Accuracy & Validation

Orbis validates against established reference implementations at every layer. Here is exactly what is tested, to what precision, and against what oracle.

Coordinate Transforms vs Skyfield

The rotation stages of the TEME→GCRS→ITRS pipeline produce IEEE 754 bit-identical output (0 ULP — zero Units in the Last Place) to Python Skyfield on all tested platforms. The derived geodetic and topocentric outputs are validated against Skyfield to tight numerical tolerances, but are not bit-exact today.

The 0-ULP rows assert IEEE-754 ULP distance against hex-captured Skyfield reference values. The geodetic and topocentric rows assert assert_in_delta against decimal Skyfield references at the tolerances shown (oracle_test.exs); they are tolerance-tested, not bit-exact.

The transform includes IAU2000A nutation (1365 terms), IAU2006 precession, frame bias, and precise time scale conversions (UTC→TAI→TT→TDB→UT1). The FMA discipline in mat3_vec3_mul matches numpy's vectorized behavior.

Test tag: :skyfield_parity — run with mix test --include skyfield_parity. All four rows above are tagged :skyfield_parity, and CI runs mix test --include skyfield_parity --exclude spk_file (see .github/workflows/ci.yml), so all four are exercised on every push and pull request.

SGP4 Propagation: < 1 mm vs Skyfield

SGP4 propagation uses the published sgp4 Rust crate in AFSPC compatibility mode. This is a clean-room Rust implementation that differs from Skyfield's bundled C extension by sub-nanometer amounts (different floating-point expression evaluation order and FMA contractions).

The oracle test verifies position distance is < 1 mm for the ISS at 274 minutes from epoch.

Orbit Determination: Vallado Reference

IOD methods are validated against David Vallado's valladopy Python implementation using the textbook examples.

The deterministic methods (Gibbs, Herrick-Gibbs) assert ULP distance on their outputs (iod_test.exs): the velocity components assert max_ulp = 0 and the inter-vector angles theta12/theta23 assert max_ulp = 2 (near-0-ULP, not strict 0 ULP).

* The velocity reference values are decimal literals transcribed from valladopy output (e.g. 5.5311472050176125), not captured float.hex() values. A decimal round-trip backs the ULP=0 velocity assertions, which is weaker than the hex-float capture discipline used for the coordinate transforms; treat the velocity ULP=0 as near-bit-exact rather than a hex-float oracle.

The iterative methods (Gauss, Lambert) converge to the same result within 1e-12 relative tolerance, which is the tolerance used by Vallado's own test suite.

Conjunction Assessment

Validated against the Iridium 33 / Cosmos 2251 collision of 2009-02-10:

• Time of closest approach: within ~1 hour of the known collision time (conjunction_test.exs asserts tca_hours within 1.0 of 22.1)
• Miss distance: under 10 km (event-level sanity check, min_dist < 10.0 km; consistent with SGP4/TLE accuracy limits — not a precise-value oracle)

RF Primitives

FSPL uses the standard inverse square law formula:

FSPL = 32.45 + 20·log₁₀(f_MHz) + 20·log₁₀(d_km)

These are tolerance-only checks with no committed oracle or golden vector. fspl/2 asserts assert_in_delta 0.01 dB against hand-computed numbers written in test comments (rf_test.exs); eirp/2 asserts exact equality on trivial dB arithmetic; the remaining RF functions (C/N₀, link margin, wavelength, dish gain) assert only sign and monotonicity. All RF math is textbook dB arithmetic, but it is not cross-validated against an external reference implementation.

JPL Ephemeris

The SPK/BSP reader is tested at 0 ULP vs Skyfield for Mars and Venus only (Earth-relative positions, 6 components, max_ulp = 0 against Skyfield reference values in oracle_test.exs; the references are stored as decimal literals). Sun, Moon, and Earth positions are covered only by distance-magnitude sanity bounds (within ~20,000 km of the expected lunar distance / 0.02 AU of 1 AU in ephemeris_test.exs); they are not 0-ULP verified.

Test tag: :spk_file — requires /tmp/de421.bsp.

Not verified in CI. CI runs mix test --include skyfield_parity --exclude spk_file, so the Mars/Venus 0-ULP test is excluded from CI. The de421.bsp fixture it depends on is not committed to the repository, so the only way to exercise this row is locally with the file present: mix test --include spk_file after placing de421.bsp at /tmp/de421.bsp.

What Is NOT Validated

• Atmospheric density (NRLMSISE-00): Implemented from the public-domain C translation but not cross-validated against a reference implementation. Results are physically reasonable but not precision-verified.

• Pass prediction timing: Uses the full topocentric pipeline for elevation, but rise/set times depend on the scan resolution (step_seconds option) and bisection precision.