Taiyin Semi-Analytical Ephemeris

A frozen-coefficient semi-analytical ephemeris covering calendar years −3000 through +3000. It has no runtime data files, uses only the Python standard library, and is published as taiyin-ephemeris-semi-analytic.

• Mercury through Pluto and the Earth–Moon barycenter use compact series independently fitted to JPL DE441.
• Planetary harmonics are generated from one sine/cosine pair per fundamental angle, so periodic terms require only multiplication and addition.
• The Moon uses the truncated XL1 lunar theory table from Shouxing Astronomical Ephemeris (寿星天文历/寿星万年历), followed by an independently fitted DE441 residual correction.
• Earth and Moon heliocentric positions are reconstructed from the EMB and the geocentric lunar vector.

Command line

The input epoch is Julian Date on the TDB time scale:

pip install taiyin-ephemeris-semi-analytic
taiyin-semi-analytic 2451545.0 301

From a source checkout, the original one-file-style demo command remains:

python3 ephemeris.py 2451545.0 301

The command prints JSON containing:

• xyz_km: heliocentric ICRF Cartesian coordinates in kilometres;
• spherical_icrf_rad_km: spherical longitude, latitude and radius derived from that same ICRF vector, in radians, radians and kilometres;
• ecliptic_lbr_j2000_rad_km: J2000 ecliptic longitude, latitude and radius, in radians, radians and kilometres;
• explicit target, center and frame metadata.

Python API

from taiyin_semi_analytic import (
    acceleration_icrf,
    position_velocity_acceleration_icrf,
    position_velocity_icrf,
    ecliptic_lbr_j2000,
    position,
    result,
    spherical_icrf,
    velocity_icrf,
)

xyz = position(2451545.0, 4)  # Mars
icrf_spherical = spherical_icrf(2451545.0, 4)
ecliptic_lbr = ecliptic_lbr_j2000(2451545.0, 4)
pv = position_velocity_icrf(2451545.0, 4)
pva = position_velocity_acceleration_icrf(2451545.0, 4)
v = velocity_icrf(2451545.0, 4)
a = acceleration_icrf(2451545.0, 4)
record = result(2451545.0, 4)

Both spherical functions return (longitude, latitude, radius). Angles are in radians and radius is in kilometres. spherical_icrf() uses the ICRF axes; ecliptic_lbr_j2000() returns the conventional L/B/R coordinates referred to the J2000 mean ecliptic and equinox.

The full derivative APIs return named tuples with Cartesian position in kilometres, velocity in kilometres/day, and acceleration in kilometres/day². If only one derivative is needed, velocity_icrf() / velocity_ecliptic_j2000() return a plain three-element velocity tuple, while acceleration_icrf() / acceleration_ecliptic_j2000() return a plain three-element acceleration tuple. The corresponding position_velocity_ecliptic_j2000() and position_velocity_acceleration_ecliptic_j2000() functions return the full quantities in the J2000 ecliptic frame. All derivatives are with respect to the TDB Julian Date and are analytic derivatives of the fitted series. The derivative APIs intentionally use Cartesian XYZ only; the spherical and L/B/R functions above are position-only APIs. This avoids ambiguous longitude wrapping and singular latitude rates. If spherical rates are needed, convert the returned Cartesian state with the application's own coordinate convention. The planetary, P03, and lunar phase-polynomial derivative tables are frozen in the package; the hot path then evaluates ordinary floating-point Horner polynomials and trigonometric chain rules. A private Jet implementation is kept under legacy/reference_jet.py only as a numerical cross-check during development. Position, velocity, and acceleration use separate scalar evaluators; the combined named-tuple APIs are only convenience wrappers.

Supported target IDs:

All returned vectors are Sun-centered. IDs 301 and 399 are therefore also heliocentric, not geocentric.

Accuracy

Held-out validation against DE441 over calendar years −3000 through +3000 gave the following heliocentric angular RMS values for the frozen planetary series:

The corrected geocentric lunar model measured 0.704″ angular RMS and 0.263 km radial RMS on held-out 32-day-grid epochs; maximum errors on that grid were 5.22″ and 1.52 km.

Design lineage

Steve Moshier's PLAN404 was an important inspiration for the compact semi-analytical representation and harmonic-recursion evaluator used here. The planetary series were developed by fitting to JPL DE441.

The lunar ecliptic-of-date coordinates are rotated to the J2000 ecliptic with the published P03 precession model of Capitaine, Wallace, and Chapront.

Files

• taiyin_semi_analytic/core.py: evaluator and public implementation.
• taiyin_semi_analytic/coefficients.py: frozen coefficients.
• taiyin_semi_analytic/derivative_coefficients.py: frozen first- and second-derivative coefficient tables generated from the fitted coefficients.
• taiyin_semi_analytic/__main__.py: python -m taiyin_semi_analytic entry.
• ephemeris.py: source-tree command-line demo wrapper.
• pyproject.toml: wheel/sdist and console-script configuration.
• tests/test_ephemeris.py: standard-library regression tests.
• NOTICE: attribution and third-party provenance.

The project is licensed under Apache License 2.0. The attributed Shouxing lunar table retains its upstream provenance notice; see NOTICE.