HamCall (April 1991)

home *** CD-ROM | disk | FTP | other *** search

/ HamCall (April 1991) / HAMCALL CD-ROM (Buckmaster)(April 1991).BIN / amateur / traksat / traksat.doc < prev next >

Wrap

Text File | 1990-10-14 | 205KB | 2,544 lines

╔═════════════════════════════════╗ ║ ║ ║ ▀▀█▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ ║ ║ █ █▀█ █▀█ █ █▀█ █▀█ ▀█▀▀▀ ║ ║ █ █ █ █ █ █ █ █ ║ ║ █ █ █▀█ █▀█ ▀▀█ █▀█ █ ║ ║ █ █ █▄█ █ █ █▄█ █▄█ █ ║ ║ █ ║ ║ █ ║ ║ Version 1.5 ║ ╚═══╦═════════════════════════╦═══╝ ║ ║ ║ Paul E. Traufler ║ ║ 111 Emerald Dr. ║ ║ Harvest, Al 35749 ║ ║ (205) 726-5511 ║ ║ ║ ╚═════════════════════════╝ Satellite Tracking Program 22 January, 1990 ******************************************************************** * * * TRAKSAT is free for NON-COMMERCIAL use only. * * * ******************************************************************** * * * If you find TRAKSAT useful and would like to use it in a * * commercial operation please call or write for more information. * * * ********************** ********************* * * * Paul E. Traufler * * 111 Emerald Dr. * * Harvest, Al. 35749 * * 205-726-5511 (work) * * 205-830-8450 (home) * * * *************************** TRAKSAT makes no warranty of any kind, either express or implied, including but not limited to implied warranties of merchantability and fitness for a particular purpose, with respect to this software and accompanying documentation. Paul E. Traufler, author of TRAKSAT, SHALL NOT BE LIABLE FOR ANY DAMAGES (INCLUDING DAMAGES FOR LOSS OF BUSINESS PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION) ARISING OUT OF THE USE OF OR INABILITY TO USE TRAKSAT. TRAKSAT Satellite Tracking Program Page 2 TABLE OF CONTENTS ----------------------------------------------------------- INTRODUCTION ........................................... 4 THEORY OF SATELLITE MOTION ............................. 5 HARDWARE REQUIRED TO RUN THE PROGRAM ................... 6 RUNNING THE PROGRAM .................................... 7 READ SATELLITE DATA (MAIN MENU OPTION ONE) ............. 8 TRACKING STATIONS (MAIN MENU OPTION TWO) ............... 10 REAL-TIME MODE (MAIN MENU OPTION THREE) ................ 12 DELTA-TIME MODE (MAIN MENU OPTION FOUR) ................ 13 GRAPHICS (MAIN MENU OPTION FIVE) ....................... 16 TABULAR OUTPUT (MAIN MENU OPTION SIX) .................. 19 VISIBILITY (MAIN MENU OPTION SEVEN) .................... 22 QUITTING THE PROGRAM (MAIN MENU OPTION EIGHT) .......... 23 NORAD/NASA 2-LINE SATELLITE DATA ....................... 24 WHAT ARE THE MEAN CLASSICAL ELEMENTS ................... 26 MODELS FOR PROPAGATION OF NORAD ELEMENT SETS ........... 32 THE PROPAGATION MODELS ................................. 32 COMPATIBILITY WITH NORAD ELEMENT SETS .................. 33 PROGRAM LIMITATIONS AND ASSUMPTIONS .................... 34 A BRIEF EDITORIAL ...................................... 34 SPECIAL THANKS ......................................... 35 QUESTIONS AND COMMENTS ................................. 36 OBTAINING NORAD SATELLITE DATA SETS .................... 38 FILES REQUIRED FOR TRAKSAT ............................. 39 BIBLIOGRAPHY ........................................... 40 Trademarks used in this document ----------------------------------------------------------------- IBM is a registered trade mark of International Business Machines Corporation. Microsoft MS, MS-DOS, QuickC, are registered trademarks of Microsoft Corporation. TRAKSAT Satellite Tracking Program Page 3 INTRODUCTION Ever since college I have been interested in satellites and tracking methods. I have often looked up into the night sky and thought, "I know satellites are up there but can I predict when and where to look to see one". I have several small programs to calculate different satellite related quantities but there was not one program available to do all the things I felt a satellite tracking program should do. After several years of working in the aerospace field, I decided that I could take on such a programing task. I started it all with a program called STS, it was geared towards tracking the space shuttle, but used the same basic orbital calculations. STS, version .95, is available on several BBS around the country, see the references at the end of this document. For a first attempt at such a satellite tracking program I was some-what pleased with the results. But I felt there is room for improvement and that is where TRAKSAT steps in. TRAKSAT is a general purpose satellite tracking program, by that I mean any satellite that has a NORAD, NASA 2-Line element set can be used. There are some limitations in the program along with some assumptions, the reader is directed to the section on limits and assumptions for further study. The solution to the satellite motion which is used by TRAKSAT is completely analytic and therefore requires no numerical integration. This makes the program fast, even faster when a coprocessor is used, since the solutions can be evaluated at arbitrarily large, or small, time intervals. The purpose of this program is to provide the user with a means of propagating NORAD element sets in time to obtain tracking information of the space object. TRAKSAT Satellite Tracking Program Page 4 THEORY OF SATELLITE MOTION A complete development of the theory required to predict the position of an artificial satellite about the earth is not presented here because this is not proper place for it. Such a development would require a volume in itself and would be more of a distraction than an aid to the potential user. Only enough of the concepts required for a general understanding plus the final results are given. References to detailed works from which these results are derived are provided for the more than casually interested reader. At the end of the TRAKSAT operating instructions is a brief overview of the fundamentals used in this program and is included to help the reader understand the motion of an artificial satellite about the earth. TRAKSAT Satellite Tracking Program Page 5 HARDWARE REQUIRED TO RUN THE PROGRAM In order to run the program the user will need the following hardware; IBM or compatible PC,XT,AT,PS/2,386, Floppy or Hard Disk, Text mode display (25x80), and CGA, EGA, VGA graphics (used for plotting only), Math coprocessor is NOT required for TRAKSAT, (if a coprocessor is present it will be used *). * It should be noted that a coprocessor will be 3 to 4 times faster than the emulator version. If the user plans on using the real-time tracking mode, a coprocessor will "smooth out" the time steps to such a small delta as to appear instantaneously. At any rate the real-time mode runs as fast as the host computer can calculate the data and update the screen. ****************** * IMPORTANT NOTE * ****************** If the user will be running TRAKSAT on a 360K floppy drive, no graphics will be available. The TRAKSAT program takes up about 298K and the earth data file is approximately 120K, far more than the total amount a 360K floppy can hold. The non-graphics modes can still be used, however the write to disk file mode will not have very much room for data. The best solution to the problem would be run TRAKSAT from a hard disk! The prices of hard disks have come down to a point where practically all computers have them. If the user needs a "good reason" to buy a hard disk, perhaps TRAKSAT can convince them to do so. ****************** * IMPORTANT NOTE * ****************** To print out the document, TRAKSAT.DOC use the DOS copy command. The syntax to use would be "COPY TRAKSAT.DOC PRN", without the quoatation marks. TRAKSAT Satellite Tracking Program Page 6 RUNNING THE PROGRAM To start TRAKSAT you type "TRAKSAT", without the quotation marks, at the DOS prompt. After the opening screen has been displayed the TRAKSAT main menu will appear. The main menu is the core of the program, i.e. from this menu the user can setup satellite data, tracking station data, and output selections. Here is an main menu example; ╔═══════════════════════════════════════════════════════════════╗ ║ ║ ║ Date: 12/25/1989 Time: 18:32:22 ║ ║ ║ ╠═══════════════════════════════════════════════════════════════╣ ║ ╔═════════════════════════╗ ║ ║ ║ TRAKSAT ║ ║ ║ ╠═════════════════════════╣ ║ ║ ║ MAIN MENU ║ ║ ║ ╠═════════════════════════╣ ║ ║ ║ (1) Read Elements ║ ║ ║ ║ (2) Tracking Stations ║ ║ ║ ║ (3) Real Time Tracking ║ ║ ║ ║ (4) Delta Time Mode ║ ║ ║ ║ (5) Ground Tracks ║ ║ ║ ║ (6) Output Data ║ ║ ║ ║ (7) LOS Visibility ║ ║ ║ ║ (8) QUIT ║ ║ ║ ║ Enter Option (1 - 8) ║ ║ ║ ╚═════════════════════════╝ ║ ║ ║ ║ ║ ╚═══════════════════════════════════════════════════════════════╝ the date and time will be the current system values. The date format used is mm/dd/yyyy, while the time format is hh:mm:ss, based on a 24 hour clock, i.e. 14:00:00 is the same as 2 PM. From this menu the input data and output data can be directed. If the user enters other than the listed options numbers an error message will appear at the bottom left of the screen. If the file TRAKSAT.DEF is present the default tracking station from that file will be displayed to remind the user of the default tracking station. To change the default tracking station data see section; Tracking stations. ****************** * IMPORTANT NOTE * ****************** All error messages are displayed for 3 SECONDS, then depending on what the error was, program control will return to the user to correct the problem. It is recommended that the user NOT press any keys while the error message is being displayed, any key presses may cause other error messages to appear. TRAKSAT Satellite Tracking Program Page 7 READ SATELLITE DATA (MAIN MENU OPTION ONE) The main menu option 1 will call the read satellite data menu. This program uses the NASA, or NORAD 2-line satellite element data file format to read data into the program, (in this text the use of NORAD refers to NASA 2-Line or NORAD satellite element data sets). For a full explanation of the NASA 2-line satellite element data sets see section; NASA 2-Line Satellite Data. The read satellite data screen will appear; ╔═════════════════════════════════════════════════════════════════════╗ ║ ╔═══════════════════════════════════════════════════════╗ ║ ║ ║ ║ ║ ║ ║ READ NASA 2-LINE SATELLITE FILE ║ ║ ║ ╠═══════════════════════════════════════════════════════╣ ║ ║ ║ ║ ║ ║ ║ Enter Satellite Filename: [NASA629.TXT ] ║ ║ ║ ║ Enter Search String: [ ] ║ ║ ║ ╟───────────────────────────────────────────────────────╢ ║ ║ ║ ║ ║ ║ ╟───────────────────────────────────────────────────────╢ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ╚═══════════════════════════════════════════════════════╝ ║ ╚═════════════════════════════════════════════════════════════════════╝ the cursor will be placed at the satellite filename position. The program will display the current satellite filename, if this choice is acceptable for the user just press RETURN. If a different satellite data file is desired the user will type in the satellite data filename. The next line requires the name of the satellite to track, a maximum length of 12 characters is allowed. The program will check if the file is present and display an error message if the data file is NOT found. To help the new user a NORAD satellite date file is included with TRAKSAT, see section; Satellite Data Sets. The search method used by the program will locate the first occurrence of what was typed in for a search string when compared to the satellite names, i.e. typing in "mi" could locate the satellite named "Mir". The search is NOT upper/lower case sensitive. If a match is found the full name is displayed and the user is asked to accept this data or read for the next occurrence. If the user does not know ANY satellite names they can enter a carriage return, return or enter, and ALL of the satellite names will be displayed one at a time. TRAKSAT Satellite Tracking Program Page 8 ****************** * IMPORTANT NOTE * ****************** TRAKSAT is limited to the first 200 satellites in any data file. If the user has more than 200 satellites in a data file they will need to remove, using a text editor, satellite data sets as to include the desired data set in the 200 limit. This may not prove to be a limitation for most users as most satellite data set have less than 150 data sets. If no match is found a error message is displayed and the user will try another match. If the file is found and the satellite name has been located the screen will appear like; ╔═════════════════════════════════════════════════════════════════════╗ ║ ╔═══════════════════════════════════════════════════════╗ ║ ║ ║ ║ ║ ║ ║ READ NASA 2-LINE SATELLITE FILE ║ ║ ║ ╠═══════════════════════════════════════════════════════╣ ║ ║ ║ ║ ║ ║ ║ Enter Satellite Filename: [NASA629.TXT ] ║ ║ ║ ║ Enter Search String: [Mir ] ║ ║ ║ ╟───────────────────────────────────────────────────────╢ ║ ║ ║ Found MIR ║ ║ ║ ╟───────────────────────────────────────────────────────╢ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ Satellite Name [MIR ] ║ ║ ║ ║ ║ ║ ║ ║ Keep Reading Satellite File (y/n) [Y] ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ╚═══════════════════════════════════════════════════════╝ ║ ╚═════════════════════════════════════════════════════════════════════╝ the next step would be for the user to type a "N" to stop reading the satellite data file and return to the main menu. The routine that reads the NASA 2-line satellite data does a check- sum on the data to insure that the data is correct. If the check- sum fails the user is notified with only a warning message, the data may NOT be correct. The user can still use this data but the results it produces may not be accurate. For a full explanation of NASA 2-line satellite element sets see section; NASA 2-Line Satellite Elements. TRAKSAT Satellite Tracking Program Page 9 TRACKING STATIONS (MAIN MENU OPTION TWO) The next option, number 2, will only need to be run once, unless a different tracking station is used, by the user. The program defaults to using Huntsville, Al. as the tracking station, if the user does not want to use the default option they can select a city from the city data file. The cite data file has over 700 of the larger U.S. cities latitude and longitudes in it. The tracking station search works very much like the satellite name search. The user is asked for a search string and the first occurrence is displayed, then the next one and so on, until no more matches are found. If the user accepts a match some additional data is asked for by the program. The altitude above mean sea level in meters, hours from Greenwich, daylight savings flag (1 = daylight savings, 0 = standard time) , and timezone name, are required for the tracking station. If the altitude of the tracking station are not known the user can enter zero with out to much loss in accuracy. If the user can not find a match to the city data then they will need to use a text editor to add the city data in the file TRAKSAT.CTY. Below is an example for Huntsville, Al.. ╔═══════════════════════════════════════════════════════════════╗ ║ ╔═══════════════════════════════════════════════════════╗ ║ ║ ║ READ TRACKING SITE DATA FILE ║ ║ ║ ╠═══════════════════════════════════════════════════════╣ ║ ║ ║ ║ ║ ║ ║ Enter Search String: [Hun ] ║ ║ ║ ║ ║ ║ ║ ╟───────────────────────────────────────────────────────╢ ║ ║ ║ Found: Hun ║ ║ ║ ╟───────────────────────────────────────────────────────╢ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ Tracking Station Name [HUNTSVILLE, AL ] ║ ║ ║ ║ Keep Reading Tracking Data File (y/n) [n] ║ ║ ║ ║ HUNTSVILLE, AL ║ ║ ║ ║ Enter Altitude Above Sea Level (M) [228.6 ] ║ ║ ║ ║ Enter Hours From UT, i.e. CST = -6 [-6] ║ ║ ║ ║ Enter Daylight Savings, i.e. 1 = Daylight [0] ║ ║ ║ ║ Enter 3 Character Timezone Name, i.e. CST [CST] ║ ║ ║ ╚═══════════════════════════════════════════════════════╝ ║ ╚═══════════════════════════════════════════════════════════════╝ the program pauses for a few seconds to allow the user to review the data for any errors. TRAKSAT Satellite Tracking Program Page 10 ****************** * IMPORTANT NOTE * ****************** If the tracking station changes from the default values the file TRAKSAT.DEF will hold the last saved tracking station data. While running the program if a new tracking station is selected the user will be asked if the old tracking station data should be overwritten or not. If the user saves the current data then the next time TRAKSAT is run that new data will be the default else the old TRAKSAT.DEF will be used. A text editor can be used to change the TRAKSAT.DEF data also, the user will be on his or her own using this method, it is not recommended. After the tracking station has been chosen the main menu will appear waiting for the next user choice. TRAKSAT Satellite Tracking Program Page 11 REAL-TIME MODE (MAIN MENU OPTION THREE) If the user would like to track in real-time, press 3, the program defaults to this mode at start-up. The screen will not change if this mode has been selected. The real-time mode will update the screen as fast as the hardware will allow. For an XT class machine with no coprocessor, the update time may be 1 to 2 seconds. An AT class computer with a coprocessor can whip along at about 0.5 seconds per update. The powerful and fast 386 coprocessor equipped machine can sing along at 0.2 seconds per update. The average user will not require this great of detail but it is included for the advanced user. ****************** * IMPORTANT NOTE * ****************** The time is read from the system clock, and as such is only as accurate as the setting of this clock. The software date and time can be set before running TRAKSAT to insure the correct time. Refer to your DOS manuals to use the time and date functions. A brief note about tracking satellites. The accuracy of the data is the most important part of the prediction process. NORAD does track some 8000+ objects in orbit around the earth, and maintains a data base of the objects. The earth modeling and perturbations are the most important factors in satellite tracking. This program uses the NORAD element sets mainly because they are available and have reasonably good accuracy. If the user would like to "see" a satellite in the night sky the precision of 1 or 2 seconds is not important, several minutes may not even be that important. This is not to say that the average person can not locate the satellite, it is going to pass over some site sooner or later, its the time of the passing that is of importance. It could be said that if you tell me where to look for the satellite and tell me about when I should be looking for it the chances are it will be spotted. The sky is a big place and it would be almost impossible to locate a satellite without any help from programs such as TRAKSAT. TRAKSAT Satellite Tracking Program Page 12 DELTA-TIME MODE (MAIN MENU OPTION FOUR) If the user would like to track a satellite from say todays date to some future date, the delta time mode is the choice to use. The basic idea is track from some starting date to some stopping date. At any rate the user will be confronted with the delta time mode screen; ╔══════════════════════════════════════════════════════════╗ ║ ║ ║ ║ ║ ╔═══════════════════════════════════════════════╗ ║ ║ ║ DELTA TIME MODE ║ ║ ║ ╟───────────────────────────────────────────────╢ ║ ║ ║ STARTING DATE AND TIME (UT) ║ ║ ║ ║ ║ ║ ║ ║ YEAR [ ] ║ ║ ║ ║ MONTH [ ] ║ ║ ║ ║ DAY [ ] ║ ║ ║ ║ HOUR [ ] ║ ║ ║ ║ MINUTE [ ] ║ ║ ║ ║ SECOND [ ] ║ ║ ║ ║ TIME STEP (MIN) [ ] ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ╚═══════════════════════════════════════════════╝ ║ ║ ║ ║ ║ ╚══════════════════════════════════════════════════════════╝ the user will need to "fill in the blanks". The year expects the full year, i.e. 1990 not 90. TRAKSAT Satellite Tracking Program Page 13 An example is included for the user to "get the idea" on entering the starting date information. This example starts on 26 december, 1989 at 0 hours UTC, and uses a 1 minute time step. The user can enter smaller or larger time steps depending on the requirements of the user. ╔══════════════════════════════════════════════════════════╗ ║ ║ ║ ╔═══════════════════════════════════════════════╗ ║ ║ ║ DELTA TIME MODE ║ ║ ║ ╟───────────────────────────────────────────────╢ ║ ║ ║ STARTING DATE AND TIME (UT) ║ ║ ║ ║ ║ ║ ║ ║ YEAR [1989] ║ ║ ║ ║ MONTH [12] ║ ║ ║ ║ DAY [26] ║ ║ ║ ║ HOUR [0 ] ║ ║ ║ ║ MINUTE [0 ] ║ ║ ║ ║ SECOND [0 ] ║ ║ ║ ║ TIME STEP (MIN) [1.0 ] ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ╚═══════════════════════════════════════════════╝ ║ ║ ║ ╚══════════════════════════════════════════════════════════╝ TRAKSAT Satellite Tracking Program Page 14 An approach most people use is to pick a 2-3 minute time step and check the output for any passes near the tracking station for that day. Then return back to the delta time mode and use a smaller time step to obtain a better estimate of the satellite visibility. The next step for the user is the lenght of time for the propagation. The format is hours,minutes,and seconds. Below is an example for 12 hours, 30 minutes, 0 seconds; ╔══════════════════════════════════════════════════════════╗ ║ ║ ║ ╔═══════════════════════════════════════════════╗ ║ ║ ║ DELTA TIME MODE ║ ║ ║ ╟───────────────────────────────────────────────╢ ║ ║ ║ LENGTH OF PROPGATION ║ ║ ║ ║ ║ ║ ║ ║ HOUR [12] ║ ║ ║ ║ MINUTE [30] ║ ║ ║ ║ SECOND [0 ] ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ╚═══════════════════════════════════════════════╝ ║ ║ ║ ╚══════════════════════════════════════════════════════════╝ after the length of propagation is entered the program will return to the main menu. TRAKSAT Satellite Tracking Program Page 15 GRAPHICS (MAIN MENU OPTION FIVE) Option number five, from the main menu, controls the graphics plotting. If the user selects it the program will test for a graphics adapter and based on the type of graphics hardware will select the "highest" graphics mode supported. An example would be; VGA mode 640x480 pixels, EGA mode 640x350 pixels, CGA mode 640x200 pixels, HGC mode 720x348 pixels. ****************** * IMPORTANT NOTE * ****************** The Hercules graphics mode requires running the driver MSHERC.COM, this is the driver supplied with several Microsoft programing languages, before using the TRAKSAT program. Type "MSHERC" and then "TRAKSAT" to start the program. I can not test this mode as I do not have any Hercules graphics cards. I'm currently looking for someone with a Hercules card to do a full test on TRAKSAT, anyone want to offer a helping hand? If the hardware does NOT support graphics an error message will be displayed and the program will return to the main menu. After the graphics mode is entered the program proceeds to draw a Mercator projection map of the world. The upper left corner is at latitude 90 degrees and longitude -180 degrees, while the lower right corner is latitude -90 degrees and longitude 180 degrees. The grid spacing is 30 degrees from both the latitude and the longitiude. A "+" will be plotted for the tracking station coordinates, the coordinates from TRAKSAT.DEF or the currently loaded data. The plotting process may take a minute or two on a slow XT type computer, something under 10 seconds on the particular computer I use. The file EARTH.DAT contains the world map data, some 8200 points in all. This file is compressed to save space and reduce the reading time. If the EARTH.DAT file is not found an error message will be displayed and the program will return to the main menu again. After the world map is displayed the simulation begins. The starting position for the satellite is marked as a yellow circle, this was added to help locate the starting position. The screen will plot the orbital ground trace of the chosen satellite along with other valuable data. The top line will have the UTC date and time, while the second line will have the local date and time displayed. The lower lines will have the tracking data displayed. TRAKSAT Satellite Tracking Program Page 16 An example of the output screen would be; -----------------------▌ TRAKSAT Version 1.5 ▐-------------------- | | | UTC 21:37:26.1 Date 12/26/1989 Satellite Name: MIR | | Local 15:37:26.1 Date 12/26/1989 Tracking Station: HUNTSVILLE,AL | | | | | | (no world map drawn in this example) | | | | Lat 45.1635° Azimuth 309.1281° Range 7115.4 Km | | Long -175.3926° Elevation -30.1331° Rev # 22120 NOT Visible | | | ----------------------------------------------------------------------- The Lat and Long are the satellite latitude and longitude. The Azimuth and Elevation are as seen from the tracking station, while the Range is the distance from the satellite to the tracking station. The azimuth is always between 0 and 360 degrees with north being 0, east 90 south 180 and so on. The elevation will be always be between -90 and +90 degrees. If the elevation is < 0 the satellite is below the horizon as seen from the tracking station. The Rev # is based on the input data starting revolution number plus the number of revs per day times the days past the epoch date, i.e. the formula; rev = rev_epoch + (mean motion(rev/day) * (epoch date - date). The epoch refers to the NORAD satellite data set, see section; NORAD/NASA 2-Line Satellite Data, for a full explanation of the input data. The last item displayed is based on if the satellite is visible from the tracking station. See main menu option seven for a complete description of the methods used by TRAKSAT to test for visibility. ****************** * IMPORTANT NOTE * ****************** To stop the display the user can press any key and the screen will "freeze". The user will need to press any key again to continue the simulation. If the user presses ESC, escape key, the simulation will stop the the user will be returned to the main menu. TRAKSAT Satellite Tracking Program Page 17 ****************** * IMPORTANT NOTE * ****************** The ground track will continue until the user stops the simulation by pressing return twice. After 8-9 ground tracks have been plotted the screen will be "very busy", the user can re-draw the screen by pressing ESC, than pressing main menu option five again. The world map will be drawn again along with the new orbitial ground tracks. This will cut down on the screen "clutter". TRAKSAT Satellite Tracking Program Page 18 TABULAR OUTPUT (MAIN MENU OPTION SIX) TRAKSAT can also produce a tabular output of the satellite tracking data, the output is in a text mode not graphics. If the user picks main menu option six, the program will display another menu asking if the output is to go to a file or the screen. I chose NOT to include the option for a printer mainly because of all the different printers and the problems that go along with different hardware. However, the file option output can be edited and printed out by the user if so desired. At any rate, the screen will look like; ╔══════════════════════════════════════════════════════╗ ║ ║ ║ ╔═════════════════════════════════════╗ ║ ║ ║ OUTPUT DATA TO SCREEN/FILE ║ ║ ║ ╟─────────────────────────────────────╢ ║ ║ ║ ║ ║ ║ ║ S = Output to Screen ║ ║ ║ ║ F = Output to File ║ ║ ║ ║ ║ ║ ║ ║ Choice (S,F) [ ] ║ ║ ║ ║ ║ ║ ║ ║ A = All Passes ║ ║ ║ ║ V = Visible Passes ║ ║ ║ ║ ║ ║ ║ ╚═════════════════════════════════════╝ ║ ║ ║ ╚══════════════════════════════════════════════════════╝ the user has to enter S or F. If the user presses any other keys than the S or F the program will default to using the screen for the output. If the user presses the S key the program will display a header with some of the tracking station data and the units of the data. Below is an example of the screen output; Tracking Station: HUNTSVILLE, AL Satellite: Mir DATE TIME (UTC) AZIM ELEV RANGE LAT ELONG Rev V HR:MN:SEC DEG DEG KM DEG DEG Mon 22Jan90 01:41:51.06 25.72258 0.1630 2276.5282 51.771845 287.0473 22529 1 Mon 22Jan90 01:41:51.17 25.73887 0.1589 2276.9845 51.772019 287.0583 22529 1 Mon 22Jan90 01:41:51.22 25.74631 0.1570 2277.193 51.772099 287.0633 22529 1 this example was run using the real-time mode and the default tracking station, Huntsville, Al.. In this case the ELONG is the satellites EAST longitude, i.e. that is ELONG is between 0 and 360 degrees, and is measured east from the Greenwich meridan. An example of the east longitude could be Cape Canaveral Air Force Station, which has a ELONG of 279.45 degrees, this equals a WEST longitude of -80.55 degrees. The other output quanities are the same as in main menu option five. TRAKSAT Satellite Tracking Program Page 19 The user will notice that the header is stationary just the data is scrolling. This option is useful for a quick view of tracking data, since no graphics are used. If the user was in delta-time mode the step between outputs would be the delta time step value set in main menu option four. ****************** * IMPORTANT NOTE * ****************** To stop the display the user can press any key and the screen will "freeze". The user will need to press any key again to continue the simulation. Pressing ESC will return the user to the main menu. The other option, F, will place the tracking data output into a file. The file name will consist of the first 8 characters of the satellite name with the extension ".PRT" added to the end. The name of the output file will be displayed for the user. An example could be the satellite Mir, the filename for output would be "Mir.PRT". ****************** * IMPORTANT NOTE * ****************** The program will produce the file xxxxxxx.PRT, the x being the current satellite name, if one is not found, but will OVERWRITE an old one if found. The user will have the responsibility to re- name the file after completing a run if they would like to save the output. The output in the file is very similar to the screen output option. Below is an example of the file output mode; TRAKSAT Version 1.5 Tracking Station: HUNTSVILLE, AL [ Line Of Sight (LOS) Visiblity ] Satellite: Mir DATE TIME (UTC) AZIM ELEV RANGE LAT ELONG Rev V HR:MN:SEC DEG DEG KM DEG DEG Mon 22Jan90 01:45:33.40 48.60 -8.41 3411.85 49.88 308.80 22529 0 Mon 22Jan90 01:45:33.56 48.61 -8.42 3412.76 49.87 308.82 22529 0 Mon 22Jan90 01:45:33.67 48.62 -8.42 3413.39 49.87 308.83 22529 0 again this example used the real-time mode. This output is a standard 80 columns, for printers or the 25x80 text screen. In this case the ELONG is the satellites EAST longitude, i.e. that is ELONG is between 0 and 360 degrees, and is measured east TRAKSAT Satellite Tracking Program Page 20 from the Greenwich meridan. The other output quanities are the same as in main menu option five. If the file mode and the real-time mode are chosen the screen will display the number of records that have been written to file. The program DOES check the remaining disk space and stops the program if the record space exceeds available disk space. The data prior to exceeding the disk space is written and an error message is displayed, no data will be lost. It is recommended that the real-time mode NOT be used for file output, mainly because of the large files that could be produced. If the file mode and delta-time mode are chosen the screen will display the same record count as above, but also the total number of records to calculate. This method produces the smallest file size the user requires. The total number of records to calculate would be; total_records = (stop_time - start_time)/delta_time. The size of the file is approximately 82 bytes per record, therefore 1440 records, one day at 1 minute interval, will produce a file size of about 118K. ****************** * IMPORTANT NOTE * ****************** To stop the display the user can press any key and the screen will "freeze". The user will need to press any key again to continue the simulation. Pressing ESC will return the user to the main menu. The option has been added to TRAKSAT version 1.5 to display only the visible passes, based on the setting of the flag for main menu option 7, or ALL passes. The program will default to ALL if a return is pressed. TRAKSAT Satellite Tracking Program Page 21 VISIBILITY (MAIN MENU OPTION SEVEN) There are two different methods used by TRAKSAT to determine visibility. The first method is simply when the elevation is greater than 0 degrees the satellite will be visible to the tracking station. This method is called line of sight (LOS) in the program. It should be noted that at most tracking sites 0 degrees elevation is not visible due to ground based obstructions, i.e. trees buildings, and other such objects. A rule of thumb is if you hold out your arm straight and stick out your thumb horizontal to the ground so it appears to touch the horizon the upper edge of your thumb is about 10 degrees elevation. The second method, optical visibility, requires the satellite to be above zero degrees elevation also, however the satellite must be sun-lite while the tracking station is in darkness. This method would be used for viewing satellites with the aid of say binoculars. If the lighting conditions are favorable a "bright" satellite can be seen with the naked eye also. The best time for these favorable lighting conditions usually occur at sun rise and sun set, as seen at the tracking site. The type of visibility is set from the main menu, the default is to use the LOS method. If the user would like to change the visibility method, select main menu option number seven. The main menu will always print the type of visibility test that will be performed by the program. This menu option is a toggle function, i.e. selecting option 7 changes from one method to the other. ****************** * IMPORTANT NOTE * ****************** With either method the visual magnitude is NOT calculated. Such a calculation would require knowledge about the emissivity of the satellite, and atmospheric conditions, neither of which is readily available to the user. TRAKSAT Satellite Tracking Program Page 22 QUITTING THE PROGRAM (MAIN MENU OPTION EIGHT) This option will stop the TRAKSAT program and return the user to DOS. If the tracking station data was changed during the program execution, the user will be asked if the new data should replace the old default data. That choice is up to the user to decide. The old data will be displayed along the the current data to help the user with the choice. TRAKSAT Satellite Tracking Program Page 23 NORAD/NASA 2-LINE SATELLITE DATA NORAD maintains general perturbation element sets on all resident space objects. These element sets are periodically refined so as to maintain a reasonable prediction capability on all space objects. In turn, these element sets are provided to users. The input file of current orbital elements can be obtained form several BBS around the country. One such BBS is the Celestial BBS at (513) 427-0674 in Fairborn, Ohio the SYSOP is TS Kelso. See section; Obtaining Satellite Data, for more information on obtaining satellite data. I have included a file of the latest elements, as of 16 January, 1990, for over 120 orbiting satellites. See section; Files Required To Run TRAKSAT. ****************** * IMPORTANT NOTE * ****************** The following was downloaded from Celestial BBS. Effective January 1986, this system began posting the most recent element sets received from NASA/Goddard Space Flight Center for several categories of satellites: Amateur Radio, Earth Resources, Manned Spacecraft, Navigation, Weather, and NASA's 30 Day Specials (which contain objects launched within the last 30 days and are often easy to spot visually). More specifically, these include the following satellites or satellite series: OSCAR, Radio Sputnik, UOSAT, Cosmos, LandSat, SeaSat 1, SPOT, Mir, Salyut 7, Soyuz, LDEF, US Space Shuttle, NAVSTAR (GPS), GOES, Meteor, and NOAA. These elements will be maintained in ASCII format in the file. Data for each satellite will consist of three lines in the following format: AAAAAAAAAAA 1 NNNNNU NNNNNAAA NNNNN.NNNNNNNN +.NNNNNNNN +NNNNN-N +NNNNN-N N NNNNN 2 NNNNN NNN.NNNN NNN.NNNN NNNNNNN NNN.NNNN NNN.NNNN NN.NNNNNNNNNNNNNN Line 1 is a eleven-character name. Lines 2 and 3 are the standard Two-Line Orbital Element Set Format identical to that used by NASA and NORAD. The format description is: Line 2 Column Description 01-01 Line Number of Element Data 03-07 Satellite Number 10-11 International Designator (Last two digits of launch year) 12-14 International Designator (Launch number of the year) 15-17 International Designator (Piece of launch) 19-20 Epoch Year (Last two digits of year) TRAKSAT Satellite Tracking Program Page 24 21-32 Epoch (Julian Day and fractional portion of the day) 34-43 First Time Derivative of the Mean Motion (rev/day^2) or Ballistic Coefficient (Depending of ephemeris type) 45-52 Second Time Derivative of Mean Motion (Blank if N/A) 54-61 BSTAR drag term if GP4 general perturbation theory was used. Otherwise, radiation pressure coefficient. 63-63 Ephemeris type 65-68 Element number 69-69 Check Sum (Modulo 10) (Letters, blanks, periods = 0; minus sign = 1; plus sign = 2) Line 3 Column Description 01-01 Line Number of Element Data 03-07 Satellite Number 09-16 Inclination [Degrees] 18-25 Right Ascension of the Ascending Node [Degrees] 27-33 Eccentricity (decimal point assumed) 35-42 Argument of Perigee [Degrees] 44-51 Mean Anomaly [Degrees] 53-63 Mean Motion [Revs per day] 64-68 Revolution number at epoch [Revs] 69-69 Check Sum (Modulo 10) All other columns are blank or fixed. Example: NOAA 6 1 11416U 86 50.28438588 0.00000140 67960-4 0 5293 2 11416 98.5105 69.3305 0012788 63.2828 296.9658 14.24899292346978 For a description of the mean orbital elements see section; What Are The Mean Classical Elements. Note that the International Designator fields are usually blank, as issued in the NASA Prediction Bulletins. All epochs are UTC. Satellites will be ordered by their NASA Catalog Number. The data file will be updated as soon as possible after receipt of new element sets or whenever element sets are received for the Space Shuttle. TRAKSAT Satellite Tracking Program Page 25 The following pages contain a brief overview of the methods used in TRAKSAT and are included to help the reader understand the mechanics of a orbiting satellite about the earth. WHAT ARE THE MEAN CLASSICAL ELEMENTS Five independent quantities called "orbital elements" are sufficient to completely describe the size, shape and orientation of an orbit. A sixth element is required to pinpoint the position of the satellite along the orbit at a particular time. The classical set of six orbital elements are defined as: 1. a, semi-major axis, a constant defining the size of the conic orbit. 2. e, eccentricity, a constant defining the shape of the conic orbit. 3. i, inclination, the angle between the Z axis, i.e. like the North Pole, and the angular momentum vector, h = R X V, i.e. the vector R crossed with the vector V. 4. Ω, longitude of the ascending node, the angle, in the fundamental plane, between the direction of the vernal equinox and the point where the satellite crosses the fundamental plane in a northerly direction, (ascending node). This angle is measured counterclockwise when viewed from the north side of the fundamental plane. 5. w, argument of periapsis, the angle, in the plane of the satellite's orbit, between the ascending node and the periapsis point, measured in the direction of the satellite's motion. 6. T, time of periapsis passage, the time when the satellite was at periapsis. 6a. Sometimes the time of periapsis passage is replaced by the true anomaly, v, the angle, in the plane of the satellite's orbit, between perigee and the position of the satellite at the particular time, t0, called the epoch. * (To convert from T to v) v = (360 deg) * t0 / T TRAKSAT Satellite Tracking Program Page 26 The sharp reader will notice that the NORAD elements do NOT include the semi-major axis, a. It is possible to calculate the semi-major axis with the data in a NORAD elements set. The approach would be; 1. Convert the mean motion into degrees per second. and calculate the time to complete one orbit, this will be called the period. 2. Using the period and the earth's gravitational constant, mu, the semi-major axis can be calculated. (equations used) xn_s = (mean motion * 360)/86400 per = 360/xn_s a = ((per^2 * mu)/(4*π^2))^(1/3) mu = 3.986012d+14 km^3/sec^2. The starting point for the study of motion of one body orbiting another, such as an artificial satellite about the earth, is always the two-body problem; i.e., two point masses attracted to each other according to Newton's Law of Universal Gravitation, the inverse square law. The solution is well-known; the two bodies move about each other in conic sections. For bounded motions, such as those of an earth satellite, this conic is either a circle or an ellipse. The problem can be formulated in different ways, but is always convenient to chose a coordinate system with the origin centered at one of the bodies. The position of the second body then can be specified, for example, by giving its initial cartesian position and velocity coordinates and then integrating the equations of motion to find the future positions and velocities. The cartesian system is not the most convenient one in which to represent the motion because an analytic solution cannot be obtained and the integrations must be done numerically. By adopting a polar coordinate system, one is able to effect an analytic solution referred to above which can be specified in terms of six constants of motion; five orbital elements, a,e,i,w,Ω and the time of pericenter passage T. The last constant can be, and usually is, replaced by the mean anomaly M which is a linear function of time. This is a very convenient way to specify the initial position and velocity of a satellite and it also allows an easy visualization of the motion. The position and velocity of the satellite at any future time can be specified in terms of these six constants, a,e,i,w,Ω,M and time. In realistic applications, such as artificial satellites about the earth, there are forces acting on the satellite in addition to the inverse square force although this is the dominate one. Other gravitational forces are due to distant bodies such as the moon and sun but the principal additional gravitational forces are due to the non-sphericity of the earth. All of the gravitational forces are conservative and can be represented by a potential function. In addition to these extra gravitational TRAKSAT Satellite Tracking Program Page 27 forces, there are non-conservative forces such as atmospheric drag. All of these forces other than the inverse square force are called perturbations. The prediction of motion considering these additional forces is called Perturbation Theory. The orbital elements, constant for pure two-body motion, become slowly varying functions of time when the perturbations are considered. Differential equations describing the time rates of change of the elements are called the Lagrange Planetary Equations, LPE and can be found in any standard book on celestial mechanics. Considering conservative forces only, which can be represented by a potential function, the part of the potential other than the two-body part is conventionally called the disturbing function, represented by R, and the LPE are: . a = 2 / n a * ( δR / δM ) . e = (-(1-e²)^½ / na²e)*δR/δw+(1-e²/na²e)*δR/δM . i = cot i/(na²(1-e²)^½ * δR/δw - δR/(δΩna²(1-e²)½) . w = (1-e²)^½ * δR / na²eδe - cot i * δR/(na²(1-e²)^½)*δi) . Ω = δR/(na² sin i *(1-e²)^½) * δi) M = n - 2δR/naδa - 1-e² * δR/(na²e * δe). * where δ is the partial derivative starting from the very simple representation of the gravitational potential between two point masses of magnitude m0 and mi separated by distance r as; V = -G * (m0 * mi)/r one can, by applying this to a satellite of mass m0 and to every infinitesimal mass point mi of the earth and integrating over the whole earth, arrive at the following potential function for the earth; ∞ n ∞ n m V=-µ/r(1-Σ JnPn (sinδ)(re/r)^ +Σ Σ Jnm (re/r)^ Pn^ (sinδ)cos(m(α-α))). n=2 n=2m=1 mn The first term is the one giving pure two-body motion and the additional terms are the perturbing terms. The first sum, zonal harmonics, represents the flattening and other distortions relative to the equator and the second sum, tesseral harmonics, represents the non-uniformity of the earth in longitude. If, as is frequently done, one assumes that the earth possesses rotational symmetry, then the second sum vanishes. The neglect of the second sum usually produces no noticeable effects except in the case of geosynchronous satellites. Then one must consider those terms which cause slow long-period drifts of the geosynchronous position. TRAKSAT Satellite Tracking Program Page 28 For close earth satellites one can usually take about three terms from the first sum and get very accurate results; even the first term alone will produce very satisfactory results in most cases for short-time periods. The Jn are constants which depend on the mass distribution in the earth and are deduced from analysis of observed satellite motions. The currently accepted values of J2, J3, and J4, which are used in TRAKSAT, are; -3 J2 = 1.082616 X 10 -6 J3 = -2.53881 X 10 -6 J4 = -1.65597 X 10 . The Pn (sin δ) are Legendre polynomials of index n and are even functions of sin δ for n even and odd functions for n odd. The J2 term describes the flattening of the earth and the J3 term the so-called pear shape. J2, which is three orders of magnitude larger than J3, gives rise to secular changes in the elements w, Ω, and M while J3 gives rise to long_period oscillations in e and w. In general, even harmonics cause long-period and secular changes in the elements, and odd harmonics cause long-period oscillations. Short-period oscillations can result from all terms; but since J2 is so much larger than the other coefficients, generally only the J2 short-period terms are considered. Secular terms are those which monotonically increase or decrease with time. For first order solutions this change with time is linear. Long-period terms are those which oscillate with a period of typically one to two months, and short-period terms are those which oscillate with a period of one orbital period or some rational fraction of it. To finish formulating the problem, the disturbing function is expressed in terms of the orbital elements and then the appropriate partial derivatives are taken and substituted into the LPE. One then has a coupled set of first order non-linear ordinary differential equations. Because they are non-linear, they can be solved only by various approximation methods. The usual method is to assume that the solutions can be represented in some type of power series expansion in a small parameter and arrive at sets of approximation equations which can be a close representation of the real motion, at least over short-time periods. TRAKSAT Satellite Tracking Program Page 29 The complete solution consists of the sum of the secular terms, short-period terms, and the long-period terms; i.e. a = a + a + a . osc s sp lp TRAKSAT Satellite Tracking Program Page 30 ****************** * IMPORTANT NOTE * ****************** I have not included the actual equations used in the program in this document for obvious reasons, i.e. they are long and hard to type in with a word processor. If you have an interest in these equations they are in several references I have listed. TRAKSAT Satellite Tracking Program Page 31 MODELS FOR PROPAGATION OF NORAD ELEMENT SETS NORAD maintains general perturbation element sets on all resident space objects. These element sets are periodically refined so as to maintain a reasonable prediction capability on all space objects. In turn, these element sets are provided to users. The most important point to be noted is that not just any prediction model will suffice. The NORAD element sets are "mean" values obtained by removing periodic variations in a particular way. In order to obtain good predictions, these periodic variations must be reconstructed (by the prediction model) in exactly the same way they were removed by NORAD. Hence, putting NORAD element sets into a different model (even though the model may be more accurate or even a numerical integrator) will result in degraded predictions. All space objects are classified by NORAD as near-Earth (period less than 225 minutes) or deep-space (period greater than or equal 225 minutes). Depending on the period, the NORAD element sets are automatically generated with the near-Earth or deep- space model. The program will calculate the satellite period and know which prediction model to use. THE PROPAGATION MODELS Two mathematical models for prediction are used by TRAKSAT. The first of these, SGP4, was developed by Ken Cranford in 1970 (see Lane and Hoots 1979) and is used for near-Earth satellites. This model was obtained by simplification of the more extensive analytical theory of Lane and Cranford (1969) which uses the solution of Brouwer (1959) for its gravitational model and a power density function for its atmospheric model (see Lane, et al 1962). The next model, SDP4, is an extension of SGP4 to be used for deep-space satellites. The deep-space equations were developed by Hujsak (1979) and model the gravitational effects of the moon and sun as well as certain sectoral and tesseral Earth harmonics which are of particular importance for half-day and one-day period orbits. TRAKSAT Satellite Tracking Program Page 32 COMPATIBILITY WITH NORAD ELEMENT SETS The NORAD element sets are currently generated with either SGP4 or SDP4 depending on whether the satellite is near-Earth or deep- space. For SGP4 and SDP4 users, the mean motion is first recovered from its altered form and the drag effect is obtained from the SGP4 drag term (B*) with the pseudo-drag term being ignored. The value of the mean motion can be used to determine whether the satellite is near-Earth or deep-space (and hence whether SGP4 or SDP4 was used to generate the element set). From this information the program will decide whether to use SGP4 or SDP4 for propagation and hence be assured of agreement with NORAD predictions. TRAKSAT Satellite Tracking Program Page 33 PROGRAM LIMITATIONS AND ASSUMPTIONS The ephemeris equations DO include the zonal harmonics, through 2nd order, of the gravitational potential. This implies a gravitational field produced by an oblate spheroidal earth unsymmetrical with respect to the equator, pear-shaped. In other words, the ephemeris equations contain J2, J3, and J4 terms. The currently accepted values of J2, J3, and J4, which are used in TRAKSAT, are; -3 J2 = 1.082616 X 10 -6 J3 = -2.53881 X 10 -6 J4 = -1.65597 X 10 . The earth equatorial radius used by TRAKSAT is; 6378.135 Km, while the flattening factor used is 1/298.257. The program TRAKSAT models only elliptical orbital motion about the earth. That is, the orbital eccentricity must be less than one and greater than zero. Very small eccentricities are acceptable, i.e. such as 1.0E - 5. A BRIEF EDITORIAL One of the first decisions to be made when setting out to write a program is the choice of a programming language. I'm an Aerospace Engineer working for a company in Huntsville, Al. My job title is; Trajectory Analysis Engineer. I work with NASA, mostly the shuttle program, and design trajectories for several upcoming shuttle missions. I have written large trajectory simulations programs, for the most part they were written in FORTRAN. I know FORTRAN is not the best language to use for programs that use graphics, but Microsoft has come up with the ideal solution. Microsoft FORTRAN, version 4.0 and higher, can call BASIC, C, and PASCAL routines. Microsoft FORTRAN version 5.0 also contains graphic routines that were used in TRAKSAT, these graphic routines are the same as used in QuickC version 2.0. Most of the TRAKSAT program is written in FORTRAN to get the best speed and high precision mathematics and C, QuickC version 1.01, for some useful utilities. I have found this combination to be very powerful and useful for writing programs. TRAKSAT Satellite Tracking Program Page 34 SPECIAL THANKS I would like to take this opportunity to thank the many people who helped me either directly or indirectly on this program. First of all my wife, Anita, who understands why I have a hobbie like computers and enjoy working with them. She has not complained about the many hours, in excess of 300 hours, I have spent working on TRAKSAT. Dave Ransom Jr., of Rancho Palos Verdes, CA. has kept me going when my interest in the program was slipping away. I did use the city data from his excellent program ASTROCLOCK. I would highly recommend his program to any person interested in astrodynamics. The documentation supplied with ASTROCLOCK is in itself very interesting reading and very well done. I could only hope that someday TRAKSAT will have that level of professionalism. I would also like to thank TS Kelso, SYSOP of the Celestial BBS where current satellite data can be downloaded. Several satellite tracking programs are also available on his BBS along with a vast amount of satellite information. John Williams and Dr. Jeff Wallach, from the Dallas DataLink BBS, have been very helpful in this project also. They have offered data and a helping hand with TRAKSAT. The DataLink BBS has a vast amount of satellite information along with other interests. I would recommend it to others interested in satellite tracking. TRAKSAT Satellite Tracking Program Page 35 QUESTIONS AND COMMENTS I would very much like to hear from anyone interested in this program and astrodynamics in general. I have not included the source code to TRAKSAT MAINLY because most people do not have a Microsoft FORTRAN compiler nor a working knowledge of FORTRAN. As for the choice of FORTRAN compiliers there are many fine products out and I have used many of them. Lahey, RM make several FORTRAN compiliers that have many features and work very well. However, the only compilier that supports mixed language is Microsoft. For this reason alone I would recommend it to others interested in programming. At this time I feel that TRAKSAT is still going through some "growing pains" and I would like the chance to improve it and add new features. The only way this can happen is if you, the user, takes the time to leave me messages or mail on problems or suggestions. I will try to answer your messages in a timely manor. For the most part I have already received several good ideas and helpful hints for improving TRAKSAT. I would suggest the user to obtain a coprocessor if they do not have one already. A coprocessor speeds up math intensive programs, such as TRAKSAT, to a level that was only dreamed about a few years ago. Please feel free to contact me to discuss TRAKSAT or other computer problems. I can reached through the RPV BBS; RPV BBS Rancho Palos Verdes, Ca. 213-541-7299 24 hours, 2400/1200 baud. This BBS is owned and operated by Dave Ransom Jr.. I call up the BBS once or twice a week to check my mail and do some file transfers. This BBS is geared towards Astronomical interests. The latest version of ASTROCLOCK can be downloaded from this BBS also. Other BBS's I frequent are; Celestial RCP/M DataLink RBBS System Fairborn, Ohio Dallas, Texas 513-427-0674 214-394-7438 24 hours, 2400/1200 baud, 24 hours, 2400/1200 baud. I can also be reached at work or home, please no calls after 10 PM Central Standard Time. Please leave a phone number and the best time to call on any messages that require by personal attention. TRAKSAT Satellite Tracking Program Page 36 The last, and slowest method to reach me is with the U.S. mail secvice, I will respond with a phone call if at all possible. Paul E. Traufler 111 Emerald Dr. Harvest, Al. 35749 Phone (work) 205-726-5511 Phone (home) 205-830-8450 To obtain the latest version of TRAKSAT, several BBS around the country keep in online. If you would like to save on the long distance charges, contact myself and I will try to find a local BBS that I can upload TRAKSAT to. For a small fee I will mail TRAKSAT on a disk, 360K, 1.2M, if that is the easiest way to obtain the latest version. If you send a self addressed AND stamped disk-mailing package, with the proper disk format, I will return mail it. Please contact the author for more information. TRAKSAT Satellite Tracking Program Page 37 OBTAINING NORAD SATELLITE DATA SETS The following BBS's have the current satellite data files; Celestial RCP/M Fairborn, Ohio SYSOP: TS Kelso 513-427-0674 24 hours, 2400/1200 baud, 8 bit NO parity 1 stop. Datalink RBBS System Dallas, Texas SYSOP: Dr. Jeff Wallach 214-394-7438 24 hours, 2400/1200 baud, 8 bit NO parity 1 stop. TRAKSAT Satellite Tracking Program Page 38 FILES REQUIRED TO RUN TRAKSAT The following files should have been included in the archive file; TRAKSAT.EXE The program. TRAKSAT.DEF The default data for the tracking station. TRAKSAT.CTY The city file for tracking stations. TRAKSAT.DOC TRAKSAT program documentation. EARTH.DAT World map data file. NASA629.TXT This is the latest NORAD satellite data set, (as of 16 Jan, 1990, element set #629) READ.ME Latest notes about the program, (This file may NOT be present). MSHERC.COM This utility is used for Hercules graphics. TRAKSAT Satellite Tracking Program Page 39 BIBLIOGRAPHY THe following sources were used to prepare and test the TRAKSAT program. Meeus, Jean, ASTRONOMICAL FORMULAE FOR CALCULATORS, 3rd Edition, Willmann-Bell, Inc., Richmond, VA. 1985. Duffett-Smith, Peter, PRACTICAL ASTRONOMY WITH YOUR PERSONAL COMPUTER, Cambridge University Press, New York, NY. 1986. Danby, John, FUNDAMENTALS OF CELESTIAL MECHANICS, 2nd Edition, Willmann-Bell, Inc., Richmond, VA. 1988. Bate-Mueller-White, FUNDAMENTALS OF ASTRODYNAMICS, Dover Publications, Inc. New York, NY. 1971. Forsythe-Malcolm-Moler, COMPUTER METHODS FOR MATHEMATICAL COMPUTATIONS, Prentice-Hall, Inc. Englewood Cliffs, NJ. 1977. USAF-Ford Aerospace Corporation, ORBITAL MECHANICS, O&M Training Section, Sunnyvale, CA. 1982. Moulton, F. R., CELESTIAL MECHANICS, Macmillan Company, New York, NY. 1960. Brand, L., VECTOR ANALYSIS, John Wiley and Sons, New York, NY. 1957. Geyling-Westerman, INTRODUCTION TO ORBITAL MECHANICS, Addison Wesley, Whippany, NJ. 1971. Brouwer, D., "Solution of the Problem of Artificial Satellite Theory without Drag", Astronomical Journal 64, 378-397, November 1959. Hilton, C.G. and Kuhlman, J.R., "Mathematical Models for the Space Defense Center", Philco-Ford Publication No. U-3871, 17-28, November 1966. Hoots, F.R., "A Short, Efficient Analytical Satellite Theory". AIAA Paper No. 80-1659, August 1980. Hoots, F.R., "Theory of the Motion of an Artificial Earth Satellite", accepted for publication in Celestial Mechanics. Hujsak, R.S., "A Restricted Four Body Solution for Resonating Satellites with an Oblate Earth", AIAA Paper No. 79-136, June 1979. Hujsak, R.S. and Hoots, F.R., "Deep Space Perturbations Ephemeris Generation", Aerospace Defense Command Space Computational Center Program Documentation, DCD 8, Section 3, 82-104, September 1977. TRAKSAT Satellite Tracking Program Page 40 Kozai, Y., "The Motion of a Close Earth Satellite", Astronomical Journal 64, 367-377, November 1959. Lane, M.H. and Cranford, K.H., "An Improved Analytical Drag Theory for the Artificial Satellite Problem", AIAA Paper No. 69- 925, August 1969. Lane, M.H., Fitzpatrick, P.M., and Murphy, J.J., "On the Representation of Air Density in Satellite Deceleration Equations by Power Functions with Integral Exponents", Project Space Track Technical Report No. APGC-TDR-62-15, March 1962, Air Force Systems Command, Eglin AFB, FL. Lane, M.H. and Hoots, F.R., "General Perturbations Theories Derived from the 1965 Lane Drag Theory", Project Space Track Report No. 2, December 1979, Aerospace Defense Command, Peterson AFB, CO.