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AMATEUR RADIO BY GARRY CRATT, VK2YBX Using 2-line Keplerian elements to track amateur satel­lites Several low-cost computer programs are now available to accurately keep track of satellites. This article explains the origin of this data & shows how easy it is to put it to use. Considering the increasing interest in satellite reception by amateurs, it is not surprising that the demand for 2-line orbital elements to predict the location of a satellite at any particular time is also increasing. In addition, the prolifera­ tion of personal computers makes the calculation and display of satellite data in real time a relatively simple matter. Fortunately, Keplerian data is freely available to ama­ teurs, primarily through computer bulletin boards. However, in order to properly understand Keplerian elements, some history is in order. Orbital mechanics, as applied to artificial earth satellites, is based largely on celestial mechanics, initially founded on the work of James Kepler and Issac Newton and expanded on by mathematicians during the 18th and 19th centuries. Eventu­ally, the theory became so accurate that when astronomers ob­served discrepancies between their observations and the theoreti­cal results, they were able to determine that the errors were caused by variations in their astronomical timescales. In 1956, astronomers changed the time scale from one based on the rotation of the Earth (universal time) to a new scale based on the orbital motion of the Earth around the Sun (ephemeras time). With the advent of atomic timekeeping, astronomical timescales Fig.1: this “screen-grab” shows the menu page for the STSORBIT PLUS satellite tracking program. were eliminated completely and the ability to predict orbital locations became supremely accurate. Computer programs One of the spin-off products of the US space effort was the creation of the computer program known as “STSORBIT PLUS”, de­signed and used by NASA to track satellites, including the Space Shuttle. There is now a public domain version of this program available on many computer bulletin board services. In addition, AMSAT offer their own program, “INSTANT TRACK”. By “plugging in” the latest data sets or Keplerian ele­ments, it is possible to very accurately predict the location of a satellite at any particular time. This is very useful for tracking amateur satellites in polar orbits and satellites used for rebroadcasting television programs that are not located in geostationary orbit. In theory, the centrifugal force resulting from the speed of a satellite is balanced against the gravitational pull of the Earth and this keeps a satellite orbit constant. In practice, however, gravitational forces from the Sun and the Moon, plus atmospheric drag (applicable to satellites at an altitude of 1000km or less), have the effect of degrading the orbit. For this reason, it is important to use current elements. Moreover, some satellites are deliberately launched into low Earth or polar orbits, in order to provide coverage over all major land masses. These satellites might orbit the Earth once every 90 minutes or so, so a computer “prediction” for future passes is of paramount importance to amateur operators. Table 1 shows the primary orbital August 1994  63 Table 1: Keplerian Elements Data for each satellite consists of 3 lines in the following format: Name 1 NNNNNU NNNNNAAA NNNNN.NNNNNNNN + .NNNNNNNN +NNNNN-N N NNNNN 2 NNNNN NNN.NNNN NNN.NNNN NNNNNNN NNN.NNNN NNN.NNNN NN.NNNNNNNNNNNNNN COLUMN DESCRIPTION LINE 1 1 Line number of element data 2 Blank 3-7 Satellite number 8 Not used 9 Blank 10-11 International designator (last 2 digits of launch year) 12-14 International designator (launch number of the year) 15-17 International designator (piece of launch) 18 Blank 19-20 Epoch year (last 2 digits of year) 21-32 Epoch day (Julian day & fractional portion of the day) 33 Blank 34-43 1st time derivative of mean motion (0.1 revs per day) 44 Blank 45-52 2nd time derivative of mean motion (0.01 x revs per day) 53 Blank 54-61 Radiation pressure co-efficient 62 Blank 63 Ephemeras type (specified ephemeras theory used) 64 Blank 65-68 Element number 69 Checksum LINE 2 1 Line number of element data (ie 2 for line 2) 2 Blank 3-7 Satellite number 8 Blank 9-16 Inclination in degrees 17 Blank 18-25 Right ascensions of the ascending node in degrees 26 Blank 27-33 Eccentricity in tenths of units 34 Blank 35-42 Argument of perigee in degrees 43 Blank 44-51 Mean anomaly in degrees 52 Blank 53-63 Mean motion in revolutions per day 54-68 Revolution number at epoch 69 Checksum 64  Silicon Chip parameters used in satel­lite data elements, while Table 2 shows actual 2-line data elements for a few popular satellites. In order to make use of these Keplerian element sets, which can be downloaded from their international source on a weekly basis, it is first advisable to obtain a copy of a suitable tracking program such as “ TRAKSAT ”, “ INSTANT TRACK ”, “STSORBIT PLUS” or “PC-TRACK”. As elements are distributed, they are allo­cated a incremental number such as TLE428 (the last three numbers signify the set). Of course, downloading Keplerian elements from computer bulletin boards does require some level of computer literacy; ie the ability to create directories, download data, etc. Running STSORBIT PLUS STSORBIT PLUS has the ability to track multiple satellites in real time. Fig.1 shows the menu page for STSORBIT PLUS. At initial installation, create a directory called “STS”. After installation, the program will issue a prompt for local UTC time offset (eg, Sydney has +10 hours difference). After complet­ing this, the main menu of STSORBIT PLUS will present a variety of options. The first and most important step is to set the Earth sta­tion location. F10 from the main menu gives a sub-menu where F2 allows the user to set new local co-ordinates. The user can then insert a capital city location, which gives the program a base for position calculations. To do this, the program searches its internal database of over 1500 locations for a match. F6 selects the map type used to view the world and satel­lite orbits. Toggling the F6 key allows selection of either World, Ortho, Quad or Zoom. For slow PCs, the World map is the best selection as the program draws a very impressive and complex map of the world, complete with city names and rivers. After this initial setup, current Keplerian elements must be down­ loaded from an accurate source. These should be downloaded into the same directory as STSORBIT PLUS. To import the 2-line elements in order to track a satellite, select F2 from the main menu, then enter the 2-line element filename and the satellite name. The program will then display relevant data on the selected satellite. By now simply keying ENTER, the program will draw a map of the world and display the orbital position of the selected satellite in real time; eg, the track taken by polar orbiting satellites can easily be seen. By selecting F3 from the main menu, a “pass prediction” will be displayed for the selected location. Where to buy software Other features of this and similar programs are beyond the scope of this article. For those interested in obtaining regis­tered copies of the software mentioned in this article, the following will be of interest: • TRAKSAT is available from the author: Paul E. Traufler, 111 Emerald Drive, Harvest, AL 35749, USA. A non-registered version costs $US10, while a laser-printed operations man­ ual will cost an additional $US15. A registered version costs $US25 (add $US5.00 for shipping and handling to Australia). Commercial licenses are also available from $US50. • PC TRACK version 3.0 can be obtained from: Thomas C. John­son, 9920 S Palmer Road, New Carlisle, Ohio 45344, USA. It costs $US45 + US15 for shipping and handling. • STSORBIT PLUS is available from the Satcom BBS (phone 02 905 0849) or from the author: David H. Ransom Jr, 7130 Avenida Altisima, Rancho Palos Verde, CA 90274, USA (check costs with author before ordering). An additional map database is also available from the author for $US10. SC Allow 3-6 weeks for delivery. Table 2: Sample 2-Line Elements Optus B1 1 22087U 92054A 94191.61718487 -.00000112 00000-0 10000-3 0 4146 2 22087 0.0916 108.4637 0002995 329.9719 232.0275 1.00270935 18457 Intelsat 5 F-8 1 14786U 84023A 94190.52379876 .00000053 00000-0 00000+0 0 6425 2 14786 2.7646 69.4432 0046903 321.8887 264.9499 1.00275209 1695 Oscar 10 1 14129U 83058B 94176.41110075 -.00000306 00000-0 10000-3 0 2893 2 14129 27.0856 321.0039 6024383 189.2195 150.8337 2.05882336 54986 UoSat 2 1 14781U 84021B 94190.56754595 .00000133 00000-0 30431-4 0 7063 2 14781 97.7855 204.2441 0011153 193.8486 166.2415 14.69228336553597 Noaa 10 1 16969U 86073A 94193.01550214 .00000098 00000-0 60319-4 0 7694 2 16969 98.5052 201.2581 0012183 257.8226 102.1588 14.24897002406033 RS-10/11 1 18129U 87054A 94191.83829016 .00000023 00000-0 90572-5 0 9258 2 18129 82.9253 311.3579 0011286 326.8723 33.1722 13.72339043353150 Satellite b p y v Apogee a F2 ra ea F1 Perigee x rp Fig.2: this diagram shows the major orbital parameters of a satellite: a = semimajor axis; b = semiminor axis; ra = apogee radius; rp = perigee radius; F1 = focal point 1; F2 = focal point 2. Fig.3: STSORBIT PLUS can display data in several map formats, including World map as shown at left & Ortho map as shown at right. Note that the displays are in colour & are not shown to best advantage here. August 1994  65