Accuracy and precision

Overview

rust-ephem achieves high accuracy through modern astronomical standards and optional Earth orientation corrections:

  • GCRS positions: ~10-20 meters compared to astropy (with all corrections enabled)

  • Default accuracy: ~100 meters (without UT1/polar motion corrections)

  • LEO velocity magnitudes: 7-8 km/s (typical for Low Earth Orbit)

Accuracy Levels

The library provides multiple accuracy levels depending on configuration:

Basic (Default)

  • Accuracy: ~100 meters

  • Uses embedded leap seconds (TAI-UTC)

  • Assumes UT1-UTC = 0

  • No polar motion correction

  • Sufficient for: General satellite tracking, educational purposes

High Accuracy (UT1 enabled)

  • Accuracy: ~20 meters

  • Uses IERS Earth Orientation Parameters (EOP) for UT1-UTC corrections

  • Automatic download from JPL

  • Sufficient for: Most operational satellite tracking, astronomical observations

Maximum Accuracy (UT1 + Polar Motion)

  • Accuracy: ~10-20 meters

  • Uses both UT1-UTC and polar motion corrections

  • Best achievable with SGP4 propagation model

  • Sufficient for: Scientific research, high-precision applications

Enabling High Accuracy

Use the polar_motion parameter and initialize data providers:

import rust_ephem
from datetime import datetime, timezone

# Initialize UT1 and EOP data providers (downloads from JPL)
rust_ephem.init_ut1_provider()
rust_ephem.init_eop_provider()

# Create ephemeris with polar motion correction
begin = datetime(2024, 1, 1, 0, 0, 0, tzinfo=timezone.utc)
end = datetime(2024, 1, 1, 1, 0, 0, tzinfo=timezone.utc)

ephem = rust_ephem.TLEEphemeris(
    tle1, tle2, begin, end, step_size=60,
    polar_motion=True  # Enable polar motion corrections
)

# Now GCRS positions have ~10-20m accuracy

Time Scale Accuracy

Leap Seconds (TAI-UTC)

The library includes embedded leap second data:

  • Coverage: 1972 to present (28 leap seconds through 2017)

  • Accuracy: Sub-microsecond time conversion accuracy

  • No dependencies: Works offline without external files

  • Automatic: No initialization required

import rust_ephem
from datetime import datetime, timezone

dt = datetime(2000, 1, 1, tzinfo=timezone.utc)
tai_utc = rust_ephem.get_tai_utc_offset(dt)  # Returns 32.0 seconds

UT1-UTC (Earth Rotation)

UT1-UTC corrections account for Earth’s irregular rotation:

  • Data source: IERS EOP2 from JPL

  • Automatic download: First use or when cache expires

  • Coverage: ~1 year historical + 6 months predicted

  • Impact: Improves accuracy from ~100m to ~20m

  • Range: ±0.9 seconds (updated daily by IERS)

# Check availability
if rust_ephem.is_ut1_available():
    ut1_utc = rust_ephem.get_ut1_utc_offset(dt)
    print(f"UT1-UTC: {ut1_utc:.6f} seconds")

Polar Motion (xp, yp)

Polar motion describes Earth’s rotation axis movement:

  • Data source: IERS EOP2 from JPL

  • Correction magnitude: ~10-20 meters

  • Parameters: xp, yp in arcseconds

  • Optional: Disabled by default for backward compatibility

# Get polar motion values
if rust_ephem.is_eop_available():
    xp, yp = rust_ephem.get_polar_motion(dt)
    print(f"Polar motion: xp={xp:.6f}\", yp={yp:.6f}\"")

Data Caching

IERS data is automatically cached locally:

  • Cache location: $HOME/.cache/rust_ephem/latest_eop2.short

  • TTL: 24 hours (configurable)

  • Environment variables:

    • RUST_EPHEM_EOP_CACHE: Custom cache directory

    • RUST_EPHEM_EOP_CACHE_TTL: Cache time-to-live in seconds

  • Fallback: Returns zero offset if data unavailable (graceful degradation)

Moon Position Accuracy

Two methods with different accuracy levels:

Meeus Algorithm (Built-in)

  • Accuracy: ~32 arcminutes (0.5 degrees)

  • No external data required

  • Sufficient for: Spacecraft applications, general astronomy

  • Automatically used when SPICE not initialized

SPICE/ANISE (High Precision)

  • Accuracy: <1 arcsecond

  • Requires: DE440 or DE441 kernel file

  • JPL-quality ephemeris

  • Required for: Scientific research, high-precision work

# Use high-precision SPICE-based Moon positions
rust_ephem.ensure_planetary_ephemeris()  # Downloads DE440S if needed

ephem = rust_ephem.TLEEphemeris(tle1, tle2, begin, end, step_size)
moon = ephem.moon  # Now uses SPICE if initialized

Coordinate Frame Transformations

The library implements IAU-standard transformations:

  • ERFA library: Essential Routines for Fundamental Astronomy

  • Precession-nutation: IAU 2006 model (pn_matrix_06a)

  • Frame bias: Proper ICRS/GCRS alignment

  • Earth rotation: UT1-based when available

Transformation accuracy:

  • TEME → GCRS: ~10-20m (with all corrections)

  • GCRS → ITRS: ~10-20m (with polar motion)

  • ITRS → GCRS: ~10-20m (with polar motion)

Error Sources

The remaining ~10-20m position error after all corrections is due to:

SGP4 Model Limitations

  • Simplified atmospheric drag model

  • Simplified Earth gravity model (J2-J4 only)

  • No solar radiation pressure

  • TLE orbital element uncertainties

Frame Transformation Approximations

  • Numerical precision limits

  • Higher-order corrections omitted

  • Ephemeris model differences

For higher accuracy: Use SPICE-based ephemeris with high-fidelity orbit propagators (not SGP4) and precise orbit determination products.

Testing and Validation

Validation against astropy:

# Run Python integration tests
python tests/integration_test_gcrs.py
python tests/integration_test_itrs_skycoord.py
python tests/integration_test_sun_moon_skycoord.py

Expected results:

  • Position errors: <20 meters (with UT1 + polar motion)

  • Position magnitudes: 6500-8000 km for LEO satellites

  • Velocity magnitudes: 7-8 km/s for LEO orbits

  • GCRS and TEME magnitudes: Similar within ~100m

Rust unit tests:

cargo test --verbose

All tests validate:

  • Coordinate transformation accuracy

  • Time scale conversions

  • Sun/Moon position calculations

  • Edge cases and error handling

See also: Time systems for time scale details and Coordinate Frames for coordinate system information.