This post is for the benefit of SeeSat-L readers who might wish to estimate pre-launch elements of satellites, or at least understand how it can be done. I describe a method which takes advantage of the fact that new satellite launches often are the latest in s series of similar launches. Knowledge of the circumstances and initial elements of the past launches in the series provides the basis to accurately estimate the initial elements of new launches. I break the process into 10 easy steps, using today's scheduled NOAA 17 launch as an example. How easy? All of the computations to produce the estimates elements can be performed using the arithmetic functions of a pocket calculator. Familiarity with orbital elements in general, and the 2-line elements in particular, is helpful, but not an absolute requirement. For the former, I suggest the SeeSat-L faq: http://satobs.org/faq/Chapter-05.txt For the latter, I suggest this article by Dr. T.S. Kelso: http://celestrak.com/columns/v04n03/ 1. Select a suitable proxy satellite. For many years, the standard NOAA orbit has been sun-synchronous, with an initial mean-motion of about 14.1 rev/d. NOAA 16, the latest in the NOAA series, is a typical example, as shown in these recent elements: 1 26536U 00055A 02173.90461296 .00000445 00000-0 26839-3 0 8759 2 26536 98.8696 119.4446 0009698 266.0641 93.9439 14.11707074 90194 When selecting a proxy elset, make certain that the object's launch site was the same as that of the new launch. All NOAA satellites have been launched from the Vandenberg AFB, so we can safely use the same elements. Beware of changes in launch vehicle. Recent NOAAs have been launched on Titan 2 rockets; older ones were launched on Atlas rockets. For best results, try to use a proxy that was launched using the same vehicle as the new launch. 2. Obtain the proxy satellite's initial orbital elements. We assume that NOAA 17's initial orbit will have the same relationship to the circumstances of its launch as NOAA 16 did relative to its launch. Therefore, we need to obtain an elset of NOAA 16 soon after its launch. Jonathan McDowell's archive is a convenient source of such data: http://www.planet4589.org/space/elements/26500/S26536 I selected the third elset in the list, mainly because its mean motion was in close agreement with subsequent elsets: 1 26536U 00055A 00265.76707352 -.00020078 00000-0 -11203-1 0 13 2 26536 98.7886 210.5136 0009705 275.1802 115.0094 14.10880075 42 3. Obtain the date and time of the proxy satellite's launch: Jonathan McDowell provides a convenient record of all launches, including the time of launch: http://www.planet4589.org/space/log/launch.html NOAA 16 was launched on 2000 Sep 21 at 10:22 UTC 4. Compute epoch of the proxy satellite's launch. The 2-line elements express the epoch in days since the start of the year, as yyddd.dddddddd, where yy is the year of launch, and the ddd.dddddddd is the number of days since the start of the year. Sep 21 was day 265 of year 2000 (make sure to take into account leap year). Expressing 10:22 UTC as the fraction of a day yields: (10 h * 60 min/h + 22 min) / 1440 min/d = 0.43194444 d So the epoch of launch was 00265.43194444 5. Compute the difference between the epoch of the proxy elset and the launch time. 00265.76707352 - 00265.43194444 = 0.33512908 d 6. Compute the epoch of new satellite's launch. The launch is scheduled for 2002 Jun 24 at 18:22 UTC. Using the procedure described in Step 4, I obtain the launch epoch, 02175.765277778 7. Compute the epoch of the estimated elset of the upcoming launch. Simply add the results of Steps 5 and 6: 02175.765277778 + 0.33512908 = 02176.10040685 8. Compute the RAAN of the estimated elset of the upcoming launch. The RAAN (right ascension of the ascending node) states the location of the orbital plane at the epoch. It is an angle expressed in degrees. To obtain the RAAN of the orbit of the new launch, we must adjust the RAAN of the proxy elset for the Earth's rotation that has occurred in the interim. The formula is: New elset RAAN = [ Proxy elset RAAN + (New elset epoch - Proxy elset epoch) * Earth Rotation Rate ] mod 360 Substituting the previously obtained data, yields: = [ 210.5136 + ( 02176.10040685 - 00265.76707352) * 360.985647362 deg/d ) ] mod 360 Note that the difference between the two epochs must be in days. If the above two epochs were in the same year, then we could simply subtract them, but since they span more than one year (years 2000 to 2002), we must modify the calculation to take into account the number of days in each of the three years: year 2002: 176.10040685 days year 2001: 365 days year 2000: 366 - 265.76707352 days Substituting this into the formula yields: = [ 210.5136 + ( 176.10040685 + 365 + 366 - 265.76707352) * 360.985647362 deg/d ) ] mod 360 = [ 210.5136 + 641.33333333 d * 360.985647362 deg/d ) ] mod 360 = 231722.6462107 mod 360 = 242.6421 deg 9. Insert new epoch and RAAN into proxy elset. Our proxy NOAA 16 elset, from Step 2, was: 1 26536U 00055A 00265.76707352 -.00020078 00000-0 -11203-1 0 13 2 26536 98.7886 210.5136 0009705 275.1802 115.0094 14.10880075 42 To create the elset for the corresponding elset of the new launch, we need only substitute the new epoch computed at Step 7, and the new RAAN, computed at Step 8. To avoid confusion with NOAA 16 or any other launches, we should also change the catalogue number and international designator to fall outside their normal range of values: 1 70000U 02176.10040685 -.00020078 00000-0 -11203-1 0 18 2 70000 98.7886 242.6421 0009705 275.1802 115.0094 14.10880075 40 My preference is to use a pseudo-catalogue number between 70000 and 79999, because that is far above the highest official catalogue entries to-date. I avoid using values between 80000 and 89999, because U.S. Space Command's analyst elements use much of that range. For reasons unknown, unclassified analyst elements are not normally made public, though many seem to have leaked out over the years. I also avoid using values between 90000 and 99999, because some hobbyists use portions of that range for unidentified satellites and other purposes. Even if I could know with absolute certainty the actual catalogue number and international designation ahead of launch, I would not use them for the estimated elements, in order to avoid the possibility of contaminating the eventual archives of elements. Archivists may employ automated methods to extract 2-line elements from e-mail messages, SeeSat-L posts and anywhere else they may be found, so my naming method avoids their mistaking an estimated pre-launch elset for an official elset. The above elset is sufficient for the purpose of finding the object during at least the first 24 hours after launch, until an official elset becomes available. No two launched are ever identical, so a prediction time uncertainty of a few minutes is to be expected. The negative rate of decay inherited from the proxy elset is unrealistic, but its effect on predictions is likely to be smaller than the uncertainty resulting from the other estimated elsets. I find the negative decay rate irritating, so I substituted more reasonable values: 1 70000U 02176.10040685 .00000200 00000-0 11164-3 0 19 2 70000 98.7886 242.6421 0009705 275.1802 115.0094 14.10880075 40 Note that the final digit of each line is a checksum, which is computed from the preceding digits on the line. Some ephemeris generators may reject elsets that do not have a proper checksum. If you have this problem, then you will need to compute the checksum. An explanation is found in Dr. T.S. Kelso's aforementioned article: http://celestrak.com/columns/v04n03/ 10. Check the results. The above process is simple, but it is easy to make an error, so it is always a good idea to check the result. I do this by computing and comparing ephemerides for the proxy launch and the new launch, as seen from the launch site near the launch time. Here is the ephemeris of the NOAA 16 proxy elset, on the day of its launch, 2000 Sep 21, near the launch time of 10:22 UTC, from the vantage point of Vandenberg AFB, located near 34.7 N, 120.6 W, zero metres above sea-level: 21/ 9/ 2000 10:00 - 24:00 UTC J2000.0 EL > 15 Vandenberg AFB TIME %I Mvv AZ EL R.A. DEC FE VANG RANGE ALT -------- -- ---- --- -- -------- --------- ---- ---- ----- ----- 10:21:50 31 8.4 12 15 12:10:19 67:25:21 6.1 0.10 2161 870 10:23:02 UMBRA 12 24 11:08:49 74:53:55 6.1 0.15 1712 869 10:23:53 UMBRA 12 33 08:49:17 79:49:21 6.1 0.20 1415 868 10:24:30 UMBRA 12 41 05:42:48 78:32:05 6.0 0.26 1220 868 10:24:59 UMBRA 11 50 04:02:01 72:34:19 6.0 0.32 1086 867 10:25:22 UMBRA 10 58 03:17:08 65:27:46 6.0 0.38 997 867 10:25:42 UMBRA 9 66 02:51:57 57:53:49 5.9 0.43 935 866 10:26:00 UMBRA 6 74 02:35:41 50:10:10 5.8 0.46 895 866 10:26:16 UMBRA 358 82 02:24:31 42:45:19 5.6 0.48 873 866 10:26:32 UMBRA 284 88 02:15:29 35:03:13 3.1 0.49 866 866 10:26:47 UMBRA 212 82 02:08:25 27:47:54 12.7 0.48 873 865 10:27:02 UMBRA 203 75 02:02:24 20:43:17 12.4 0.47 892 865 10:27:18 UMBRA 200 68 01:56:51 13:33:46 12.3 0.43 925 865 10:27:35 UMBRA 199 61 01:51:42 06:33:01 12.3 0.40 974 865 10:27:54 UMBRA 198 54 01:46:41 -00:28:23 12.3 0.35 1042 864 Note that the pass would have been from north to south, culminating nearly overhead of the launch site about 4 min 32 s after launch. Of course, this this pass did not actually occur, but it provides a simple basis to check the pre-flight elements of the new launch, which yield the following ephemeris for today's launch, 2002 Jun 24, near the launch time of 18:22 UTC: 24/ 6/ 2002 18:00 - 24:00 UTC J2000.0 EL > 15 Vandenberg AFB TIME %I Mvv AZ EL R.A. DEC FE VANG RANGE ALT -------- -- ---- --- -- -------- --------- ---- ---- ----- ----- 18:21:50 41 7.9 12 15 14:18:43 67:26:35 6.1 0.10 2160 870 18:23:02 34 7.7 12 24 13:17:05 74:55:23 6.1 0.15 1711 869 18:23:53 28 7.6 12 33 10:57:02 79:50:19 6.1 0.20 1414 868 18:24:30 22 7.7 12 41 07:50:27 78:31:12 6.0 0.26 1219 868 18:24:59 17 7.9 11 50 06:09:59 72:32:08 6.0 0.32 1085 867 18:25:22 13 8.1 10 58 05:25:17 65:24:49 6.0 0.38 996 867 18:25:42 10 8.4 9 66 05:00:11 57:50:21 5.9 0.43 935 866 18:26:00 8 8.8 6 74 04:43:58 50:06:20 5.8 0.46 895 866 18:26:16 6 9.1 358 82 04:32:50 42:41:17 5.6 0.48 873 866 18:26:32 5 9.3 282 88 04:23:49 34:59:06 3.1 0.49 866 866 18:26:47 5 9.3 211 82 04:16:47 27:43:50 12.7 0.48 873 865 18:27:02 6 9.1 203 75 04:10:46 20:39:23 12.4 0.46 892 865 18:27:18 8 8.8 200 68 04:05:14 13:30:07 12.3 0.43 925 865 18:27:35 10 8.5 199 61 04:00:06 06:29:41 12.3 0.39 974 865 18:27:54 13 8.3 198 54 03:55:06 -00:31:21 12.3 0.35 1042 864 As expected, the ephemeris time, azimuth, elevation, angular velocity (VANG), range and altitude, all occur at the same time relative to the launch time of their respective launches, which confirms that the pre-flight elements were computed correctly. Ted Molczan ----------------------------------------------------------------- Unsubscribe from SeeSat-L by sending a message with 'unsubscribe' in the SUBJECT to SeeSat-L-request@lists.satellite.eu.org http://www2.satellite.eu.org/sat/seesat/seesatindex.html
This archive was generated by hypermail 2b29 : Mon Jun 24 2002 - 09:28:31 PDT