C.), Alpha Draconis (about 3,000 B.C.) and Vega (about 13,000 B.C. and again in about 13,000 A.D.) have been nearer to the true pole than Polaris. Polaris will actually be closest to the true pole in about the year 2,102 A.D. Some 25,000 years from now, Polaris will again be the pole star as the cycle continues. Another by-product of precession is that the standard celestial coordinate system, using units of right ascension and declination, changes gradually. The origin (0,0) of these coordinates is the point on the ecliptic of the vernal equinox, the intersection of the equator and the plane of the ecliptic. This is commonly known as "The First Point of Aries", but over the centuries since it acquired its name precession has caused it to move out of that constellation and into the constellation Pisces. Time standards and terms of reference have also changed considerably over the last fifty years adding to the possible confusion. Better technology and demands for greater precision by science and industry have been the driving causes. Over the past decade or so new standards of time measurement and reference have been adopted by the International Astronomical Union, the governing body for all astronomical measurements. Because of these changes and in order to provide a consistent standard frame of reference, astronomers select an "epoch", usually every 50 years, and base all of their measurements against that standard point in time. Until recently, the standard reference epoch has been 1950, now usually written as B1950.0 (for Besselian epoch, another story related to the time standard changes). Most references and publications have now switched to the new standard epoch, J2000.0 (Julian epoch). References requiring very high precision (such as the USNO Almanacs) or calculated positions of the planets often use the "equator and equinox of date", meaning the present epoch; in mid- 1988, for example, that is J1988.5. When looking up the coordinates for a star or other object, an astronomer must also note the epoch as well as the coordinates themselves. If the epoch is different from that used for aligning his instruments and/or is different from other objects to be ASTROCLK Astronomical Clock and Celestial Tracking Program Page 105 viewed, the data should be "precessed" or adjusted to account for precession. The vernal equinox moves westward approximately 50 seconds of arc per year. The calculation of precession is relatively complex and many writers choose to use an approximation method which is sufficiently accurate only for casual astronomical viewing or over very short time periods. Unfortunately, a computer program such as ASTROCLK can be used to cycle back and forth between epochs almost at will. The "quick and dirty" approximations of the simpler methods can yield cumulative errors that soon become unacceptable. A more rigorous calculation for precession, the Improved IAU System, was adopted in 1984; it is this method that is used in ASTROCLK. An earlier method, developed in 1897 and published in 1906 by the American astronomer Simon Newcomb, was used in earlier versions of ASTROCLK and yielded comparable results. (Similar expressions were published in Germany in 1830 by F. W. Bessel and subsequently by others.) Although these calculations take considerably more computer processing time, they produce errors that are about two orders of magnitude less than typical approximations. ASTROCLK also always resets the internal star data to Epoch J2000.0 prior to precession calculations so as to avoid cumulative errors. Since manually entered data cannot be "reset"in this way, repetitive cycling from one epoch to another will yield modest cumulative errors. The formulas employed are described in the main text and the supplement of the 1984 Astronomical Almanac. When the internal data is precessed to J1988.5, the results are in good agreement with USNO data for that epoch given in Almanac for Computers 1988, pages E2 through E10. Further complicating the picture is the fact that the Earth and the stars themselves are not stationary. The Earth's orbit about the Sun causes parallax for nearby stars but the effect is periodic and relatively small; it has been ignored for this version of ASTROCLK. The changing position of the stars is known as "proper motion". While stellar motion is extremely difficult to measure for distant stars, proper motion data has been collected on a large number of stars (including those used in this program). ASTROCLK calculates the proper motion of stars prior to calculating the effects of precession. The effects of nutation and annual aberration are also included. ASTROCLK Astronomical Clock and Celestial Tracking Program Page 106 DATES AND THE GREGORIAN CALENDAR For convenience and standardization, many astronomical calculations reference a unique point in time known as the "Fundamental Epoch". This is defined as 12:00:00 at the Prime Meridian (Greenwich) on 1 January, -4713 (often written as -4713 JAN 1.5). Note that the day starts at noon in conformance with astronomical convention and corresponds to the time at which accurate sun sights could be made. The time elapsed since then is measured in units of days and the current date and time may thus be expressed as a single number, UTC JULIAN DATE (usually known simply as the Julian Date or JD). The number of days appears to the left of the decimal point, and the time is represented by a decimal fraction of a day. Years "before Christ" or "B.C." (but not prior to 1 January 4713 B.C. for this program) are given as negative numbers with no zero year. The Julian Date should not be confused with the Day-of-the-Year, the number of days elapsed during the current year, which is popularly and incorrectly also sometimes referred to as the Julian Date. However, astronomers delight (it would seem) in changing their units of measure at depressingly frequent intervals; multiple systems are sometimes in use simultaneously. Readers are cautioned that some authors, especially in older works, include a zero year in their calendars; using that scheme, 4713 B.C. becomes year -4712. In the references I have used, for example, Meeus prefers the zero year method while Duffet-Smith uses the same method as ASTROCLK with no zero year; see BIBLIOGRAPHY for references. I find the no zero year method far more convenient and less confusing: years B.C have the same number and are simply prefixed by a negative sign. Not all astronomers would agree. To add to the potential confusion, prior to 1925 astronomers considered that each calendar day commenced at NOON, agreeing with the standard astronomical day numbering convention but in conflict with civil practice. Modern astronomical convention, however, begins the calendar day at MIDNIGHT, the same as the civil calendar, and the practice is to apply the convention to all dates -- even those prior to 1925. Care must therefore be taken when interpreting older dates and times to ensure that the date conventions employed are understood and converted if necessary. This in addition to the various calendars in use! All in all, a good argument for the use of Julian Dates which are completely unambiguous -- if you ignore Julian Ephemeris Dates! On an historical note, the Julian Date has been in use for centuries by astronomers, geophysicists, chronologers, and others who needed to have an unambiguous dating system based upon continuing day counts. In fact, the the "Julian" part of Julian Date has nothing to do with the Julian Calendar introduced by Julius Caesar in 46 B.C. The Julian Date was so named by the mathematician Scaliger when he introduced this method of day counting in 1582, allegedly after his father, Julius. True or not, the name has stayed with us regardless of its origins. The starting date of January 1, -4713, for the Julian Date was based upon the time it takes from one coincidence to the next of a solar cycle (28 years), a lunar cycle (19 years), and the ASTROCLK Astronomical Clock and Celestial Tracking Program Page 107 Roman Indiction (a Roman tax cycle of 15 years imposed by the Emperor Diocletion during the period 284-305 A.D. and whose connection to astronomy completely escapes me). However, the product of those three cycle periods yields 7980 years, the Julian Period. That period is of interest only with respect to the selection of the starting time and date for the day counting method, at which time all of the cycles, counted backwards, were in coincidence. The real purpose of selecting such a date, of course, was that it be distant enough in time that the resulting day numbers would always be positive for events of interst. Not too surprisingly, most historical dates were not recorded using their Julian Date; for ancient dates, of course, the Julian Calendar hadn't been invented yet, and for more recent dates it was not (and still is not) in popular use. Enter the calendar in all its varieties. Calendars have long been an important part of almost every known civilization, especially those dependent upon agriculture. Being able to predict the time for planting and harvest was essential if the community was to continue to have an adequate food supply. Stonehenge in England, for example, is generally acknowledged to have been an astronomical observatory of sorts, used to predict the equinoxes and probably was also used for various religious and social events as well. Except for the stones themselves and their careful alignment, little else is known of the society they represent. But, given the massive effort that was involved in its construction, the importance of the calendar and the prediction of the seasons to its builders is clear. The ancient Egyptians watched Sirius (known to them as Sothis) for its appearance close to the Sun in the morning sky, the First Heliacal Rising. This marked the start of their 365 day calendar and coincided with the rising of the Nile and the fertilizing of the Egyptian plain by her waters. Almost without exception, every civilization of note used a calendar, although their accuracy varied considerably. The calendar having the most direct bearing on our present system is the Roman Republican Calendar of ancient Rome and her empire. Although the year started on the first of what is now March (after Mars, the planet and also the God of War), the basic structure of the calendar is quite similar to that in use today. Its immediate successor, the Julian Calendar, came about as a result of centuries of "adjustments" (more properly called intercalation, the addition of extra days in the calendar) to accommodate social, political, religious or other goals. Rulers and court astronomers would insert or delete days seemingly almost at random. By the time of Julius Caesar, the Roman Republican Calendar was more than two months out of synchronization with the seasons and nothing was happening when it was supposed to. Spring was occurring in winter months, winter in the fall, and so forth. Caesar's Greek astronomer, Sosigenes, (inherited from Cleopatra of Ptolemaic Egypt) figured out what should be done: a "final adjustment" of 67 days would be made and the (then) last month of the year, February, would be given an extra day every four years. As a consequence, the year 46 B.C. became known as "The Year of Confusion" and is the longest year on record, some 432 days. Although the Julian Calendar was not consistently used for civil ASTROCLK Astronomical Clock and Celestial Tracking Program Page 108 purposes until 8 A.D., the need for a "standard" dating method has led chronologers to extrapolate the Julian Calendar back in time, calling it the Julian Proleptic Calendar to distinguish it from other calendars in use. Under the Julian Calendar, therefore, each year contained 365 days unless the year was divisible by four, in which case the year contained 366 days. The additional day was inserted at the end of February. The average length of the Julian year was thus 365.25 days. Given the relatively simple instruments and mathematics of the time, the calendar that was devised then was remarkably accurate and it continued in force until 1582. Unfortunately, however, the tropical year (the time required for the Earth to make one complete orbit around the sun and the fundamental unit of our calendar) is actually 365.242199 days rather than the 365.25 days used for the Julian Calendar. By 1582 that relatively small annual error, 0.007801 days or about 11 minutes 14 seconds, had accumulated and the calendar was again out of step with the seasons, this time by some ten days. Following a number of false starts by prior pontiffs, Pope Gregory XIII ordered the use of an improved calendar, now known as the Gregorian Calendar and in general civil use throughout most of the world (sometimes in conjunction with an older, religious calendar). The new calendar directed that the dates 5 October through 14 October 1582 inclusive were to be abolished and that henceforth all centennial years, years ending in "00", be leap years only if divisible by 400. Therefore, 1700, 1800 and 1900 would NOT be Leap Years under the new calendar; 1600 and 2000 would still be Leap Years as before. Using the new Gregorian method, 400 civil years contained 400 * 365 + 100 - 3 or 146097 days and the average length of the civil year was 365.2425 days for a remaining error of approximately 0.0003 days. After all that fuss and bother, the calendar is still some 26 seconds per year too long, but it will take almost 3,000 more years, or until about 4882 AD, for us to accumulate a one day error. Some references (Encyclopaedia Britannica, for one) assert that a further adjustment has been proposed to the Gregorian Calendar: eliminate the Leap Year in years evenly divisible by 4000. This would reduce the error even further and it would be some 20,000 years before a one day error would be accumulated! Perhaps because the year 4000 A.D. is yet some time distant and much may happen between then and now, most authors do not mention or calculate the 4000 year adjustment. Given the lack of unanimity in my sources, ASTROCLK also does not use the 4000 year cycle in its calculation of future dates and the adjustment does not apply to past dates. The Gregorian Calendar, or the "New Style" as it was then called, was of course immediately adopted by the catholic countries: France, Portugal, Spain, and Italy as well as by Denmark and the Netherlands. Catholic Scotland adopted it in 1600 but since England did not, this caused considerable confusion between the two countries. The German Protestants waited 120 years or so, and it was not until 1752 that England and her colonies finally adopted the new calendar. By then the error had risen to 11 days (1700 was a Leap Year under the Julian Calendar ASTROCLK Astronomical Clock and Celestial Tracking Program Page 109 and was not under the Gregorian Calendar), and 3 September through 13 September 1752 inclusive were abolished, accompanied by much confusion and widespread disturbances. Even after formal adoption of the new calendar, many English communities still clung to the "Old Style" and the legend "O.S." may still be seen on old tombstones. Following the French Revolution, France abandoned the Gregorian Calendar for a new calendar beginning on September 22, 1792; its use was short lived, however, and France returned to the fold on January 1, 1806 and resumed use of the Gregorian Calendar. Good news travels slowly, it seems. Japan adopted the "new" calendar in 1873 and China followed in 1911. But it wasn't until the Bolsheviks came to power in 1917 and Pope Gregory had been dead for more than 300 years that the Russians changed their calendar. By then the error had further increased, to 13 days, still the difference in 1988. (Halloween, October 31, 1988 is October 18, 1988 using the Julian Calendar.) Not to be outdone by the West, however, the Russians adopted the Greek Orthodox calendar rule for a centennial year such that it is a leap year only if, after dividing the year by 900, the remainder is either 200 or 600. The Soviet calendar is about five times more accurate than the original Gregorian Calendar. Because of all of this change and confusion, ASTROCLK simply follows the original Gregorian Calendar as adopted in October of 1582 as the default calendar method. Dates prior to October of 1582 (and prior to 46 B.C. as well) are based upon the Julian Calendar. However, as an option, ASTROCLK can use the British date for the adoption of the Gregorian calendar in 1752, or it can use the strict Julian calendar for all dates. Local dates in other countries which did not immediately adopt the Gregorian calendar must be adjusted for the period from October, 1582 (or September, 1752 if that calendar is selected) through the date of adoption. Dates for countries which use or used other calendars are left as an exercise for the reader. By setting ASTROCLK's internal CALENDAR FLAG (see SETTING PROGRAM OPTIONS for details), dates may easily be converted between the three calendar conventions. For example, select the Perpetual Calendar (Display Mode 6), set the desired date (using F3), then observe the date and calendar differences as you change from one calendar convention to another (using ALT-F10). Because ASTROCLK monitors the computer's internal clock (which includes the current date), real time operation using the Julian Calendar is not allowed; the situation is confusing enough without ASTROCLK having to ignore part of the computer's time data. Naturally, all three calendar conventions show the same date prior to October of 1582; after September of 1752, both Gregorian calendars are in synchronization and may be operated in real time. Quite oblivious to religion, politics and computers, the Julian days have been spinning right along since 4713 B.C. They have served their purpose well for astronomers and other scientists. However, the true Julian Date (JD) is a rather large number (4 February 1988 = 2447195.5) and the precision of some calculators and micro-computer software is inadequate to the task. Fortunately for those calculators and computers, the ASTROCLK Astronomical Clock and Celestial Tracking Program Page 110 International Astronomical Union (IAU) at their Dublin meeting in 1955 adopted a special Dublin Julian Date (DJD) starting at noon on January 0, 1900 or 1900 January 0.5 and which may be defined as DJD=JD-2415020. The date can be confusing, however, since there obviously is no 0th of January; the selected date is a matter of astronomical convenience and actually is the same as 1899 December 31.5. The resulting number has only five digits to the left of the decimal point (3 February 1988 = 32175.5). Both methods, JD and DJD, are used internally by various ASTROCLK routines. Note that the Julian Date cycles at noon rather than at midnight as is the more usual practice for civil time; this can easily cause confusion in calculations. The Modified Julian Date (MJD) is a third method of recording the Julian Date which also only requires five digits (3 February 1988 = 47195.0) and is sufficient for most modern purposes. Introduced in the late 1950's by space scientists, it is defined as MJD=JD-2400000.5. An interesting side effect of this purely mathematical definition is the rather unlikely starting point of midnight (00:00:00 UT) on 17 November, 1858. Like DJD above, this method reduces the precision required for calculations but it also subtracts a half day so that the day starts at midnight in conformance with civil time reckoning. Although still mathematically accurate, MJD loses its advantage of lower precision requirements if used prior to about 1600 A.D. It is frequently used as a substitute for the true Julian Day by many scientific organizations and publications. The MJD has been sanctioned by various international commissions such as the International Astronomical Union (IAU), the Consultative Committee for Radio (CCIR), the advisory committee to the International Telecommunications Union (ITU), and others who recommend it as a decimal day count which is independent of the civil calendar in use. In addition to MJD, NASA also sometimes uses what they call the Truncated Modified Julian Date or TJD; it is simply MJD less the first digit, or TJD=JD-2440000.5. Like MJD, the day starts at midnight rather than at noon (3 February 1988 = 7195.0). The range of usefulness for TJD, based upon its having fewer digits, is generally restricted to the current century. Mathematically, of course, it is as accurate as any of the other methods. Summarizing, the four standard methods of Julian day counting in common use are: 00:00:00 UT Name Starting Date 04 FEB 1988 Related to JD ---- ------------- ----------- ------------- JD -4713 JAN 1.5 2,447,195.5 MJD 1858 NOV 17.0 47,195.0 JD-2400000.5 DJD 1900 JAN 0.5 32,175.5 JD-2415020.0 TJD 1968 MAY 24.0 7,195.0 JD-2440000.5 The Julian Ephemeris Date (JED) is a slightly different method of day counting based upon Ephemeris Time (ET, used pre- 1984) and Terrestrial Dynamical Time (TDT, used post-1983); JED differs from the conventional Julian Date (JD) by a matter of some seconds in this century (extrapolated to be 56.3 seconds in ASTROCLK Astronomical Clock and Celestial Tracking Program Page 111 1989, according to the Astronomical Almanac 1989). The actual difference, called Delta T = ET/TDT-UT, is calculated well after the fact using astronomical observations. For most astronomical calculations, JED and JD may be used more or less interchangeably unless high precision is required. However, for solar, lunar, and planetary calculations, JED is usually required as an invariant time system independent of the Earth's motion. Readers should use care because many authors are somewhat casual on the subject and may use the abbreviation "JD" to refer to either or both JD and JED, and the correct usage may not be obvious. The Julian Epoch (JE) and Besselian Epoch (BE) are two additional astronomical dating methods, generally used when lower precision is required or when the phenomenae of interest change slowly with time; star catalogs and planetary tables are common examples. The epoch dating methods are based upon the Julian Century (36525 days) and the Tropical Century (36524.2199 days) respectively. Texts written prior to about 1984 will write the epoch without a prefix letter and the Besselian Epoch is assumed (as in B1950.0). Again, however, recent authors often neglect to add the prefix even when different epoch dating methods are assumed; B1950.0 and J2000.0 are frequent examples. Most recent star catalogs and publications reference astronomical data to the current standard epoch, J2000.0. However, NASA and many planetary tables and formulae still reference the prior standard epoch, B1950.0, and some current data is referenced to the equinox of date (or mid-year), such as J1988.5. Conversion is often required in order that all data use the same reference epoch. Last of all, Greenwich Sidereal Date (GSD) represents the date using the sidereal day rather than the mean solar day. The starting point for GSD is about 0.6 days earlier than JD but, due to the shorter sidereal day, the date increases more rapidly than JD; GSD is presently some 6700 days ahead of JD. I have not seen it used in calculations, but the Astronomical Almanac includes GSD in some of its tables. The following list shows the value of these eight dating methods at 00:00:00 UT on 04 FEB 1988: JD 2447195.500000 MJD 47195.000000 DJD 32175.500000 TJD 7195.000000 JED 2447195.500649 JE J1988.091718 BE B1988.092741 GSD 2453896.370521 All of these dating methods are calculated by ASTROCLK and used as required in its calculations. Display Mode 7, Julian Date Information, displays this information except for GSD, which is found using Display Mode 8, Precision Time Display #1. ASTROCLK Astronomical Clock and Celestial Tracking Program Page 112 WHAT TIME IS IT? This is a crucial question for astronomers and navigators alike and is one of the reasons the two disciplines have been so closely linked from time immemorial. Of course, both are interested in the stars themselves, the first for scientific reasons and the second for more practical purposes. From the earliest recorded history, references are found to Polaris and Kochab, each the pole star at different times, and the nearby Big Dipper, two of whose stars serve as a "pointer" to Polaris. Their principal use was as aids to navigation, both on land and on sea. Not only does Polaris indicate true North with a fair degree of accuracy, but its height above the horizon represents the approximate latitude of the observer, the angle down from the pole or up from the Equator. So long as navigation was restricted to relatively confined areas, such as the Mediterranean Sea, voyages stood a reasonably good chance of reaching their intended destinations if the navigator knew his direction and approximate speed. Polaris (and later the magnetic compass, first described by an Englishman in 1180 but probably in use much earlier) could establish the direction being traveled and the observation of speed, winds, and tides could be combined with that direction to determine a ship's probable course and position, a procedure known as "dead reckoning". Elaborate charts covered with rhumb lines (lines corresponding to various wind directions) were produced in the 13th century to aid the navigator in setting and plotting his true course. But as ships ventured further and further from known landmarks, it became clear that this was not enough. Knowing only their latitude (North-South position) and the direction of the pole star, sailors found that they were often nowhere near their destination. When sailing down the West coast of Africa, the Portuguese, for example, adopted the practice of sailing South to the desired latitude, then sailing East for however long it took until they reached their destination. Columbus used this same technique on his return trips to America. To further complicate matters, the carefully drawn rhumb line charts assumed a flat surface; the greater the distance traveled the greater the error due to the fact that the Earth is a sphere and not a plane. In an interesting footnote to history, the ancient Greeks had concluded that the Earth was a sphere and described a more or less circular orbit about the Sun -- or vice versa. Starting some time around 450 B.C. give or take a few years and continuing for more than 700 years, Greek astronomers proposed astronomical theories and counter-theories culminating in Ptolemy's Almagest in the middle of the second century AD. Erathosthenes (276-196 B.C.) made the first fairly accurate determination of the Earth's diameter. He noticed that at Syene, Egypt (near present Aswan), sunlight struck the bottom of a vertical well at noon. At the same time and date in Alexandria, 5000 stadia north of Syene, he noticed that the Sun's rays made an angle with the vertical of about 1/50 of a circle (about 7 degrees). He therefore calculated that the Earth's circumference must be 50 * 5000 or 250,000 ASTROCLK Astronomical Clock and Celestial Tracking Program Page 113 stadia. Unfortunately, there were several stadia (the Greek unit of length) in use and, depending upon which one you assume Erasthones was using, his calculation could have been accurate to within 1 percent or 20 percent too large. Somewhere along the way this important bit of information, the spherical Earth, was lost, misplaced or simply not believed and by the middle ages many people in Europe were certain that the Earth was flat. I'm not convinced that any of the great navigators of the time were quite so naive and ill informed, but maps drawn with that assumption in mind became less and less accurate as voyages covered greater distances. But the Earth, of course, really is a sphere (an oblate spheroid, actually) and what was needed were maps based upon latitude and longitude, not simply bearings. In 1569 Gerardus Mercator published his world map based on a "true projection suitable for navigation" and within a few decades navigators had maps and tables which would permit the approximate determination of position. The Mercator Projection is still used today for many types of maps. Unfortunately, the maps of the day were not always accurate, especially for unexplored areas of the globe, and even when they were accurate everything depended upon being able to estimate longitude as well as latitude. The fifteenth and sixteenth centuries saw notable advances, particularly in England, in the determination of longitude using techniques such as lunar distances or the eclipses of the satellites of Jupiter. The first astronomical ephemeris by Regiomontanus was published in Nurnberg in 1474 and other increasingly accurate ephemerides (tables of astronomical data) useful to navigators were produced over the next two hundred years. In 1675 the Royal Observatory was founded in Greenwich with the specific object of providing the sailor with astronomical data of the precision required for reliable navigation. Medieval astronomers knew that the time of a lunar eclipse could be used to determine the local longitude, but that wasn't very handy on a day to day basis. By the sixteenth century it was also recognized that longitude could be determined by noting the precise time and the position of the stars. Away from a stable land platform and good instruments, however, knowing the time accurately was all but impossible and time was a critical factor in the longitude calculations. In 1714, following a series of naval disasters caused by bad navigation, the English Parliament established the Board of Longitude to address the problem. The Board offered a prize of 20,000 pounds sterling, a princely sum in those days, to anyone who could determine longitude to an accuracy of thirty miles after a voyage of six weeks. An Englishman by the name of John Harrison ultimately won the prize on his fourth attempt using a marine chronometer fashioned in the shape of a watch. And so began the practice of determining position at sea by taking timed observations of the stars and planets. The Royal Greenwich Observatory, situated on the Thames River downstream from London, provided essential time services to the Royal Navy and merchant seamen alike, and each captain would carefully set his chronometer upon departure. Small wonder that chronometer was among the most carefully guarded objects on board ASTROCLK Astronomical Clock and Celestial Tracking Program Page 114 ship, for their very lives might well depend upon its continuing accuracy. With little need for precision evident ashore, however, local time was often a rather casual affair and based upon apparent solar time, the time indicated by a sundial. Each town or village would establish its own local time independent of its neighbors. But apparent solar time is subject to considerable variation as a result of the Earth's elliptical orbit and the changes in the speed of rotation of the Earth. The difference from day to day is relatively small, but the cumulative difference can add up to about fifteen minutes over the course of several months, a phenomena known as the Equation of Time. The gradual improvement of clocks and watches during the seventeenth century made these variations more obvious and forced the use of mean solar time, apparent solar time averaged over a year, and eventually caused the establishment of uniform time zones. The railroads became prime movers in the push to standardize timekeeping; schedules would be impossible to understand if every stop used a different time convention. Most countries in Europe therefore established single time zones using the time determined at a single point such as Greenwich or Paris, but the United States was forced by its size to adopt multiple time zones in order to keep local times reasonable compared to the Sun. As transportation and communication speeds continued to improve, the various time zones were ultimately standardized in 1884 with Greenwich selected as the Prime Meridian, and thus GMT or Greenwich Mean Time became a worldwide standard. [However, until 1925, 0 hours GMT occured at noon rather than at midnight, another source of possible confusion. The use of the designation GMT has now been discontinued for the most part and replaced by UTC, Coordinated Universal Time.] The globe was marked with 24 standard meridians spaced at 15 degree (one hour) intervals and the meridian at 180 degrees was designated the International Date Line. Most time zones are now an integral number of hours different from Greenwich, corresponding to the nearest standard meridian, and a few are at a half hour multiples for local convenience (India, for example). However, there still remain some odd zones here and there. The accuracy and precision of our time measurements have continued to improve as technology has advanced and in response to the demands of the scientific and industrial community. Traditionally, the fundamental unit of time measurement, the second, was defined as 1/86,400 of a mean solar day. With the improved accuracy of timekeeping came the need for a more absolute standard and at the Dublin conference in 1955 the second was redefined as 1/31,556,925.9747 of the tropical year as measured on 1900 January 0.5, the same point selected for the start of the Dublin Julian Date (DJD). This didn't last too long, however, and in 1964 the International Committee on Weights and Measures officially adopted the transition between two specific energy levels of cesium-133 as the definition of the second with the introduction of the atomic clock. Timekeeping has now become internationally standardized and the official custodian of the world's clocks is the Bureau International de l'Heure (BIH) in Paris. Here in the United ASTROCLK Astronomical Clock and Celestial Tracking Program Page 115 States time standards and observation are the responsibility of the National Bureau of Standards (NBS) and the U. S. Naval Observatory (USNO). In 1965, after almost three hundred years as the de facto time standard in the world, the Royal Greenwich Observatory was restructured into more of a pure research organization and has subsequently lost interest in, and ceased most support for, time and time standards. With the standardization and improved accuracy of our timekeeping has come increased complexity. The old phrase Greenwich Mean Time or GMT has now been officially discontinued by most of the world, Great Britain and to a lesser extent the United States (because of our close cooperation with Great Britain on the Astronomical and Nautical Almanacs and related works) being almost alone in continuing to use it, and then primarily for navigators. Old habits die slowly, however, and many people continue to use the old phrase, often unaware of the change in name. GMT has generally been replaced by Coordinated Universal Time, UTC, which is the time broadcast by the National Bureau of Standards via WWV in Boulder, Colorado, and WWVH in Honolulu, Hawaii, as well as other national radio time services. For most purposes, those requiring accuracy to about one second, GMT and UTC may be considered interchangeable. Individuals with a military or aviation background will recognize ZULU Time, also equivalent to Universal Coordinated Time. For scientific work requiring high precision, however, things are not nearly so simple. There are now four "standard" Universal Times which take into account in varying degrees the various phenomena that cause changes in time measurements over long periods. In addition, a number of other time systems are used including International Atomic Time (TAI) and Terrestrial Dynamical Time (TDT). In 1984 TDT replaced Ephemeris Time (ET) as the astronomical standard of time, the time system actually used by most astronomers and computed well after the fact. UTC, tied to the (irregular) rotation of the Earth, is currently "slow" relative to TDT by slightly less than one minute; extrapolated values given in the Astronomical Almanac 1989, Page K9, are 55.8 seconds for 1988 and 56.3 seconds for 1989. For the present, all calculations within ASTROCLK assume UT1 and ignore differences with other UT time standards. The following simplified definitions describe the various time standards in general use at the present time, or which have been in common use during this century. A.1 U.S. Naval Observatory Atomic Time, used from January 1, 1958 through December 31, 1971. ET = A.1 + 32.15 seconds. Replaced by TAI (qv) on January 1, 1972. ET Ephemeris Time, replaced in 1984 by Terrestrial Dynamical Time (qv). GAST Greenwich Apparent Sidereal Time. Greenwich Hour Angle of the true equinox of date. GMST Greenwich Mean Sidereal Time. Greenwich Hour Angle of the mean equinox of date. ASTROCLK Astronomical Clock and Celestial Tracking Program Page 116 GMT Greenwich Mean Time, a term now used almost exclusively in the United Kingdom and for navigation. Most modern references now use UT1 (qv) instead. Prior to 1925, 0 hours GMT occured at noon rather than at midnight; care must be used when referencing older documents to take this change into account. TAI International Atomic Time. The unit of TAI time is the SI (Systeme International) second. This time standard is based upon the analysis of the atomic time standards of many countries and is related to the radiation of Cesium 133. "Atomic time, in the general relativistic sense, probably keeps the proper time of a moving observer in a gravitational field." [Taff, p 102, see BIBLIOGRAPHY.] TAI was adopted as a standard on January 1, 1972, replacing A.1 (USNO Atomic Time) which was used from January 1, 1958. TDT Terrestrial Dynamical Time, used for astronomical ephemerides for observations from the surface of the Earth. TDT/ET = TAI + 32.184 seconds. For most purposes, ET (up to 1983 December 31) and TDT (from 1984 January 1) can be regarded as a continuous time scale. In 1989, TDT is ahead of UT by approximately 56.3 seconds; the difference is 56.7 seconds for 1990. TDB Barycentric Dynamical Time, used for high precision astronomical ephemerides referred to the barycenter (center of mass) of the solar system. TDB never varies from TDT by more than 1.7 milliseconds and is not used by ASTROCLK. TDB was previously known as Coordinate Time. UT0 Classical universal time, based upon the mathematical relationship between mean solar time and mean sidereal time. Not directly used or calculated in ASTROCLK. UT1 UT0 corrected for precession, the polar motion of the Earth. This slow wobbling motion describes a circle about 30 feet in radius over a period of approximately 25,800 years. The combined gravitational fields of the Sun and Moon acting upon the non-spherical Earth cause the direction of the Earth's rotation axis to gyrate slowly. UT1 is now the official designation for, and is the same as, Greenwich Mean Time, GMT. In program ASTROCLK, the abbreviation UT is used to mean UT1 and is used for all calculations and displays unless specifically noted otherwise. Except in the Precision Time Displays, ASTROCLK ignores the difference between UT1 and UTC, considering them identical. UT2 UT1 corrected for a slight (maximum seasonal difference of approximately 0.035 second) periodic variation in the speed of rotation of the Earth caused by the ASTROCLK Astronomical Clock and Celestial Tracking Program Page 117 varying distances and relative directions of the Sun and Moon which in turn continuously alter the strength and direction of the gravitational field. Not used or calculated in ASTROCLK. UTC Coordinated Universal Time. UTC was originally a smoothed version of UT2 (pre-1972) and is now based directly upon TAI. On January 1, 1972 the difference between TAI and UTC was exactly 10 seconds. Since that date, adjustments of exactly one second are made as required on June 30th or December 31st in order to keep UTC and UT1 within 0.9 seconds of each other. When a change is required, the last minute of those months will have 59 or 61 seconds. UTC is the basis for most radio time services (including WWV/WWVH) and our civil and legal time systems. It is also, of course, the time signal most of us use to synchronize time-dependent equipment and (directly or indirectly) to set our clocks. As noted above, ASTROCLK generally assumes UT1=UTC unless noted otherwise; the difference is less than the setting/running errors of the average micro- computer system clock. ZULU A distinctive phonetic acronym having no particular meaning. ZULU time is equivalent to UTC and is used in commercial avaition and by the U. S. military services in order to avoid confusion over local time zones. ASTROCLK Astronomical Clock and Celestial Tracking Program Page 118 PRECISION AND ACCURACY TESTS A number of tests have been performed to examine the precision and/or accuracy of various calculations made by ASTROCLK. The principal data used for testing and comparison are derived from: Astronomical Almanac 1988 and 1989 (both usually refered to as AA, unless a more specific reference is required), USNO Almanac for Computers, 1988 (AFC88); USNO Floppy Almanac 1988 and 1989 (FA generally, or FA88 and FA89 if required); USNO Interactive Computer Ephemeris (ICE); Astronomical Formulae for Calculators (AFC); and, Astronomy with Your Personal Computer (AYPC). See BIBLIOGRAPHY for the full references. Unless noted otherwise, all tests and comparisons were made using a Zenith Z- 248 computer (IBM PC/AT compatible with 80286 processor) equipped with an 80287 math coprocessor. Representative tests were repeated on a Zenith Z-183 laptop (IBM PC/XT compatible with 80C88 processor) with or without a math coprocessor with no differences observed other than execution speed. Strict mathematicians and scientists may complain about the precision to which data is typically displayed by ASTROCLK. The reader is reminded at various points in this text that the displayed precision may exceed the accuracy of the data, a practice which is definitely frowned upon in scientific circles, but I plead special circumstances for ASTROCLK. First and foremost, ASTROCLK has been developed over a considerable period of time, and the process still continues. The accuracy of all data have been consistently improved over that time, and many items have gradually been improved to the point where the accuracy and the displayed precision are roughly the same -- the desired objective. In some cases, stellar Apparent Geocentric Equatorial Coordinates for example, the improvement has reached the limits of the QuickBASIC compiler and the accuracy is essentially equal to the best available sources. Second, many different items are displayed using the same units and in multiple formats but having different or unknown accuracy; it is convenient from a programming standpoint to use common subroutines for display purposes. Attempting to tailor the display each of the dozens of quantities calculated by ASTROCLK to the probably accuracy is impractical. Finally, even in cases where the accuracy is known to be lower than the displayed precision, trends and relative magnitudes of change can be observed and are reasonably accurate; these second order effects are of some interest to me (and perhaps others), and would be lost if the data were truncated to the known accuracy. COMPILER Microsoft QuickBASIC, Version 4.50, is the language used for ASTROCLK. Code may be executed in a quasi-interpretive mode or it may be compiled to an executable file. Two different Microsoft programs, QB and BC, are used for the two methods respectively. The distribution version of ASTROCLK is the compiled version of the code. When required for precision, the double-precision ASTROCLK Astronomical Clock and Celestial Tracking Program Page 119 floating point format has been used for numeric data; this eight byte format has a precision of 15 or 16 digits and an approximate magnitude range of from 4.9E-324 to 1.8E+308. [As of Version 8903, the program could still be compiled with QuickBASIC Version 4.00b, but that compatibility may not be maintained and will not be tested for future ASTROCLK versions.] Unfortunately, testing (and confidence) is complicated by the fact that the interpreted version appears to be very sensitive to the order of evaluation and/or to mixing variable types within an expression. For example, using Version 4.00 (since updated to Version 4.50), typical calculated results for mean sidereal time varied by plus or minus 0.000011 hours simply by changing the type of variables. Compiled results were the same for all calculations tested, regardless of type or order, and have been used for all comparisons with other data. In spite of the interpreter situation, however, I have concluded that the flexibility and ease of use of QuickBASIC outweighs concern over its problems. In any event, the accuracy and precision seem sufficient for the intended use in ASTROCLK. CALENDAR DATES The calendar algorithms used are either modeled upon those given in AFC and AYPC or have been developed specifically for ASTROCLK. The calendar displays for October, 1582 and September, 1752 use special algorithms to allow for the 10 or 11 missing days. The default ASTROCLK calendar strictly follows the Julian Calendar from its adoption in 46 B.C. through the Gregorian Calendar at its adoption in 1582. Alternatively, the user may select the strict Julian Calendar for ALL dates, or select the British date of adpotion of the Gregorian Calendar in 1752. See the section SETTING PROGRAM OPTIONS for additional details. Dates prior to 46 B.C. are merely an extension of the Julian Calendar back into time, known as the Julian Proleptic Calendar, and bear no particular relationship to calendar(s) in actual use. For times subsequent to 46 B.C., extensive tests have disclosed no errors. Dates for countries adopting the Gregorian Calendar subsequent to October, 1582 or September, 1752 must be adjusted manually. The intercalation proposed and/or adopted for 4000 A.D. and thereafter on a 4000 year cycle has not been included. As a matter of personal preference and in company with some (but not all!) of my references, I have adopted a year numbering scheme which includes no zero year. Readers should note that other authors prefer year numbering WITH a zero year, and feelings seem to run high on the subject. Mathematically, of course, any continuous set of numbers must include zero. However, common usage does not include a zero year. The confusion and errors which may result from converting common years such as 4713 B.C. into year number -4712 seem too high a price to pay to maintain conformance with the mathematical niceties. Since opinion and practice in the astronomical community is divided anyway, the reader must always check negative dates to determine the year numbering system being used by a given author. ASTROCLK Astronomical Clock and Celestial Tracking Program Page 120 JULIAN DATES Julian Dates have been compared with various Astronomical Almanacs and other sources and are exact. The algorithm used is modeled upon that given in AFC. The Julian Date calculations should be accurate from -4713 onward. Note that ASTROCLK uses a year numbering scheme with no year zero (see above); other authors prefer a scheme with a zero year. The day count is also presented in three other formats: MJD, DJD, and TJD. See the section JULIAN DATES AND THE GREGORIAN CALENDAR for additional discussion. UNIVERSAL TIMES Coordinated Universal Time (UTC), the time broadcast by WWV/WWVH and others, is not the same as Universal Time (UT=UT1) but the difference is maintained at less than 0.9 seconds and for most purposes this difference can be ignored. ASTROCLK assumes UT for all time and date calculations and displays with one exception: the Precision Time Display. In this case, the correct UTC time is calculated and displayed to full accuracy for the period 1972 through 1989 when data from AA, Pages K8 and K9, may be applied. Outside this time period, I have made more or less arbitrary assumptions to supply missing data. AA does not include data for Delta UT = UT-UTC; the following tabulation was made using ASTROCLK data for 00:00:00.00 UT and the UT date shown. 1988 DELTA UT = UT - UTC (seconds) ---------------------------------- JAN 1 +0.18 JUL 1 -0.06 FEB 1 +0.14 AUG 1 -0.11 MAR 1 +0.10 SEP 1 -0.15 APR 1 +0.06 OCT 1 -0.19 MAY 1 +0.02 NOV 1 -0.23 JUN 1 -0.02 DEC 1 -0.27 TERRESTRIAL DYNAMICAL TIME Delta T, defined as TDT/ET - UT, is determined retro- spectively approximately one year after the fact. Since most planetary phenomena require the use of TDT/ET but ASTROCLK is based upon UT, Delta T is required to relate the two time scales. Data for reduction of UT versus TDT (Terrestrial Dynamical Time) times are given in AA, Pages K8 and K9, annually for the period 1620 through 1987 with extrapolated data for 1988 through 1990. ASTROCLK uses the published values for Delta T as of 0h UT January 1 each year for the available interval. For simplicity, I have assumed that Delta T varies linearly from datum to datum; interpolation would probably yield more accurate results, but the difference would not be significant for most of ASTROCLK's calculations. Prior to 1984, the designation changes to Ephemeris Time (ET). The two time scales are considered continuous by ASTROCLK. Data for the future behaviour of the rotation of the Earth ASTROCLK Astronomical Clock and Celestial Tracking Program Page 121 is, of course, mostly well-informed speculation. However, it determines how Universal Time will change with respect to Terrestrial Dynamical Time and, in the context of ASTROCLK, is required for planetary positions especially. Similarly, while the data for the last several hundred years can at least be inferred from historical records with some degree of confidence, little or no accurate information exists for ancient times. A number of formulae have been published which allow the estimation of Delta T over extended periods. Versions of ASTROCLK prior to 8848 calculated Delta T using a formula by Meeus (AFC); Version 8848 changes to a formula by Morrison and Stephenson (1982) and used by Bretagnon and Simon (1986). [See BIBLIOGRAPHY for reference.] The two methods produce values of Delta T that differ by about three hours at 4000 BC, out of approximately thirty hours. I have no particular reason to believe one formula more accurate than the other, but I switched to Bretagnon and Simon because their planetary position formulae are widely recognized as some of the more accurate which are suitable for micro-computers. Their planetary data, therefore, form a useful basis for comparison with ASTROCLK's planetary position calculations at any instant in time; using the same time scales makes this comparison far simpler. However, TDT or ET should be used with caution outside the period 1620 through 1990. INTERNATIONAL ATOMIC TIME (TAI) Data for reduction of TAI versus UTC times (Delta AT) is given in AA, Page K9, annually for the period January, 1972 through July, 1985. I do not recall any subsequent Leap Seconds until December 31, 1987 and have therefore increased Delta AT to +24 on January 1, 1988. Prior to its adoption as a standard in 1972, TAI is replaced by USNO A.1 (see below). Subsequent to 1988, I have arbitrarily adjusted TAI by inserting one or more Leap Seconds so that the difference between UT and UTC is always less than one second. The difference between TAI and TDT/ET is 32.184 seconds. TAI should be used with caution outside the period January 1972 through December 1988. USNO ATOMIC TIME (A.1) Prior to the adoption of International Atomic Time, the U.S. Naval Observatory maintained its own atomic time standard, known as A.1. On January 1, 1958, the difference between A.1 and UTC was exactly zero seconds. By January 1, 1972 (when TAI was adopted), the difference was ten seconds. In calculating Delta AT for A.1, I have assumed a linear rate of change and that adjustments are made on June 30th or December 31st as appropriate to maintain the proper relationship with UT. The difference between A.1 and ET is 32.15 seconds. SIDEREAL TIMES Greenwich mean and apparent sidereal times at 00:00:00 UT for each day of the year are given in AA, pages B8 through B15; selected dates are also given in AFC88, page A3, or they may be ASTROCLK Astronomical Clock and Celestial Tracking Program Page 122 computed for any time using FA. ASTROCLK computed Greenwich Mean Sidereal Times are exact compared to AA and FA88 using the Precision Time Display #1, Display Mode 8. The displayed values for Greenwich Apparent Sidereal Times have a lower accuracy (due to the complex calculations required to compute nutation and the Equation of the Equinoxes); the accuracy is substantially better than 0.01 seconds. A comparison using FA88 for 1 January at 0h UT and 12h UT at each of the decades 1950 through 1990 showed GMST to be exact at the displayed precision of 0.0001 seconds for all samples, and GAST to have an average error of -0.0007 seconds and maximum errors of +0.0013 and -0.0025 seconds. The GAST average error works out to about 1/100,000,000 (10E-8). LMST is GMST adjusted for the local longitude and is therefore as accurate as the longitude data. LAST also depends upon longitude; using the same longitude for ASTROCLK and FA88, comparison of LAST showed results comparable to GAST. The algorithms for time calculations in general and for the sidereal time calculations in particular were revised and refined at Version 8826 and again at Version 8831, with an improvement in accuracy of at least an order of magnitude. The Precision Time Displays were also added at Version 8826. [Thanks to Ward Harman for detecting an error at other than 0h UT.] If you wish to calculate the data shown in AA, switch to the Precision Time Display #1. Display Mode 8, and enter the time and date in UT using Function Key F3 as follows (April 1988 is used as an example): 0U (time: 00:00:00 UT) 1,4,1988 (date: APR 1, 1988) Use Function Key F7 to select the desired data format. PRECESSION Precessing the preset internal star database, derived from USNO FA88 data, from J2000.0 to J1988.5 yields coordinates in good agreement with USNO Almanac for Computers 1988 to the precision given there, although the accuracy decreases slightly for declinations nearer the poles. Beginning with Version 8905, the precession method was changed from Newcomb (B1900.0) to Improved IAU System (J2000.0) as described in the main text and the supplement to the 1984 Astronomical Almanac. The resulting precessed data are little changed. Representative test results are shown below. Prior to precessing any star in the internal star database, ASTROCLK automatically restores all data to J2000.0 in order to eliminate cumulative errors. Proper motion for objects entered manually may also be entered, or set to zero if not known; tracking data which is precessed over long periods of time when proper motion parameters are set to zero should be used with caution. Solar system objects should always be entered with proper motion parameters set to zero. Care should be taken when manually entering data to ensure that the data epoch is the same as that of the internal database. ASTROCLK Astronomical Clock and Celestial Tracking Program Page 123 In order to maintain consistent data within ASTROCLK, the internal star database should first be precessed to a data epoch, then manual data referenced to that epoch should be entered. After that, all data may be precessed to the final epoch; using this procedure, both the manually entered data as well as the internal data will all refer to the same epoch. SAMPLE PRECESSION DATA FOR J1988.5 AFC88 ASTROCLK # Star Name SHA/DEC SHA/DEC ---------------------------------------------- 0 Polaris 325.0618 325.064979 89.2126 89.212613 10 Aldebaran 291.1851 291.185085 16.4868 16.486829 20 Procyon 245.3249 245.324922 5.2551 5.255091 30 ACrux 173.5116 173.512040 -63.0354 -63.035405 40 Kochab 137.3174 137.317359 74.2025 74.202525 50 Nunki 76.3618 76.361780 -26.3118 -26.311751 The data from AFC88 (Almanac for Computers 1988) is given there for Mean Place (J1988.5) as shown. The data from ASTROCLK has been precessed from J2000.0 to J1988.5 using Function Key F8. Note slightly degraded accuracy near the North and South poles. SHA: Sidereal Hour Angle in degrees, first line. SHA is related to Right Ascension (in hours) by the formula SHA=360-RA*15. The data format shown for ASTROCLK is obtained using Function Key ALT-F7 (for SHA) and Function Key F7 (for degrees and decimal fractions of a degree). DEC: Declination in degrees, second line. The data format shown for ASTROCLK is obtained using Function Key F7 (for degrees and decimal fractions of a degree). A similar comparison with the Astronomical Almanac 1989, Appendix H ("Bright Stars, J1989.5"), yields accuracies of 0.1 seconds in Right Ascension and 1 second of arc in Declination when the ASTROCLK data are rounded to the same precision as that given in the Astronomical Almanac. In its discussion of rigorous precession, the Astronomical Almanac 1989 includes an example of the reduction of celestial coordinates for a fictitious star on page B40. The time is given ASTROCLK Astronomical Clock and Celestial Tracking Program Page 124 as 0h TDT 1989 JAN 1. Entering the relevant example data (including proper motion, but not parallax or velocity) into ASTROCLK yields the following data: EQUATORIAL COORDINATES [J2000.0]: RIGHT ASCENSION (hours): 14:39:36.09 DECLINATION (degrees): -60 50'07.13" APPARENT COORDINATES [J1989.0]: RIGHT ASCENSION (hours): 14:38:49.34 DECLINATION (degrees): -60 47'17.56" The J2000.0 Equatorial Coordinates shown above are the mean data at the standard epoch, essentially identical to those entered from the Astronomical Almanac. The Right Ascension is correct when the data is rounded to the precision shown; the Declination is low by 0.01 arcseconds and results from internal rounding and/or precision errors. The computed J1989.0 Apparent Geocentric Equatorial Coordinates given in the Astronomical Almanac are: RIGHT ASCENSION (hours): 14:38:49.394 DECLINATION (degrees): -60 47'17.49" Even without the inclusion of velocity factors, the results from ASTROCLK agree with the Astronomical Almanac to -0.05 seconds in Right Ascension and +0.07 seconds in Declination. These errors approach the limits imposed by the double precision floating point representation of numbers within QuickBASIC and probably represent the best accuracy attainable in this context. Beginning with Version 8903, the internal or external catalog value for the visual magnitude of the selected star or object is displayed at the lower right of the window border in the Tracking Display, Display Mode 0. SOLAR POSITION CALCULATIONS The computation of the position of the Sun is crucial to many of ASTROCLK's other calculations. I have selected the Apparent Geocentric Coordinates as representative of the accuracy of the calculated solar position; these values are more or less "at the end of the line" in the series of solar calculations and therefore should provide a good basis for comparision with other sources as well as implying the accuracy of prior calculations. In the table which follows, the data source is noted in the right hand column: AA is the Astronomical Almanac, 1988, Pages C4 through C18; FA is the USNO Floppy Almanac, 1988, Version 2.11.88 with time and date set automatically from ASTROCLK using ALT-F9; and, AC is ASTROCLK, Version 8903, Precision Data Display #2. All data are for 0 hours TDT. Use Function Key F3 and enter "0T" to set TDT time in order to obtain the same ASTROCLK results for a given date. Note that the date displayed by ASTROCLK is UTC DATE, which differs from the TDT DATE by some +56 seconds in 1988; the UTC DATE will therefore show as the prior day for all months and the prior year for January 1. ASTROCLK Astronomical Clock and Celestial Tracking Program Page 125 Use Function Key F3 and enter "0U" to set UT time in order to obtain the same Floppy Almanac results for a given date. Note that ASTROCLK writes the UT time to the file FA.DFT but the Floppy Almanac assumes the time as TDT for Apparent Geocentric Positions calculations. [Other Floppy Almanac calculations correctly interpret the time from FA.DFT as UT.] ASTROCLK Astronomical Clock and Celestial Tracking Program Page 126 1988 APPARENT GEOCENTRIC COORDINATES OF THE SUN @ 0h TDT Right Ascen Declination Distance HH MM SS.SS DD MM SS.SS (AU) ----------------------------------------------------------------- JAN 1 18 42 32.35 -23 04 58.0 0.9832806 AA 32.351 57.98 0.9832806 FA 32.09 59.13 0.98328271 AC FEB 1 20 55 10.26 -17 22 51.2 0.9852225 AA 10.263 51.19 0.9852225 FA 10.10 52.74 0.98522551 AC MAR 1 22 48 28.17 -7 35 04.3 0.9908696 AA 28.166 04.27 0.9908696 FA 28.10 05.36 0.99087354 AC APR 1 0 42 13.66 4 32 33.1 0.9993011 AA 13.657 33.09 0.9993011 FA 13.57 32.50 0.99930318 AC MAY 1 2 33 39.46 15 04 46.1 1.0076058 AA 39.462 46.07 1.0076058 FA 39.27 45.59 1.00760326 AC JUN 1 4 36 31.28 22 03 24.4 1.0140599 AA 31.285 24.39 1.0140599 FA 30.97 24.52 1.01405250 AC JUL 1 6 40 49.08 23 06 40.5 1.0166665 AA 49.076 40.53 1.0166665 FA 48.79 41.54 1.01665800 AC AUG 1 8 45 34.69 18 01 10.9 1.0149312 AA 34.695 10.93 1.0149312 FA 34.61 11.55 1.01492350 AC SEP 1 10 41 32.50 8 16 56.4 1.0091422 AA 32.500 56.39 1.0091422 FA 32.68 54.99 1.00913318 AC OCT 1 12 29 29.89 -3 11 08.2 1.0010858 AA 29.888 08.23 1.0010858 FA 30.28 11.19 1.00107716 AC NOV 1 14 25 35.77 -14 25 48.7 0.9924284 AA 35.772 48.75 0.9924284 FA 36.18 51.13 0.99242345 AC DEC 1 16 29 14.33 -21 48 17.1 0.9860075 AA 14.332 17.11 0.9860075 FA 14.59 17.81 0.98600708 AC ASTROCLK Astronomical Clock and Celestial Tracking Program Page 127 MAJOR PLANET POSITION CALCULATIONS Care must be taken when comparing ASTROCLK's planetary data with other sources to ensure that the data are calculated for the same time, date, and epoch. No extensive accuracy comparisons have yet been performed for ASTROCLK's planetary position calculations, but spot checks against the Astronomical Almanac, USNO Floppy Almanac, Bretagnon and Simon, Sky & Telescope Magazine, and Astronomy Magazine indicate good agreement. As compared against the monthly magazine positions, ASTROCLK provides essentially the same data, and can generate the data for any date rather than for selected dates within a month. In general, predicted errors for the algorithms used by ASTROCLK are on the order of 10" for the calculated positions, and typical errors for a small number of samples have been of that order of magnitude as compared against the USNO Floppy Almanac. The position of Pluto is calculated using osculating elements as of 1988 JAN 1, and the errors will increase as the time difference from that date becomes greater. The Astronomical Almanac 1988 includes Geocentric Distance and Coordinates for the planets. The coordinates for Venus are given on pages E18 through E21. The data are given at 0h TDT for each day of 1988. Entering 0h TDT 1988 DEC 25 into ASTROCLK and selecting Venus yields the following data: Heliocentric Longitude: 214 52'30.43" Heliocentric Latitude: 2 15'35.90" Heliocentric Radius (AU): 0.722754 Appar Geocentric Longitude: 249 03'00.77" Appar Geocentric Latitude: 1 05'37.50" Geocentric Distance (AU): 1.4936045 <=== Apparent Right Ascen [J1988.9]: 16:30:05.90 <=== Apparent Declination [J1988.9]: -20 43'44.27" <=== Apparent Right Ascen [J2000.0]: 16:30:44.93 Apparent Declination [J2000.0]: -20 45'08.39" Angular Size (arcsec): 11.33 The True Geocentric Distance and Apparent Equatorial Coordinates given in the Astronomical Almanac for that date are: GEOCENTRIC DISTANCE (AU): 1.4935568 RIGHT ASCENSION (hours): 16:30:05.982 DECLINATION (degrees): -20 43'44.04" The data compare extremely well. The ASTROCLK errors are +0.0000477 AU in Geocentric Distance, -0.082 seconds in Right Ascension, and +0.24 arcseconds in Declination. Beginning with Version 8903, the approximate visual magnitude of the selected planet is also displayed on the Tracking Display, Display Mode 0, at the lower right of the window border. ASTROCLK Astronomical Clock and Celestial Tracking Program Page 128 MINOR PLANET POSITION CALCULATIONS It is difficult to directly compare minor planet data from the available sources. ASTROCLK computes all minor planet data in the same way as for major planets: apparent position as of the ecliptic and equinox of date. The Astronomical Almanac gives geocentric positions as Astrometric J2000.0 Right Ascension and Declination, and other sources use B1950.0. However, data for the major planets are available as of the ecliptic and equinox of date; using the osculating elements given in the Astronomical Almanac for the major planets and processing these data through ASTROCLK's minor planet software yields position data generally accurate to a second or arcsecond at or very near the date of osculation. This is better accuracy than ASTROCLK's internal major planet data and algorithms usually provide. I have interpreted these results to mean that my methodology is essentially accurate and correct. For example, using the minor planet catalog PLANETS.MPC (which contains osculating elements @ 1989 MAR 15.0 for the eight major planets from the Astronomical Almanac 1989), the following heliocentric and geocentric results were obtained: HELIOCENTRIC POSITION FOR MERCURY @ 1989 MAR 15.0 Longitude Latitude Radius Vec Source -------------------------------------------------- 243 44 08.0 -6 22 52.2 0.4440226 AA 1989 243 44 07.53 -6 22 52.25 0.4440219 ASTROCLK GEOCENTRIC POSITION FOR MERCURY @ 1989 MAR 15.0 Rt. Ascension Declination Delta Source -------------------------------------------------- 22 37 19.211 -11 05 56.36 1.2713558 AA 1989 22 37 19.52 -11 05 55.27 1.2713511 ASTROCLK CELESTIAL NAVIGATION CALCULATIONS ASTROCLK's celestial navigation calculations are adapted from the material presented in the Nautical Almanac 1989, pages 277 and following. ASTROCLK was tested by using the Nautical Almanac data adjusted to offset ASTROCLK's automatic internal refraction calculations, the same practice used by the Nautical Almanac. These data therefore represent the result when extremely precise altitude measurements have been taken and when the atmospheric refraction, horizon dip, course, and speed are precisely known. In practice, altitude measurements to this precision are all but impossible outside an observatory, and atmospheric refraction can seldom be predicted to an accuracy of much better than approximately 0.5 minutes of arc. Under these circumstances and using the example data on page 282 of the Nautical Almanac 1989, ASTROCLK calculates the position of a moving ship to an accuracy of 0.03 nautical miles ASTROCLK Astronomical Clock and Celestial Tracking Program Page 129 (0.05 kilometers or less than 200 feet) as compared to the results calculated in the Nautical Almanac. This level of accuracy is unlikely to be achieved in actual use. In addition to the potential errors mentioned in the previous paragraph, note in particular that ASTROCLK assumes UTC = UT (or that the computer is set to UT rather than UTC); if UTC is used, the resulting time difference (0.9 seconds maximum) can introduce an error in longitude as much as plus or minus 0.2'. The example in the text only shows that ASTROCLK will produce essentially the same result as the Nautical Almanac. The Nautical Almanac does not give the "correct" position for the example data nor does it characterize the errors to be expected using its method. By testing ASTROCLK against itself, we can measure the inherent accuracy of the calculations in another way. Setting the time to 05:00UT on 11 November 1989, the local coordinates to the preset location "CAL", and using the Target Tracking Display to make our three "star sights", the following data are obtained: Star Ho Hc Hc' ----------------------------------------------------- 12 Capella 36 22 03.11 36 20 46.88 36 20 46.93 49 Vega 25 44 32.72 25 42 36.22 25 42 36.38 51 Altair 23 23 04.13 23 20 54.20 23 20 54.40 Ho is the Apparent Altitude displayed by ASTROCLK and used as the Altitude input for star sights, Hc is the calculated Altitude displayed by ASTROCLK, and Hc' is the calculated Altitude derived from the Apparent Altitude and displayed with the navigation results. This incidentally shows that the internal refraction calculation is reversible. The results obtained are: Actual Calculated --------------------------------- -120 34 00.00 -120 34 15.96 38 09 00.00 38 09 00.63 The calculated position is 0.27 nm (0.49 km) from the actual position, a very respectable result but somewhat different from the comparison with the Nautical Almanac example. It is probably more representative of the accuracy of the celestial navigation calculations. The determination of position by dead reckoning is dependent only upon the accuracy of the initial position and the course and speed parameters. No attempt has been made to compensate for other factors such as wind and/or current; ASTROCLK assumes that the course and speed data have already been corrected for those factors as required. Determining the current position using ASTROCLK's celestial and dead reckoning navigation functions requires that the procedures given in the text be followed carefully and that accurate position fixes or star sights be used. Users should take note that the celestial navigation portion of ASTROCLK can be very sensitive to input data errors and should therefore use these functions with care. ASTROCLK Astronomical Clock and Celestial Tracking Program Page 130 J2000.0 INTERNAL STAR DATABASE Versions of ASTROCLK prior to 8811 used star data manually entered from SKY CATALOGUE 2000.0 (Sky Publishing, 1982). The current star data was extracted from FA88 Version 2.11.88 (star catalog file STAR1.CAT dated 03-02-87) and was substituted in Version 8811 and following. The visual magnitudes for each star were manually added at Version 8903. This substitution was more a matter of personal preference and judgment than the result of any explicit information regarding the inherent accuracy of one source over the other. Be that as it may, my reasons were: a more recent publication date; FA88 data are used for scientific and navigational purposes and I have therefore assumed higher accuracy for the stars selected by USNO; FA88 data are given to higher precision; and, finally, the data were transferred to ASTROCLK directly. A secondary reason for the use of the FA88 data is that the AFC88 data for J1988.5 presumably uses the same USNO master data base as FA88 and therefore provides a useful basis for the comparison of ASTROCLK's internal precession calculations (see PRECESSION above for representative results). ASTROCLK Astronomical Clock and Celestial Tracking Program Page 131 ASTROCLK MESSAGES AND ERRORS Program ASTROCLK generally tries to detect or work around anticipated error conditions which might interfere with program operation. Most non-critical error conditions or warning messages are displayed in the ASTROCLK error window at the lower left of the screen; these conditions usually do not prevent normal program operation (although the operation causing the error may not be performed). Warning messages are displayed with a BROWN (or YELLOW, depending upon your color monitor) background and the word "CAUTION" appearing in the window title; error messages are displayed with a RED background and the word "ERROR" appearing in the window title. Monochrome monitors, of course, won't display in color! The ASTROCLK error number appears in the lower right of the window border. After you understand the message, press RETURN to resume program execution. Other corrective action may be indicated in the message description below. However, certain error conditions may not be detected or processed within ASTROCLK, and may cause QuickBASIC or DOS error messages to be displayed or may cause the program to fail to operate as expected; typical such messages or conditions (shown in parentheses) are described at the end of this section. When such an error is detected, an error message is displayed giving the QuickBASIC error number and error message (if available, see Page 410 of the QuickBASIC 4.50 Reference Manual for a list of the normal error messages). Press RETURN and ASTROCLK is aborted and the user is returned to DOS. ASTROCLK Numbered Errors and Cautions: -------------------------------------- [01] CAUTION: ASTROCLK is not accurate before -4713! The date has been set prior to the year -4713 using Function Key F3. Many of ASTROCLK's date and time algorithms either fail or are inaccurate prior to -4713. You should use Function Key F3 to set a legal date. If the one of the Julian Date or Epoch formats was used for date input, the date is set to JD 0.000000 rather than the date entered; otherwise, the date is left as entered. Execution is allowed to continue after pressing RETURN. [02] Illegal Longitude! -180 <= Longitude <= 180 [03] Illegal Latitude! -90 <= Latitude <= 90 An illegal value was entered for the Longitude or Latitude when setting new local coordinates with F6. The Longitude must be between -180 degrees (west) and 180 degrees (east); the Latitude must be greater than or equal ASTROCLK Astronomical Clock and Celestial Tracking Program Page 132 to -90 degrees (south) and less than or equal to 90 degrees (north). Re-enter the correct value. [04] Illegal Rt. Ascension! 0 <= RtAscen < 24 [05] Illegal Declination! -90 <= Decln <= 90 An illegal value was entered for the Right Ascension or Declination when setting target coordinates with F5. The Right Ascension must be greater than or equal to zero hours and less than 24 hours; the Declination must be greater than or equal to -90 degrees (south) and less than or equal to 90 (north) degrees. Re-enter the correct value. [06] Illegal Altitude! -90 <= Altitude <= 90 [07] Illegal Azimuth! 0 <= Azimuth <360 An illegal value was entered for the Visual Altitude or Visual Azimuth when setting the visual coordinates with F5. The Visual Altitude must be greater than or equal to -90 degrees and less than or equal to 90 degrees; the Visual Azimuth must be greater than or equal to zero degrees and less than 360 degrees. Re-enter the correct value. [10] Catalog file not found! (Check with ALT-F10) A search of the external star catalog was requested with F5 and the external catalog could not be found. Use ALT-F10 to set the correct file name and/or path. [11] External Catalog Search cancelled by operator! While searching the external star catalog, the operator pressed the ESC key and cancelled the search. The current data are left unchanged. [12] Requested star Name/Number not found. Try again! While searching the external star catalog for a specified star name or star number, the requested item could not be found in the catalog. Verify the name or number and try again. [13] City file not found! (Check with ALT-F10) A search of the external file of city names was ASTROCLK Astronomical Clock and Celestial Tracking Program Page 133 requested with F6 and the file could not be found. Use ALT- F10 to set the correct file name and/or path. [14] Requested city not found in current city file! A search of the external file of city names was requested with F6 and the specified city or abbreviation could not be found in the file. Verify that the correct city file is being used. Check the city name or verify the city file with a text editor to see if the city is included. [22] Check PATH; should include the backslash char (\)! ASTROCLK has detected that the default path or the path just entered does not include the backslash character. The backslash character should normally be the first character of any path so that the path may be properly found. Repeat the path selection process from the start to correct the incorrect path(s). See the section SETTING PROGRAM OPTIONS for additional information. This is a CAUTION message; press RETURN to resume ASTROCLK operation. [23] Check ASTROCLK path; add a drive specification! ASTROCLK detected a drive specification (such as "D:") in the path for the Floppy Almanac but not in the path for ASTROCLK. If the path for the Floppy Almanac includes a drive then the path for ASTROCLK must also include a drive. For example, if the Floppy Almanac path is "D:\FA", then the ASTROCLK path should have the form "C:\ASTROCLK". If the drive is the same for both paths, do not include the drive in either path, e.g. "\FA" and "\ASTROCLK". If you do not intend to use the Floppy Almanac, enter SPACE to clear the Floppy Almanac path. Repeat the path selection process from the start to correct the incorrect path(s). See the section SETTING PROGRAM OPTIONS for additional information. This is a CAUTION message; press RETURN to resume ASTROCLK operation. [24] Illegal DATE requested! Check CALENDAR FLAG You have requested an illegal date which falls either in October, 1582 (Calendar Flag = 1) or September, 1752 (Calendar Flag = 2) and which was one of the dates abolished as part of the adoption of the Gregorian Calendar. Observe the calendar for the month in question using Display Mode 6 to see the days that were deleted. Check the CALENDAR FLAG using ALT-F10. ASTROCLK Astronomical Clock and Celestial Tracking Program Page 134 [25] Illegal DATE requested! Req. year NOT Leap Year! You have requested February 29th for a year which is not a Leap Year for the calendar convention currently in use by ASTROCLK. Verify the requested date and check the CALENDAR FLAG using ALT-F10. [26] Illegal DATE requested! Illegal MONTH and/or DAY! You have requested an illegal MONTH and/or an illegal DAY. The MONTH must be from 1 to 12, and the DAY must be from 0 to the maximum number of days in the MONTH. Day 0 is allowed to conform with astronomical usage. Separate each item with a comma: dd[.d],mm,yyyy. [27] Clocks must be SIMULATED/ OFF with Julian Calendar! You have requested the strict Julian Calendar using ALT-F10 while the clocks are ON. The clocks are set OFF; ASTROCLK cannot operate in real time with the Julian Calendar. You may, however, enable SIMULATION using ALT-F4 to observe time/date changes with the Julian Calendar. [28] CALENDAR FLAG restored to 1 = Gregorian @ 1582! After setting the CALENDAR FLAG for the strict Julian Calendar, you have pressed F4 to restart ASTROCLK's clocks. The clocks will be set ON, but the date and time will be restored to system time and the Calendar Flag set for the Gregorian Calendar as of October, 1582. ASTROCLK cannot operate in real time with the Julian Calendar. However, you may use ALT-F4 for simulated real time with the Julian Calendar. [30] Illegal PLANET name or number requested! You must enter either a valid number (1,2,4-9) or at least the first letter of the planet's name. Mercury and Mars require at least two letters, "ME" and "MA" respectively. The Earth is planet number 3, and planetary data are not calculated. Press RETURN and enter a valid number or name. [31] Requested Minor Planet NUMBER not in file! You have requested a Minor Planet number which is not included in the current Minor Planet Catalog. The range of available minor planets is shown in the upper portion of the ASTROCLK Astronomical Clock and Celestial Tracking Program Page 135 window. [32] : File not found! The Minor Planet Catalog whose path and name is shown on the first line of the error message could not be found. Check that the path and name have been correctly entered using ALT-F10. [33] is not BINARY or is CORRUPT! The Minor Planet Catalog whose path and name is shown on the first line of the error message is not a BINARY catalog OR its contents are corrupt. Check that the path and name have been correctly entered using ALT-F10. [34] Requested Minor Planet NAME not found! The requested minor planet NAME could not be matched in the current Minor Planet Catalog. The name either does not exist in the catalog or you have misspelled it. Names may be entered in upper or lower case and only sufficient letters are required to unambiguously identify the desired minor planet(s). Do not include a trailing space in the name. [35] Data for this Minor Planet is MISSING from Catalog! Although the requested Minor Planet Number is within the range of this catalog, the catalog has no data for this Minor Planet. (A blank record is included.) [40] Old version ASTROCLK.INI! File read and deleted. ASTROCLK has read file ASTROCLK.INI and it was not in the current version's format. The file was read up to the point where an error was detected and then the file was deleted. For most prior versions of ASTROCLK, all of the local coordinate and time zone information will have been read correctly; to be sure, verify this information on the screen and correct any items in error. Upon exit, ASTROCLK will write a new copy of ASTROCLK.INI in the correct format. [41] Can't delete ASTROCLK.INI! Disk write-protected/R.O.? ASTROCLK attempted to delete an old version of the file ASTROCLK.INI and the delete failed. This message will immediately follow error message #22 above. The disk may be write protected or full. ASTROCLK attempts to update the file ASTROCLK.INI each time the program completes and the ASTROCLK Astronomical Clock and Celestial Tracking Program Page 136 program expects that the disk drive will NOT be write protected. The file may be set to "Read Only" which also prevents the delete and update functions. The program will operate properly but local coordinates and other program parameters cannot be saved from one execution to the next. "Error writing ASTROCLK.INI" will also probably occur when you exit ASTROCLK. [50] ICE and FA are disabled! Use ALT-F10 to enable. You have used ALT-F9 to request the ICE or FA and both programs are disabled. Use ALT-F10 to enable one or the other and to set the proper drive and/or path. [51] Cannot run Floppy Almanac: File FA.DFT open error! [52] Cannot run ICE Ephemeris: File ICE.DFT open error! You have used ALT-F9 to request the ICE or FA and ASTROCLK is unable to open the file ICE.DFT/FA.DFT to write the current default parameter information. Check the ICE/FA and ASTROCLK paths using ALT-F10. Alternatively, your disk may be full. Press RETURN to resume ASTROCLK operation. [53] Cannot run Floppy Almanac: 1988 <= Year <= 1999 ASTROCLK's date is set prior to 15 DEC 1987 or after 15 JAN 2000 and you have used ALT-F9 to request the Floppy Almanac. If you have a version of the Floppy Almanac which will execute outside those dates, you must exit ASTROCLK using F9 and run it manually. Alternatively, change to ICE for dates from 1800 through 2049. ASTROCLK resumes normal operation after pressing RETURN. [54] Cannot run ICE Ephemeris: 1800 <= Year <= 2049 ASTROCLK's date is set prior to 1800 or after 2049 and you have used ALT-F9 to request the ICE. ICE actually will only execute for dates from December 21, 1800 through June 7, 2049. ASTROCLK resumes normal operation after pressing RETURN. [60] NAVIGATION mode disabled; Set with F10 [F10 + F2]. The navigation made is currently disabled. Use Function Keys F10 + F10 to set the UT ZONE OFFSET, then use Function Keys F10 + F2 to set the navigation data. ASTROCLK resumes normal operation after pressing RETURN. ASTROCLK Astronomical Clock and Celestial Tracking Program Page 137 [61] Must set UT ZONE OFFSET TIME using F10 + F10! This function cannot be performed until you set the UT ZONE OFFSET using Function Keys F10 + F10. ASTROCLK resumes normal operation after pressing RETURN. [62] Invalid Navigation Data! Must set using F10 + F2. The navigation data is not valid or has been disabled by the use of Function Key F6. Use Function Keys F10 + F2 to re-enable existing data or enter new data. ASTROCLK resumes normal operation after pressing RETURN. [63] Invalid Navigation Data! Requires 2 Star Sights." ASTROCLK requires a minimum of 2 star sights in order to calculate the position. Data for Star #1 is required, and data must be entered for either Star #2 or Star #3 or both. ASTROCLK resumes normal operation after pressing RETURN. [99] QuickBASIC 4.50 ERR = nn An error has been detected by QuickBASIC during execution of ASTROCLK. "nn" is the QuickBASIC Run-Time Error Code, as described in Table D-1, Page 476, of the QB4 Language Reference Manual. is the plain text description of the detected error. After RETURN is pressed, execution of program ASTROCLK is aborted and the user is returned to the DOS prompt. NOTE: All expected errors have been trapped by other error routines, as described above. If you receive this error message, please report the circumstances to Dave Ransom either by mail or to the BBS at (231) 541-7299. Other ASTROCLK, QuickBASIC and DOS Errors: ------------------------------------------ Error writing ASTROCLK.INI This error message occurs as you exit ASTROCLK and may indicate that your disk is full or write protected. The disk drive used for ASTROCLK must NOT be write protected since updated information is written to the disk upon exit. The error may also be related to a change in ASTROCLK version, or the file may have been manually edited and the format changed. ASTROCLK terminates but ASTROCLK.INI may not be updated to reflect current data. To correct the problem, delete file ASTROCLK.INI. The next time you use ASTROCLK, the default coordinates (Rancho Palos Verdes, CA) will appear; use Function Key F6 to re- enter your local coordinates. ASTROCLK Astronomical Clock and Celestial Tracking Program Page 138 (DOS SHELL fails to execute) No error message is displayed but when Function Key F9 is pressed ASTROCLK pauses momentarily and then continues normal execution without displaying the DOS prompt. Either insufficient memory is available to execute COMMAND.COM or COMMAND.COM cannot be located. If present, remove any RAM DISK from your CONFIG.SYS file and do not execute any large Terminate and Stay Resident (TSR) programs when using ASTROCLK. See your DOS documentation for use of the SET command to verify the COMSPEC parameter (which gives the location of COMMAND.COM). (ALT-F3 fails to set software clock) The message "Bad command ..." may be seen briefly at the lower left of the screen. Verify that your version of DOS provides the program RTCLOCK to set the software clock from the hardware clock AND that the program can be found using the current DOS path. If you are using a batch file called RTCLOCK.BAT to set your clock, verify its operation and that it can be found using the current DOS path. See also the section PROGRAM OPERATION for further information. (SHIFT-F3 fails to set alarm time, alarm sounds immediately) The alarm must be set using LOCAL TIME and the selected time may not be more than 23 hours in the future. If the alarm time would have occurred within the past hour, the alarm will immediately sound and the alarm window at the lower right will appear then immediately disappear. (ALT-F9 fails to execute the USNO Floppy Almanac or ICE) Insufficient memory may be available to execute the Floppy Almanac or ICE. See "DOS SHELL fails to execute" above. The version of FA required for the current date may not be present: a different version of FA is required for each calendar year named "FA88.EXE" for 1988, "FA89.EXE" for 1989, and so forth. ASTROCLK Astronomical Clock and Celestial Tracking Program Page 139 A BRIEF EDITORIAL One of the first decisions that has to be made when writing software is the choice of programming language. Of course, for the individual who only wishes to use the end product and doesn't care how it was done, it couldn't make less difference as long as the software gets the job done. Each programming language has its strong points and its weaknesses, and personal preference usually plays a strong role in the choices that are made. For ASTROCLK, my choice is Microsoft's QuickBASIC. I've written software professionally for many years using quite a few different computers and languages and have frequently encountered the attitude that "BASIC isn't real programming, it's just a hobby." The people who feel that way should really check out Microsoft's QuickBASIC, Version 4.50, before they are helped off their soapbox. BASIC has undergone a major evolution in the past several years. While it may not be suited to every job, the times that a BASIC programmer must resort to assembly language or some other higher level language are diminishing at an extremely rapid rate. It has been a real pleasure for me to rediscover BASIC and I use it frequently. Unlike "C", for example, BASIC is a language that I can be away from for an extended time and not have to start all over when I resume using it. For the other side of the coin, however, see also the COMPILER discussion under PRECISION AND ACCURACY TESTS. There is another factor that strongly influenced my decision to use QuickBASIC to implement ASTROCLK. As has been written elsewhere, BASIC in one form or another is the "lingua franca" of micro-computers. If my efforts are to be instructive or useful to the greatest number of interested computer users and would-be programmers, they must be understandable to the majority of those individuals. Writing in C or Fortran may result in "better" code, but I would cut myself off from too many people who are not familiar with those programming languages. BASIC, and Microsoft's QuickBASIC in particular, is relatively easy to understand and the software product is easily obtained, well documented and inexpensive. One of the items on my list of pet peeves is "shareware" or "userware", as it is commonly called. While I don't begrudge an author the opportunity to recoup some of his or her investment in a program, I am not completely convinced that our free bulletin board systems are an appropriate marketplace. But even if they are, some authors go far beyond a simple request for a modest donation if you like and use their software. Threats of legal action annoy me almost as much as "free" programs that are crippled unless and until you send in money; given the quality of some of this software, any amount sometimes seems exorbitant. I'd rather use supported commercial software that performs as advertised right out of the box. I hope the individuals who practice these threats and deceptions quietly starve; in the mean time, they are embarrassing honest folk everywhere. What ever happened to "freeware"? It's now rare indeed to find software that is really free, and even more rare to find the source for that software. And the source can be a terrific ASTROCLK Astronomical Clock and Celestial Tracking Program Page 140 learning tool for the interested programmer and hobbyist alike. Maybe I just remember the days of CP/M too well, when you didn't consider (or trust) public software unless the source was available. You didn't get many unpleasant surprises when someone was willing to sign his name and show you how it was done. I owe a considerable debt to those authors who provided their source in the past. Perhaps the recent outbreak of so-called computer viruses will encourage more users to demand, and authors to include, the source for their programs. I certainly hope so! My thanks to Dave Evers of Quincy, Illinois, for his public domain WINDOW TOOLS, a version of which was adapted for use in ASTROCLK. While it wouldn't have been that difficult to write the simple window routines I needed, it was nice to have some QuickBASIC routines already debugged, documented, and which included the source code. A project like ASTROCLK can continue indefinitely; so far, it's been going on for over two years. Being considered for future versions are Lunar tracking data, times for rising and setting, and various other items large and small that may or may not ever happen. Portions of code to implement new features may appear from time to time in ASTROCLK and are either not used or are commented out. As new or improved features are contemplated, I try to strike a balance between accuracy and reasonable computational times -- a battle I seem destined to lose one way or the other. Already, a math coprocessor is the only way to keep all operations in strict real time when the clocks are running and you wish to view planetary data. Program ASTROCLK is free for non-commercial use. Use it if you like it, discard it if you don't. There are no warranties of any kind. Version 8806 was the first public release of ASTROCLK in February of 1988. While I don't know of any obvious or catastrophic bugs after many versions, updates, and corrections, I will probably never feel sufficiently confident to say there aren't any. Microsoft's QuickBASIC 4.50 IS NOT included and IS required to compile the source files. The compiled version, ASTROCLK.EXE, is a stand-alone program and does not require QuickBASIC support. Comments and suggestions are welcome, and any error or bug reports will be greatly appreciated. Use the mail or call the bulletin board system (BBS) at the number below and leave a message for "SYSOP" or "Dave Ransom". The BBS has an automatic power controller; if it doesn't answer by the third ring, hang up, and then call back in TWO MINUTES. (It's an older computer, and those two minutes are used for boot-up and BBS housekeeping chores.) The BBS will always have the most recent version of ASTROCLK in compressed format; ASTROCLK is located in the ASTRONOMY area, File Area #5. Updated versions are posted at irregular intervals, typically every four to eight weeks. Use program PAK, Version 2.10 or higher (also available on the BBS), to decompress the files. (213) 541-7299 [24 hours, 2400/1200 baud] ASTROCLK Astronomical Clock and Celestial Tracking Program Page 141 The BBS version of ASTROCLK is available in three compressed files (currently approaching a total of about 500K), and download times are considerable. Individuals without access to a modem or who wish to avoid toll charges for these large files may obtain a complete set of ASTROCLK disks with the current version (MS-DOS DS/DD, specify 5-1/4" 360K or 3-1/2" 720K) by sending US $20.00 to cover disks, postage and handling. David H. Ransom, Jr. 7130 Avenida Altisima Rancho Palos Verdes, CA 90274 ASTROCLK Astronomical Clock and Celestial Tracking Program Page 142 BIBLIOGRAPHY The following principal sources have been consulted during the preparation and/or testing of Program ASTROCLK and this text. ------, THE ASTRONOMICAL ALMANAC 1984. U. S. Government Printing Office, Washington, DC, 1983. ------, THE ASTRONOMICAL ALMANAC 1988. U. S. Government Printing Office, Washington, DC, 1987. ------, THE ASTRONOMICAL ALMANAC 1989. U. S. Government Printing Office, Washington, DC, 1988. ------, THE ASTRONOMICAL ALMANAC 1990. U. S. Government Printing Office, Washington, DC, 1989. ------, THE NAUTICAL ALMANAC 1989. U. S. Government Printing Office, Washington, DC, 1987. ------, NBS TIME & FREQUENCY DISSEMINATION SERVICES, NBS Special Publication 432. U. S. Government Printing Office, Washington, DC, 1979. Acker, Agnes and Jaschek, Carlos, ASTRONOMICAL METHODS AND CALCULATIONS. John Wiley & Sons, New York, NY, 1986. [First published in French in 1981.] Bretagnon, Pierre and Simon, Jean-Louis, PLANETARY TABLES AND PROGRAMS FROM -4000 TO +2800. Willmann-Bell, Inc., Richmond, VA, 1986. Burgess, Eric, CELESTIAL BASIC. Sybex Inc., Berkeley, CA, 1982 Carroll, Tim S., THE FLOPPY ALMANAC USER'S GUIDE, 2nd Edition. Nautical Almanac Office, United States Naval Observatory, Washington, DC, 1988. Danby, J. M. A., FUNDAMENTALS OF CELESTIAL MECHANICS, 2nd Edition. Willmann-Bell, Inc., Richmond, VA, 1988. Doggett, LeRoy E. et al, ALMANAC FOR COMPUTERS 1988. Nautical Almanac Office, United States Naval Observatory, Washington, DC, 1988. Duffett-Smith, Peter, ASTRONOMY WITH YOUR PERSONAL COMPUTER. Cambridge University Press, New York, NY, Reprinted (with corrections) 1986. [NOTE: The disk available from Cambridge University Press, containing the programs from this text, does NOT include the 1986 corrections (as of mid-1988). In particular, subroutine PELEMENT, Page 141, contains errors in the DATA statements for Mercury and Mars, lines 3725 and 3800; see text for ASTROCLK Astronomical Clock and Celestial Tracking Program Page 143 corrections.] Duffett-Smith, Peter, PRACTICAL ASTRONOMY WITH YOUR CALCULATOR, 2nd Edition. Cambridge University Press, New York, NY, 1981. Espenshade, Edward B., Jr., Editor, GOODE'S WORLD ATLAS, 17th Edition. Rand McNally & Co., Chicago, IL, 1987. Hirshfeld, Alan and Sinnot, Roger W., Editors, SKY CATALOGUE 2000.0. Sky Publishing Corp., Cambridge, MA, 1982. Hobbs, Richard R., MARINE NAVIGATION 2, 2nd Edition. Naval Institude Press, Anapolis, MD, 1987. Lawrence, J. L., BASIC ASTRONOMY WITH A PC. Willmann-Bell, Inc., Richmond, VA, 1989. [NOTE: A diskette is also available with the BASIC programs for IBM-compatible PC's.] Meeus, Jean, ASTRONOMICAL FORMULAE FOR CALCULATORS, 4th Edition. Willmann-Bell, Inc., Richmond, VA, 1988. [NOTE: The 4th Edition is identical to the 3rd Edition with the exception of an added Chapter 43 giving formulae for the position of Pluto.] Menzel, Donald H. and Pasachoff, Jay M., A FIELD GUIDE TO THE STARS AND PLANETS, 2nd Edition. Houghton Mifflin Co., Boston, MA, 1983. Sinnott, Roger W., monthly column "Astronomical Computing", Sky & Telescope Magazine, various issues 1984 through 1989. Taff, Laurence G., CELESTIAL MECHANICS. John Wiley & Sons, New York, NY, 1985.