Astro.Coordinates (Astro v2.1.0)

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Coordinate transformations for high-precision lunar and solar position calculations.

Provides:

  • Conversion of UTC DateTime to TDB seconds past J2000.0 (the time argument used by JPL ephemerides).
  • Conversion of TDB seconds back to UTC DateTime.
  • Rotation of ICRF/J2000 Cartesian coordinates to the true equator and equinox of date using IAU 1980 precession and nutation.
  • Conversion of equatorial Cartesian to spherical (RA, Dec, distance).
  • Greenwich Apparent Sidereal Time (GAST) for the topocentric iteration.

Time scale convention

JPL ephemeris data is in TDB (Barycentric Dynamical Time). For the purpose of rise/set calculations, TDB ≈ TT to within 2 ms; this difference is negligible and TDB is treated as TT here.

ΔT = TT − UTC varies over time; see Astro.Time.delta_t/1 for the unified computation.

Reference

Precession: Lieske et al. (1977), A&A 58, 1–16. Nutation: IAU 1980 series, Wahr (1981), Meeus Ch.22 (top 17 terms). GAST: Meeus Ch.12 with equation of the equinoxes.

Summary

Functions

cartesian_to_spherical(arg)

Converts equatorial Cartesian coordinates to spherical coordinates.

dynamical_time_from_moment(moment)

Converts a moment to dynamical time (TDB seconds past J2000.0).

dynamical_time_to_moment(dynamical_time)

Converts dynamical time back to a moment.

gast(dynamical_time)

Computes Greenwich Apparent Sidereal Time (GAST) in degrees.

icrf_to_true_equator(arg, dynamical_time)

Rotates a J2000.0 ICRF Cartesian vector to the true equator and equinox of date, applying IAU 1980 precession and nutation.

julian_centuries_from_dynamical_time(dynamical_time)

Returns Julian centuries from J2000.0 for the given dynamical time.

Functions

cartesian_to_spherical(arg)

@spec cartesian_to_spherical({float(), float(), float()}) ::
  {float(), float(), float()}

Converts equatorial Cartesian coordinates to spherical coordinates.

Arguments

  • {x, y, z} is an equatorial Cartesian position vector in kilometers.

Returns

  • {ra_deg, dec_deg, distance_km} where right ascension is in degrees in the range [0, 360), declination is in degrees in the range [-90, 90], and distance is in kilometers.

dynamical_time_from_moment(moment)

Converts a moment to dynamical time (TDB seconds past J2000.0).

Delegates to Astro.Time.dynamical_time_from_moment/1.

Arguments

  • moment is a moment (fractional days since epoch).

Returns

  • TDB seconds past J2000.0 as a float.

dynamical_time_to_moment(dynamical_time)

Converts dynamical time back to a moment.

Delegates to Astro.Time.dynamical_time_to_moment/1.

Arguments

  • dynamical_time is TDB seconds past J2000.0.

Returns

  • A moment (fractional days since epoch) as a float.

gast(dynamical_time)

@spec gast(float()) :: float()

Computes Greenwich Apparent Sidereal Time (GAST) in degrees.

GMST is computed from UT1 (≈ UTC) using Meeus equation 12.4, then corrected by the equation of the equinoxes (Δψ · cos ε) to obtain GAST.

Arguments

  • dynamical_time is TDB seconds past J2000.0. ΔT is subtracted internally to recover UT1 for the sidereal rotation rate.

Returns

  • GAST in degrees, normalized to the range [0, 360).

icrf_to_true_equator(arg, dynamical_time)

@spec icrf_to_true_equator({float(), float(), float()}, float()) ::
  {float(), float(), float()}

Rotates a J2000.0 ICRF Cartesian vector to the true equator and equinox of date, applying IAU 1980 precession and nutation.

The precession matrix uses Lieske (1977) angles and the nutation uses the top 17 terms of the IAU 1980 series via Astro.Earth.nutation/1.

Arguments

  • {x, y, z} is a Cartesian position vector in the ICRF/J2000 frame, in any consistent unit (typically kilometers).

  • dynamical_time is TDB seconds past J2000.0.

Returns

  • {x', y', z'} in the true equator and equinox of date frame, in the same units as the input.

julian_centuries_from_dynamical_time(dynamical_time)

Returns Julian centuries from J2000.0 for the given dynamical time.

Delegates to Astro.Time.julian_centuries_from_dynamical_time/1.

Arguments

  • dynamical_time is TDB seconds past J2000.0.

Returns

  • Julian centuries from J2000.0 as a float.