Overview & Extraction Notes

Source

AIAA 2006-6753-Rev1, Vallado, D.A., Crawford, P., Hujsak, R., & Kelso, T.S. (2006, Rev 1: 2008). Source PDF: AIAA-2006-6753-Rev1.pdf (646 KB, 92 pages).

This paper represents the most significant effort to reconcile 25 years of divergent SGP4 implementations. It documents the bugs, provides corrected C++ and FORTRAN 90 source code, supplies 518 test vectors across 29 satellites, and formally defines the TEME coordinate frame that SGP4 output occupies.

Why This Paper Exists

Spacetrack Report No. 3 (1980) contained the canonical SGP4/SDP4 algorithms, but no authoritative digital source files were ever distributed. Over the following quarter century, independent reimplementations introduced divergent bugs, and compensating fixes were applied without coordination. By the early 2000s, multiple organizations ran code that all claimed to be “SGP4” but produced materially different results.

The divergence was partly a consequence of the transcription problem — the invisible column 72 boundary in FORTRAN IV fixed-format source, combined with the absence of any authoritative digital distribution.

Rev-1 was the first comprehensive effort to:

1. Document the specific bugs and their orbital effects
2. Provide corrected source code in both FORTRAN 90 and C++
3. Supply extensive test cases covering edge cases and failure modes
4. Define the TEME coordinate frame precisely enough for interoperability
5. Establish a baseline that the broader community could synchronize against

The “Official” vs. “Unofficial” Problem

No Truly Official Public SGP4

There is no truly “official” SGP4 outside AFSPC’s classified operational systems at Cheyenne Mountain. The operational version that generates TLE data is embedded within SPADOC and has never been publicly released. All public versions — including STR#3 — are snapshots of a separate “standalone” codebase maintained by technical offices.

By 2006, three major public versions were in circulation:

Version	Origin	Key Differences
STR#3 (1980)	AFSPC standalone	Mixed precision, original bugs
GSFC (1996)	NASA Goddard / SeaWiFS	Some fixes from 1990 standalone
Dundee (Crawford)	Independent researcher	Most comprehensive external fix history

These differed in their handling of the secular integrator, Kepler convergence criteria, Lyddane singularity, and negative inclination values. Rev-1 synthesized insights from all three into a single non-proprietary version believed to be compatible with the operational code.

Single vs. Double Precision

The original STR#3 FORTRAN mixed single-precision and double-precision arithmetic. Rev-1 uses full double precision throughout, eliminating an entire class of precision-related discrepancies. This is the primary cause of the 1—2 km differences observed when comparing Rev-1 output against the original test vectors.

Key Bugs Fixed

Rev-1 documents five categories of bugs, each demonstrated by specific satellite numbers that triggered the failure:

1. Lyddane Singularity

Affected satellites: 04632, 14128, 20413, 23177, 23599

The Lyddane modification to Brouwer’s theory introduces a singularity at low inclination that the original code did not guard against. These satellites, with near-equatorial orbits, caused division-by-zero or catastrophic cancellation in the short-period corrections.

2. Negative Inclination

Affected satellites: 25954, 28626

The TLE fitting process occasionally produces slightly negative inclination values. The original code assumed $I \geq 0$ and computed $\sin(I)$ and $\cos(I)$ without bounds checking, leading to sign errors that propagated through the perturbation calculations.

3. Secular Integrator State Saving

Affected satellite: 09880

The deep-space secular integrator uses a 720-minute step size and must save its state between calls. The original code had a state-saving bug where the integrator’s accumulated perturbations were not properly preserved across propagation calls, producing discontinuous jumps for deep-space objects.

4. Kepler’s Equation Convergence

Affected satellite: 23333

For high-eccentricity orbits ($e > 0.9$), the Newton-Raphson iteration in the original code could fail to converge within 10 iterations. Rev-1 improved the convergence logic and increased the iteration limit for these cases. Satellite 23333 is a Molniya-type orbit with $e \approx 0.74$ that exposed the boundary of the original solver.

5. Perigee Height Thresholds

The original code used three perigee height thresholds (98, 156, and 220 km) to select different atmospheric drag treatments. The threshold logic contained off-by-one comparisons that could select the wrong drag regime for satellites near these boundaries.

TEME Coordinate Frame

TEME Is Not J2000

SGP4 output is in the TEME frame. Using it as J2000, GCRF, or any other standard inertial frame introduces errors that grow with propagation time. A 3-day propagation shows 23.6 m difference between “of date” and “of epoch” nutation alone.

Before Rev-1, SGP4 output was loosely described as “ECI” (Earth-Centered Inertial) without specifying which of several possible inertial frames was meant. Rev-1 formally defined the output frame as TEME — True Equator, Mean Equinox — characterized by:

• True equator: the instantaneous Earth equatorial plane including nutation
• Mean equinox: a simplified equinox direction using only 4 of the 106 IAU-80 nutation terms
• Not J2000: TEME is a “of date” frame that rotates slowly relative to J2000
• Not TOD: TOD uses all 106 nutation terms; TEME uses only 4

The Appendix C provides the complete transformation matrices for converting TEME to J2000 and ITRF, including worked numerical examples.

Nutation at Propagation Time vs. TLE Epoch

A subtle question: when computing the TEME-to-J2000 transformation, should the nutation matrix be evaluated at the propagation time or at the TLE epoch? Rev-1 demonstrates that this choice produces a 23.6 m position difference over just 3 days. The “of date” approach (nutation at propagation time) is the correct one.

Test Case Design

Rev-1 provides 29 test satellites (expanded from STR#3’s single near-earth and single deep-space test case) covering the full range of orbital regimes:

Category	Count	What It Tests
Near-earth normal	8	Standard LEO propagation
Low perigee	4	Atmospheric drag regime selection
Decaying orbits	3	Orbital decay and re-entry handling
12-hour resonance	4	Molniya-type deep-space resonance
24-hour resonance	3	GEO-type resonance
Low inclination	3	Lyddane singularity region
High eccentricity	2	Kepler convergence stress
Sub-orbital	2	Below 100 km perigee

The complete test case data (518 vectors) is provided in Appendix D and Appendix E.

Cross-Reference: STR#3 vs. Rev-1

Aspect	STR#3 (1980)	Rev-1 (2006/2008)
Language	FORTRAN IV (fixed format)	FORTRAN 90 + C++
Precision	Mixed single/double	Full double precision
Test cases	25 vectors, 2 satellites	518 vectors, 29 satellites
Constants	WGS-72 hardcoded	WGS-72 and WGS-84 selectable
Output frame	Undefined “ECI”	TEME (formally defined)
Integrator	720-min step, state bug	720-min step, state bug fixed
Kepler iteration	10 max, no $e$ guard	Improved convergence for high $e$
Lyddane fix	None	Singularity guard for $I \approx 0$

Extraction Inventory

Component	Files	Content
Main body	9	Sections I—VII (590 lines of transcribed text)
Appendix A	1	Organization comparison table
Appendix B	1	TLE format specification
Appendix C	1	TEME coordinate frame definition and transformations
Appendix D	1	29 test satellite TLEs with metadata
Appendix E	1	518 test vectors (position and velocity)

Section Navigation

Introduction and History Detailed account of SGP4's evolution from 1965 to 2006

Program Interface Issues Configuration control, data formats, and coordinate systems

Appendix C: TEME Full transformation equations with worked numerical examples

Appendix D: Test Cases 29 test satellites covering all orbital regimes