Possible SGP4 compatibility issues: e = 1e-4 boundary and THDT constant

soaringred · September 29, 2026, 6:46am

Hi all,

I’ve been comparing Orekit’s SGP4/SDP4 output against Vallado/python-sgp4 and found two small differences that appear to explain the remaining residuals.

At exactly e = 1e-4, Orekit keeps xmcof/omgcof, while Vallado/Spacetrack Report #3 drops them for e <= 1e-4. Changing the Orekit condition from < 1e-4 to <= 1e-4 restores parity for this boundary case.
In deep-space propagation, Orekit uses:

THDT = 4.3752691e-3 rad/min

while Vallado uses:

4.37526908801129966e-3 rad/min

For GEO this produces a small accumulated difference. If I substitute Orekit’s rounded value into python-sgp4 at the corresponding locations, the 30-day GEO position matches Orekit to roughly 6e-9 km, so this seems to fully explain the discrepancy.

Would the maintainers consider:

fixing the e = 1e-4 boundary, and
making the deep-space Earth rotation constant/configuration selectable, even if the current Orekit value remains the default for compatibility?

Happy to put together a small MR with tests if this sounds reasonable.

luc · September 29, 2026, 8:27am

Good catch!
Yes, you can open an issue and an associated merge request on the forge.
It may even end up in the next patch release.

Serrof · September 29, 2026, 8:09pm

Hi there,

thanks for reporting.

Can you provide the TLE behind your 6e-9km value?
We’ll add it to the tests.

Cheers

soaringred · October 4, 2026, 2:33am

Hi,

Sure. The 6e-9 km figure came from a synthetic near-GEO element set, not a
catalogued object:

1 99999U          25001.00000000  .00000000  00000-0  10000-4 0    01
2 99999   0.0500  90.0000 0001000   0.0000   0.0000  1.00273790    01

Epoch 2025-01-01T00:00:00 UTC, propagated to epoch + 43200 min (30 days), TEME, km.
Orekit 13.1.3 selects DeepSDP4 for it. The reference is python-sgp4 2.27 (Vallado’s
code, pure-Python implementation, WGS72, opsmode ‘i’).

Position at +43200 min:

Vallado as published          -20974.134611934  36572.404003287  57.554005190
Orekit 13.1.3                 -20974.134455572  36572.404095167  57.554004784
Vallado with rptim = THDT     -20974.134455566  36572.404095171  57.554004784

Velocity at +43200 min (km/s):

Vallado as published          -2.667538381620  -1.529662878230  0.006928921098
Orekit 13.1.3                 -2.667538388139  -1.529662866722  0.006928921116

So Orekit differs from the published reference by 1.8e-4 km (0.18 m) at 30 days.
Replacing Vallado’s rptim = 4.37526908801129966e-3 with TLEConstants.THDT =
4.3752691E-3 in both places it is defined (dsinit and dspace) brings the two to
within about 7e-9 km (largest component 6e-9 km), so for this case the constant
accounts for the whole difference.

The gap grows with the resonance integration: the positions agree to 5e-9 km at
+1440 min, differ by 8e-7 km at +7200 min, and by 1.8e-4 km at +43200 min.

The same effect shows up in real element sets (CelesTrak, epochs 30 Sep – 1 Oct 2026),
same setup:

INTELSAT 10-02
1 28358U 04022A   26274.28586502 -.00000012  00000+0  00000+0 0  9993
2 28358   0.0188 244.4512 0000395  25.9670 201.5399  1.00271722 81621
GOES 16
1 41866U 16071A   26274.61451617 -.00000094  00000+0  00000+0 0  9994
2 41866   0.5976  84.0380 0002277 146.5604 256.3000  1.00270988 36179
TDRS 3
1 19548U 88091B   26273.95411941 -.00000297  00000+0  00000+0 0  9994
2 19548  12.5244 340.2927 0038904 350.6418 333.3814  1.00267688126445
MOLNIYA 2-10
1 07376U 74056A   26274.09180686 -.00000203  00000+0  00000+0 0  9998
2 07376  65.2296 289.8497 6674984 267.7805  20.5563  2.01201650381865
GPS BIIR-5 (PRN 22)
1 26407U 00040A   26274.63014552  .00000023  00000+0  00000+0 0  9993
2 26407  54.8348 210.9384 0117327 304.1901 154.9947  2.00558399192089

Position at +43200 min, Vallado as published / Orekit 13.1.3:

INTELSAT 10-02  -33114.373907564  26100.502023235    -24.272710665
                -33114.373796788  26100.502166895    -24.272710676   (1.81e-4 km apart)
GOES 16         -38613.886015897  16922.654786475    459.627441704
                -38613.886074104  16922.654649626    459.627442194   (1.49e-4 km)
TDRS 3           37385.602777505 -19116.396281757  -1154.331381244
                 37385.602763490 -19116.396309460  -1154.331388077   (3.2e-5 km)
MOLNIYA 2-10     19446.693409967  -2778.368915205  38517.132654297
                 19446.693391022  -2778.368706176  38517.132746445   (2.29e-4 km)
GPS BIIR-5       24487.779842619   7754.945643631   7691.872007344
                 24487.779842619   7754.945643630   7691.872007344   (agree to 1e-9 km)

With rptim replaced by THDT in the reference, the first four agree with Orekit to
7e-8, 2.7e-6, 3e-8 and 4e-8 km. The constant only enters the resonant branches
(24 h, and 12 h with e >= 0.5), so the GPS case is a useful control: it is
deep-space but not resonant, and the two already agree.

I’ll start work on the merge request now.

Cheers