Verification Test Cases

Essentially, these cases allowed several features of SGP4 to be tested, but the answers were generally agreed upon during the testing phase of research for this paper. Cases for which there were technical questions about how the code was implemented are discussed in a subsequent section. The element sets were sorted numerically in the computer file to aid location of specific test cases, but are grouped here by effect. Comments were added to indicate what each test was accomplishing. The original SGP4 model had two types defined in the code, normal (near Earth) and ‘simplified drag’, while the original SDP4 had three types, normal (deep space), resonant (12^h Molniya style) and synchronous (24^h GEO). Table 1 shows a sample. The file (sgp4-ver.tle) is on the Internet at the web site listed at the end of the paper, and in the Appendix.

Table 1. SGP4 Verification Test Cases. These satellites highlight the primary test cases used for analysis and verification of the SGP4 code. A few other satellites are included in the full test set. The satellites used for the figures are also included, but at a reduced ephemeris density. The file gives the applicable time range in minutes from epoch (MFE). The original STR#3 tests are kept for continuity.[^9]

Satellite	Category	Comments
00005	Near Earth	TEME example satellite.
28129	Deep Space	A GPS navigation satellite in a near circular 12^h orbit.
26975	Resonant	Molniya style debris launch. Exercises the 0.5 to 0.65 eccentricity branches in deep space.
08195	Resonant	Molniya launch. Exercises the 0.65 to 0.7 eccentricity branches of the deep-space code.
09880	Resonant	Molniya launch. Exercises the 0.7 to 0.715 eccentricity branches of the deep-space code.
21897	Resonant	Molniya launch. Exercises the eccentricity branches above 0.715, with a negative Bstar value.
22674	Resonant	Rocket body, similar to 21897 (e > 0.715) but positive Bstar.
28626	Synchronous	Low-inclination (< 3 deg) geostationary orbit that shows the problems in premature correction of negative inclination at around 1130 minutes from epoch.
25954	Synchronous	Low-inclination GEO case like 28626, shows negative inclination problem at around 274 minutes from epoch.
24208	Synchronous	Geostationary orbit above 3 deg.
09998	Synchronous	Relatively high eccentricity for GEO (e = 0.027) shows secular integrator problem clearly.
14128, 04632	Synchronous	Geostationary orbit close to 0.2 radian inclination. Shows Lyddane choice problem at about 2080 minutes and about -5000 minutes from epoch.
20413	Deep Space	Long period orbit (~4 days) shows Lyddane choice at 1860 minutes from epoch. It also demonstrates processing through a leap second, although the SGP4 code is independent of any leap second processing. Leap seconds are handled in any external program using the SGP4-derived ephemerides.
23333	Deep Space	Very high eccentricity, shows Kepler solution problems in Report #3 code.
28623	Deep Space	Deep-space object with low perigee (135.75 km) that uses the branch (perigee < 156 km) for modifying the ‘s4’ drag coefficient.
16925	Deep Space	Deep-space object with very low perigee (82.48 km) that uses the second branch (perigee < 98 km) for limiting the ‘s4’ drag coefficient to 20.
06251	Near Earth	Near Earth normal drag case. The perigee of 377.26 km is low, but above the threshold of 220 km for simplified equations, so moderate drag case.
28057	Near Earth	Near Earth normal drag case but with low eccentricity (0.000 088 4) so certain drag terms are set to zero to avoid math errors / loss of precision.
29238	NE/S	Near Earth with perigee 212.24 km, thus uses simplified drag branch (perigee < 220 km) test.
28350	NE/S	Near Earth low perigee (127.20 km) that uses the branch (perigee < 156 km) for modifying the ‘s4’ drag coefficient. Propagation beyond approximately 1460 minutes should result in error trap (modified eccentricity too low).
22312	NE/S	Near Earth with very low perigee (86.98 km) that uses the second branch (perigee < 98 km) for limiting the ‘s4’ drag coefficient to 20. Propagation beyond approximately 2840 min should result in error trap (modified eccentricity too low).
28872	NE/S	Sub-orbital case (perigee -51 km, lost about 50 minutes from epoch) used to test error handling.
23177, 23599	Deep Space	Lyddane bug at less than 70 min and 380 min respectively, with atan2(), but no quadrant fix.
26900	Deep Space	Lyddane bug at 37,606 min, negative inclination at 9313 min.
29141	Near Earth	Last stages of decay. Crashes before 440 min.
11801 / 88888	Deep Space, Near Earth	Original STR#3 report test cases.