Vallado et al. Rev 3 (2006/2013): Final SGP4 Modernization

Source

Vallado, D.A., Crawford, P., Hujsak, R., and Kelso, T.S., “Revisiting Spacetrack Report #3: Rev 3,” AIAA 2006-6753-Rev3. Center for Space Standards and Innovation / Analytical Graphics, Inc. Originally presented at the AIAA/AAS Astrodynamics Specialist Conference, Keystone, CO, 2006. Revision 3 reflects code updates through 30 December 2011. 94 pages.

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Supersedes Rev 1

Rev 3 is the final public revision of the SGP4 modernization paper. It supersedes Rev 1 (2008), which was the basis for our chapter-by-chapter archive transcription. For implementation and validation purposes, Rev 3’s source code and test vectors are authoritative.

Why This Matters for SGP4

Rev 3 is the authoritative modern SGP4 reference. Every actively maintained implementation — satellite.js, python-sgp4, Skyfield, and pg_orrery — derives from or validates against the C++ source in this revision.

The revision chain:

2006  AIAA 2006-6753     Original conference paper
  |
2008  Rev 1              First revision (our primary archive transcription)
  |
  ~   Rev 2              Intermediate revision (undated)
  |
2011  Rev 3              Final public revision. Code stamped 2011-12-30.

Where the original 2006 paper cataloged 25 years of SGP4 divergence and Rev 1 provided the corrected algorithms and 518 test vectors, Rev 3 addresses the questions Rev 1 left open: which mode is “official”? What happens when propagation fails? How fast can this run at catalog scale?

This page focuses on what changed. The theory, bug history, TEME definition, and test case design documented in Rev 1 are not repeated here.

The Dual Operation Mode

The single most important addition in Rev 3 is the operationmode parameter, threaded through the entire call chain from sgp4init() down to dpper():

Mode	Character	GHA Calculation	Intrinsic Function Handling
AFSPC	'a'	Jan 0, 1970 epoch formula (THGR70, C1, FK5R)	Original FORTRAN MOD/ATAN semantics
Improved	'i'	Julian-century GMST1982 (Eq. 2 in paper)	Modern fmod/atan2 semantics

What the Modes Affect

GHA (Greenwich Hour Angle) calculation. In AFSPC mode, initl() computes the Greenwich sidereal time at epoch using the older 1970-epoch formula with combined constants. In improved mode, it uses the GMST1982 equation:

$\theta_{GMST} = 67\,310.548\,41 + (876\,600 \times 3600 + 8\,640\,184.812\,866)\,T_{UT1} + 0.093\,104\,T_{UT1}^2 - 6.2 \times 10^{-6}\,T_{UT1}^3 \quad \text{[seconds]}$

The difference is on the order of arcseconds — small, but enough to cause disagreement in verification against AFSPC-generated test vectors.

Intrinsic function handling. In dpper(), when nodep (the perturbed node) goes negative, AFSPC mode adds $2\pi$ to match the behavior of FORTRAN’s MOD function. Improved mode relies on C/C++ fmod and atan2 to handle the quadrant correctly. The difference matters for deep-space objects where lunar-solar perturbations push orbital elements through zero crossings.

Use AFSPC Mode for TLE Compatibility

TLEs are generated by AFSPC (now 18 SDS) operational code. To match their behavior — and to validate against Rev 3’s published test vectors — use 'a' mode with WGS-72 constants. The improved mode is intended for differential correction and orbit determination workflows where you control both the fitting and the propagation.

Code-Level Changes from Rev 1

Rev 3’s source code changelog documents seven categories of changes accumulated between August 2006 and December 2011:

Date	Change	Impact
Nov 2008	Early return false on error codes	Prevents silent garbage output after errors 1-4 and 6
Sep 2008	DSPACE atime optimization	Faster deep-space propagation for epochs far from propagation time
Sep 2008	operationmode parameter added	Dual AFSPC/improved behavior (see above)
Jun 2008	Small eccentricity threshold update	cc3 only computed when $e > 10^{-4}$, prevents division issues
Aug 2010	pow() replaced with direct multiplies	x*x and x*x*x instead of pow(x, 2.0) and pow(x, 3.0)
Aug 2010	Unused variable cleanup in initl()	Eliminates compiler warnings
Rev 3	Sub-orbital initialization check removed	TLEs with perigee below Earth’s surface no longer rejected at init

Error Handling

Rev 1’s sgp4() function set error codes but continued processing, meaning the caller received a position/velocity vector that could be numerical noise. Rev 3 adds explicit return false; after each error condition:

• Error 1: $e \geq 1.0$ or e < -0.001
• Error 2: mean motion $n \leq 0.0$
• Error 3: perturbed eccentricity outside $[0, 1]$
• Error 4: semi-latus rectum p < 0
• Error 6: distance from Earth center m_{rt} < 1.0 (satellite has decayed)

Sub-Orbital Check Removal

Rev 1 set error 5 and returned early when the initial perigee radius was below 1.0 Earth radii (r_p < 1.0). Rev 3 removes this check entirely. The rationale: a satellite whose TLE-epoch perigee is below the surface may still be above the surface at the requested propagation time. The runtime check (m_{rt} < 1.0 in sgp4()) catches actual decay. This matters for decaying satellites near end-of-life, when tracking accuracy is most critical.

Performance: pow() to Multiply

Replacing pow(x, 2.0) with x*x throughout the propagator is not cosmetic. The general pow() function computes $e^{n \ln x}$ — a transcendental function evaluation for what amounts to a single multiply. For catalog-scale batch processing (the whats_up query pattern), this accumulates to a measurable speedup across thousands of TLEs per call.

TEME-to-ECEF Improvements

Appendix C is restructured to lead with the operational conversion path (TEME to Earth-fixed via GMST) rather than the academic path (TEME to J2000). The worked example is updated to use 6 April 2004 as the reference date with specific UT1-UTC, polar motion, and EOP values.

The transformation matrices (Eqs. C-1 through C-4) and the 23.6-meter “of date” vs. “of epoch” demonstration using the Vanguard 1 TLE are numerically identical to Rev 1.

A terminology update throughout: “CMOC” (Cheyenne Mountain Operations Center) becomes “JSPOC” (Joint Space Operations Center), reflecting the 2005 organizational name change. A new footnote references Koskela (1967) for the historical basis of the 4-term nutation approximation that defines the TEME frame.

WGS-84 mu Discrepancy

Rev 3’s getgravconst() function uses $\mu = 398600.5$ km$^3$/s$^2$ for the WGS-84 constant set, while the text in Table 3 (Section VI.B) still lists the full-precision value $\mu = 398600.4418$ km$^3$/s$^2$. This code-vs-text mismatch is present in the original PDF. The practical difference ($0.058$ km$^3$/s$^2$) is negligible for SGP4 accuracy, but worth noting if you are validating constant sets against the paper.

Test Case Updates

The test suite retains the same 29 satellites as Rev 1. Two additions appear in the Rev 3 table descriptions:

Satellite	Category	Purpose
09998	Synchronous	High-eccentricity GEO ($e = 0.027$), exercises secular integrator
28129	Deep Space	GPS satellite, 12-hour non-resonant (e < 0.5)

The appendix header notes that satellite 23599 results differ from Rev 1 “as a result of the consistency with AFSPC option.” All Rev 3 test vectors are explicitly generated with 'a', '72' (AFSPC mode, WGS-72 constants), eliminating the mode ambiguity present in Rev 1.

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Rev 1 (2008): Full Archive Transcription The first revision that Rev 3 supersedes -- chapter-by-chapter extraction with 518 test vectors

Vallado (2006): Original Conference Paper The conference paper that started the modernization -- 25 years of divergence cataloged

Vallado & Virgili (2008): SGP4 Orbit Determination The inverse problem companion paper -- fitting TLEs using the Rev 3 propagator

STR#3: SGP4 Model The original 1980 FORTRAN that Rev 3 modernizes