From 5ef517f7c9d505947aeba586729df0adeb6a908d Mon Sep 17 00:00:00 2001 From: ApsisRS contributors Date: Sat, 26 Sep 2026 16:48:57 +0800 Subject: [PATCH] physics: add IAU 2000A nutation and IAU 2006 precession --- crates/apsis-rs/Cargo.toml | 4 + crates/apsis-rs/examples/dump_iau2000.rs | 92 + .../apsis-frames/src/iau2000/eect_table.rs | 158 + .../apsis-frames/src/iau2000/fundamental.rs | 273 + .../physics/apsis-frames/src/iau2000/mod.rs | 105 + .../apsis-frames/src/iau2000/nutation.rs | 154 + .../src/iau2000/nutation_table.rs | 5501 +++++++++++++++++ .../apsis-frames/src/iau2000/precession.rs | 180 + .../apsis-frames/src/iau2000/terrestrial.rs | 276 + crates/physics/apsis-frames/src/lib.rs | 1 + crates/physics/apsis-frames/tests/iau2000.rs | 398 ++ validation/README.md | 8 +- validation/python/time/check_iau2000.py | 156 + validation/tools/generate_eect_table.py | 98 + validation/tools/generate_nutation_table.py | 143 + 15 files changed, 7546 insertions(+), 1 deletion(-) create mode 100644 crates/apsis-rs/examples/dump_iau2000.rs create mode 100644 crates/physics/apsis-frames/src/iau2000/eect_table.rs create mode 100644 crates/physics/apsis-frames/src/iau2000/fundamental.rs create mode 100644 crates/physics/apsis-frames/src/iau2000/mod.rs create mode 100644 crates/physics/apsis-frames/src/iau2000/nutation.rs create mode 100644 crates/physics/apsis-frames/src/iau2000/nutation_table.rs create mode 100644 crates/physics/apsis-frames/src/iau2000/precession.rs create mode 100644 crates/physics/apsis-frames/src/iau2000/terrestrial.rs create mode 100644 crates/physics/apsis-frames/tests/iau2000.rs create mode 100644 validation/python/time/check_iau2000.py create mode 100644 validation/tools/generate_eect_table.py create mode 100644 validation/tools/generate_nutation_table.py diff --git a/crates/apsis-rs/Cargo.toml b/crates/apsis-rs/Cargo.toml index 258a0a5..9b3587a 100644 --- a/crates/apsis-rs/Cargo.toml +++ b/crates/apsis-rs/Cargo.toml @@ -185,3 +185,7 @@ required-features = ["rf"] [[example]] name = "integrate_network" required-features = ["network"] + +[[example]] +name = "dump_iau2000" +required-features = ["physics"] diff --git a/crates/apsis-rs/examples/dump_iau2000.rs b/crates/apsis-rs/examples/dump_iau2000.rs new file mode 100644 index 0000000..bced8e6 --- /dev/null +++ b/crates/apsis-rs/examples/dump_iau2000.rs @@ -0,0 +1,92 @@ +//! Writes the IAU 2000/2006 Earth orientation quantities computed by this +//! workspace, for cross-checking against ERFA. +//! +//! Usage: +//! +//! ```text +//! cargo run -p apsis-rs --features physics --example dump_iau2000 \ +//! > validation/data/expected/rust_iau2000.csv +//! ``` + +use apsis_frames::iau2000::{ + PolarMotion, bias_precession_nutation_matrix, celestial_to_terrestrial_matrix, + greenwich_apparent_sidereal_time, mean_obliquity, nutation_2000a, + nutation_2000a_with_2006_adjustment, precession_angles, +}; +use apsis_math::Mat3; + +/// The Modified Julian Dates sampled. They span from 1970 to 2050 so that +/// the precession is exercised over a range of a century. +const MJD: &[f64] = &[ + 40_587.0, 51_544.5, 53_000.0, 55_000.0, 57_000.0, 58_000.0, 60_000.0, 62_000.0, +]; + +/// The Terrestrial Time offset from TAI, in seconds. +const TT_MINUS_TAI: f64 = 32.184; + +/// The TAI minus UTC offset used for this check, in seconds. It is the value +/// in force from 2017 onward. +const TAI_MINUS_UTC: f64 = 37.0; + +/// Returns the TT Julian date for a Modified Julian Date on the UTC scale. +fn tt_julian_date(utc_mjd: f64) -> f64 { + // TAI = UTC + 37, TT = TAI + 32.184, so TT = UTC + 69.184 seconds. + utc_mjd + 2_400_000.5 + (TT_MINUS_TAI + TAI_MINUS_UTC) / 86_400.0 +} + +fn main() { + println!("mjd,quantity,index,value"); + for &mjd in MJD { + let tt = tt_julian_date(mjd); + let t = (tt - 2_451_545.0) / 36_525.0; + + // The obliquity, in radians. + println!("{mjd},obliquity,0,{:.17e}", mean_obliquity(t)); + + // The nutation, from the IAU 2000A model. + let nutation = nutation_2000a(t); + println!("{mjd},nutation_longitude_a,0,{:.17e}", nutation.longitude); + println!("{mjd},nutation_obliquity_a,0,{:.17e}", nutation.obliquity); + + // The nutation with the IAU 2006 adjustment. + let adjusted = nutation_2000a_with_2006_adjustment(t); + println!("{mjd},nutation_longitude_06a,0,{:.17e}", adjusted.longitude); + println!("{mjd},nutation_obliquity_06a,0,{:.17e}", adjusted.obliquity); + + // The four precession angles. + let angles = precession_angles(t); + println!("{mjd},precession_gamma_bar,0,{:.17e}", angles.gamma_bar); + println!("{mjd},precession_phi_bar,0,{:.17e}", angles.phi_bar); + println!("{mjd},precession_psi_bar,0,{:.17e}", angles.psi_bar); + println!("{mjd},precession_epsilon,0,{:.17e}", angles.epsilon); + + // The bias-precession-nutation matrix, which carries the celestial + // reference frame to the true equator and equinox of date. + let bpn = bias_precession_nutation_matrix(t); + for row in 0..3 { + for column in 0..3 { + let value = bpn.get(row, column).expect("the indices are in range"); + println!("{mjd},bpn,{},{:.17e}", row * 3 + column, value); + } + } + + // Greenwich apparent sidereal time, in radians. + println!( + "{mjd},gast,0,{:.17e}", + greenwich_apparent_sidereal_time(tt, tt) + ); + + // The celestial-to-terrestrial matrix, with zero polar motion. + let matrix = celestial_to_terrestrial_matrix(tt, tt, PolarMotion::NONE); + for row in 0..3 { + for column in 0..3 { + let value = matrix.get(row, column).expect("the indices are in range"); + println!("{mjd},c2t,{},{:.17e}", row * 3 + column, value); + } + } + } +} + +/// Keeps the matrix type in scope for the documentation build. +#[allow(dead_code)] +fn _uses_matrix(_matrix: Mat3) {} diff --git a/crates/physics/apsis-frames/src/iau2000/eect_table.rs b/crates/physics/apsis-frames/src/iau2000/eect_table.rs new file mode 100644 index 0000000..663bd2d --- /dev/null +++ b/crates/physics/apsis-frames/src/iau2000/eect_table.rs @@ -0,0 +1,158 @@ +//! The IAU 2000 complementary terms of the equation of the equinoxes. +//! +//! The table is generated from the reference implementation by +//! `validation/tools/generate_eect_table.py` and is reproduced without +//! change. +//! +//! Source: the MHB2000 model, as distributed with the IAU SOFA library +//! and implemented by ERFA. + +use super::ComplementaryTerm; + +/// The terms that do not depend on time. +/// +/// The eight multipliers apply to the arguments `l`, `l'`, `F`, `D`, `Om`, +/// the mean longitude of Venus, the mean longitude of the Earth, and the +/// general accumulated precession, in that order. +pub static CONSTANT_TERMS: [ComplementaryTerm; 33] = [ + ComplementaryTerm { + argument: [0, 0, 0, 0, 1, 0, 0, 0], + coefficients: [2640.96e-6, -0.39e-6], + }, + ComplementaryTerm { + argument: [0, 0, 0, 0, 2, 0, 0, 0], + coefficients: [63.52e-6, -0.02e-6], + }, + ComplementaryTerm { + argument: [0, 0, 2, -2, 3, 0, 0, 0], + coefficients: [11.75e-6, 0.01e-6], + }, + ComplementaryTerm { + argument: [0, 0, 2, -2, 1, 0, 0, 0], + coefficients: [11.21e-6, 0.01e-6], + }, + ComplementaryTerm { + argument: [0, 0, 2, -2, 2, 0, 0, 0], + coefficients: [-4.55e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [0, 0, 2, 0, 3, 0, 0, 0], + coefficients: [2.02e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [0, 0, 2, 0, 1, 0, 0, 0], + coefficients: [1.98e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [0, 0, 0, 0, 3, 0, 0, 0], + coefficients: [-1.72e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [0, 1, 0, 0, 1, 0, 0, 0], + coefficients: [-1.41e-6, -0.01e-6], + }, + ComplementaryTerm { + argument: [0, 1, 0, 0, -1, 0, 0, 0], + coefficients: [-1.26e-6, -0.01e-6], + }, + ComplementaryTerm { + argument: [1, 0, 0, 0, -1, 0, 0, 0], + coefficients: [-0.63e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [1, 0, 0, 0, 1, 0, 0, 0], + coefficients: [-0.63e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [0, 1, 2, -2, 3, 0, 0, 0], + coefficients: [0.46e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [0, 1, 2, -2, 1, 0, 0, 0], + coefficients: [0.45e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [0, 0, 4, -4, 4, 0, 0, 0], + coefficients: [0.36e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [0, 0, 1, -1, 1, -8, 12, 0], + coefficients: [-0.24e-6, -0.12e-6], + }, + ComplementaryTerm { + argument: [0, 0, 2, 0, 0, 0, 0, 0], + coefficients: [0.32e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [0, 0, 2, 0, 2, 0, 0, 0], + coefficients: [0.28e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [1, 0, 2, 0, 3, 0, 0, 0], + coefficients: [0.27e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [1, 0, 2, 0, 1, 0, 0, 0], + coefficients: [0.26e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [0, 0, 2, -2, 0, 0, 0, 0], + coefficients: [-0.21e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [0, 1, -2, 2, -3, 0, 0, 0], + coefficients: [0.19e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [0, 1, -2, 2, -1, 0, 0, 0], + coefficients: [0.18e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [0, 0, 0, 0, 0, 8, -13, -1], + coefficients: [-0.10e-6, 0.05e-6], + }, + ComplementaryTerm { + argument: [0, 0, 0, 2, 0, 0, 0, 0], + coefficients: [0.15e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [2, 0, -2, 0, -1, 0, 0, 0], + coefficients: [-0.14e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [1, 0, 0, -2, 1, 0, 0, 0], + coefficients: [0.14e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [0, 1, 2, -2, 2, 0, 0, 0], + coefficients: [-0.14e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [1, 0, 0, -2, -1, 0, 0, 0], + coefficients: [0.14e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [0, 0, 4, -2, 4, 0, 0, 0], + coefficients: [0.13e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [0, 0, 2, -2, 4, 0, 0, 0], + coefficients: [-0.11e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [1, 0, -2, 0, -3, 0, 0, 0], + coefficients: [0.11e-6, 0.00e-6], + }, + ComplementaryTerm { + argument: [1, 0, -2, 0, -1, 0, 0, 0], + coefficients: [0.11e-6, 0.00e-6], + }, +]; + +/// The terms whose amplitude grows linearly with time. +/// +/// The arguments are the same as for the constant terms. +pub static LINEAR_TERMS: [ComplementaryTerm; 1] = [ComplementaryTerm { + argument: [0, 0, 0, 0, 1, 0, 0, 0], + coefficients: [-0.87e-6, 0.00e-6], +}]; diff --git a/crates/physics/apsis-frames/src/iau2000/fundamental.rs b/crates/physics/apsis-frames/src/iau2000/fundamental.rs new file mode 100644 index 0000000..59b6b57 --- /dev/null +++ b/crates/physics/apsis-frames/src/iau2000/fundamental.rs @@ -0,0 +1,273 @@ +//! The fundamental arguments of the IAU 2000 nutation theory. +//! +//! The nutation series is a sum of periodic terms whose arguments are linear +//! functions of time. Each term is identified by integer multipliers applied +//! to these arguments, so the arguments must be evaluated in a fixed order. +//! +//! Two argument sets appear in the theory and they are not the same, which +//! is a detail that is easy to get wrong: +//! +//! - The **luni-solar** series uses the five Delaunay arguments in the order +//! `l`, `l'`, `F`, `D`, `Om`: the mean anomaly of the Moon, the mean +//! anomaly of the Sun, the mean argument of latitude of the Moon, the mean +//! elongation of the Moon from the Sun, and the mean longitude of the +//! Moon's ascending node. +//! - The **planetary** series uses `l`, `F`, `D`, `Om`, the mean longitudes +//! of Mercury through Uranus, the mean longitude of Neptune, and the +//! general accumulated precession in longitude. +//! +//! The reference evaluates `l'` and `D` with inline expressions while using +//! functions for the others, and the inline expressions differ in the last +//! digits from the functions of the same name in the older IERS 2003 +//! conventions. The values here are the ones the series was fitted with, so +//! the inline forms are reproduced. +//! +//! All arguments are in radians and are reduced into `[0, 2 pi)`. +//! +//! Source: the argument definitions of the MHB2000 model as implemented in +//! `eraNut00a`, with the planetary longitudes from `eraFame03`, +//! `eraFave03`, `eraFae03`, `eraFama03`, `eraFaju03`, `eraFasa03` and +//! `eraFaur03`. + +use core::f64::consts::PI; + +/// Converts arcseconds to radians. +const ARCSECOND_TO_RADIAN: f64 = PI / (180.0 * 3_600.0); + +/// The number of arcs in a full turn, in arcseconds. +const TURN_ARCSECONDS: f64 = 1_296_000.0; + +/// Returns a value reduced into `[0, 2 pi)`. +fn anp(angle: f64) -> f64 { + angle.rem_euclid(2.0 * PI) +} + +/// Returns the mean anomaly of the Moon, in radians. +/// +/// This is the Delaunay argument `l`, from the IERS 2003 expressions. +pub fn mean_anomaly_moon(t: f64) -> f64 { + let arcseconds = 485_868.249_036 + + t * (1_717_915_923.217_8 + t * (31.879_2 + t * (0.051_635 + t * (-0.000_244_70)))); + anp((arcseconds % TURN_ARCSECONDS) * ARCSECOND_TO_RADIAN) +} + +/// Returns the mean anomaly of the Sun, in radians. +/// +/// This is the Delaunay argument `l'`. The reference evaluates it inline +/// rather than through the general function, and the two differ slightly. +pub fn mean_anomaly_sun(t: f64) -> f64 { + let arcseconds = 1_287_104.793_05 + + t * (129_596_581.048_1 + t * (-0.553_2 + t * (0.000_136 + t * (-0.000_011_49)))); + anp((arcseconds % TURN_ARCSECONDS) * ARCSECOND_TO_RADIAN) +} + +/// Returns the mean anomaly of the Sun from the IERS 2003 expressions. +/// +/// This differs from [`mean_anomaly_sun`] in the last digits of the constant +/// and linear terms. The nutation series uses the inline form; the +/// complementary terms of the equation of the equinoxes use this one. +/// +/// Source: as implemented by `eraFalp03`. +pub fn mean_anomaly_sun_iers2003(t: f64) -> f64 { + let arcseconds = 1_287_104.793_048 + + t * (129_596_581.048_1 + t * (-0.553_2 + t * (0.000_136 + t * (-0.000_011_49)))); + anp((arcseconds % TURN_ARCSECONDS) * ARCSECOND_TO_RADIAN) +} + +/// Returns the mean elongation of the Moon from the Sun from the IERS 2003 +/// expressions. +/// +/// This differs from [`mean_elongation_moon_sun`] in the last digits of the +/// constant term. The nutation series uses the inline form; the +/// complementary terms of the equation of the equinoxes use this one. +/// +/// Source: as implemented by `eraFad03`. +pub fn mean_elongation_moon_sun_iers2003(t: f64) -> f64 { + let arcseconds = 1_072_260.703_692 + + t * (1_602_961_601.209_0 + t * (-6.370_6 + t * (0.006_593 + t * (-0.000_031_69)))); + anp((arcseconds % TURN_ARCSECONDS) * ARCSECOND_TO_RADIAN) +} + +/// Returns the mean argument of latitude of the Moon, in radians. +/// +/// This is the Delaunay argument `F`, the mean longitude of the Moon minus +/// the mean longitude of its ascending node. +pub fn mean_latitude_moon(t: f64) -> f64 { + let arcseconds = 335_779.526_232 + + t * (1_739_527_262.847_8 + t * (-12.751_2 + t * (-0.001_037 + t * (0.000_004_17)))); + anp((arcseconds % TURN_ARCSECONDS) * ARCSECOND_TO_RADIAN) +} + +/// Returns the mean elongation of the Moon from the Sun, in radians. +/// +/// This is the Delaunay argument `D`. The reference evaluates it inline. +pub fn mean_elongation_moon_sun(t: f64) -> f64 { + let arcseconds = 1_072_260.703_69 + + t * (1_602_961_601.209_0 + t * (-6.370_6 + t * (0.006_593 + t * (-0.000_031_69)))); + anp((arcseconds % TURN_ARCSECONDS) * ARCSECOND_TO_RADIAN) +} + +/// Returns the mean longitude of the Moon's ascending node, in radians. +/// +/// This is the Delaunay argument `Om`. +pub fn mean_longitude_node(t: f64) -> f64 { + let arcseconds = 450_160.398_036 + + t * (-6_962_890.543_1 + t * (7.472_2 + t * (0.007_702 + t * (-0.000_059_39)))); + anp((arcseconds % TURN_ARCSECONDS) * ARCSECOND_TO_RADIAN) +} + +/// Returns the mean longitude of Mercury, in radians. +pub fn mean_longitude_mercury(t: f64) -> f64 { + anp(4.402_608_842 + 2_608.790_314_157_4 * t) +} + +/// Returns the mean longitude of Venus, in radians. +pub fn mean_longitude_venus(t: f64) -> f64 { + anp(3.176_146_697 + 1_021.328_554_621_1 * t) +} + +/// Returns the mean longitude of the Earth, in radians. +pub fn mean_longitude_earth(t: f64) -> f64 { + anp(1.753_470_314 + 628.307_584_999_1 * t) +} + +/// Returns the mean longitude of Mars, in radians. +pub fn mean_longitude_mars(t: f64) -> f64 { + anp(6.203_480_913 + 334.061_242_670_0 * t) +} + +/// Returns the mean longitude of Jupiter, in radians. +pub fn mean_longitude_jupiter(t: f64) -> f64 { + anp(0.599_546_497 + 52.969_096_264_1 * t) +} + +/// Returns the mean longitude of Saturn, in radians. +pub fn mean_longitude_saturn(t: f64) -> f64 { + anp(0.874_016_757 + 21.329_910_496_0 * t) +} + +/// Returns the mean longitude of Uranus, in radians. +pub fn mean_longitude_uranus(t: f64) -> f64 { + anp(5.481_293_872 + 7.478_159_856_7 * t) +} + +/// Returns the mean longitude of Neptune, in radians. +/// +/// The reference evaluates this inline, from the MHB2000 model rather than +/// from the IERS 2003 expressions used for the other planets. +pub fn mean_longitude_neptune(t: f64) -> f64 { + anp(5.321_159_000 + 3.812_777_400_0 * t) +} + +/// Returns the general accumulated precession in longitude, in radians. +pub fn general_precession(t: f64) -> f64 { + (0.024_381_750 + 0.000_005_386_91 * t) * t +} + +/// The five Delaunay arguments, in the order the luni-solar series uses. +#[derive(Debug, Clone, Copy, PartialEq)] +pub struct DelaunayArguments { + /// The mean anomaly of the Moon. + pub l: f64, + /// The mean anomaly of the Sun. + pub l_prime: f64, + /// The mean argument of latitude of the Moon. + pub f: f64, + /// The mean elongation of the Moon from the Sun. + pub d: f64, + /// The mean longitude of the Moon's ascending node. + pub omega: f64, +} + +impl DelaunayArguments { + /// Returns the five arguments for a time in Julian centuries. + pub fn at(t: f64) -> Self { + Self { + l: mean_anomaly_moon(t), + l_prime: mean_anomaly_sun(t), + f: mean_latitude_moon(t), + d: mean_elongation_moon_sun(t), + omega: mean_longitude_node(t), + } + } + + /// Returns the arguments as an array in series order. + pub const fn as_array(self) -> [f64; 5] { + [self.l, self.l_prime, self.f, self.d, self.omega] + } +} + +/// The thirteen arguments of the planetary series, in series order. +/// +/// The order is `l`, `F`, `D`, `Om`, Mercury through Uranus, Neptune, and the +/// general accumulated precession. Note that `l'` does not appear; the +/// planetary series uses the Moon's mean anomaly, not the Sun's. +#[derive(Debug, Clone, Copy, PartialEq)] +pub struct PlanetaryArguments { + /// The mean anomaly of the Moon. + pub l: f64, + /// The mean argument of latitude of the Moon. + pub f: f64, + /// The mean elongation of the Moon from the Sun. + pub d: f64, + /// The mean longitude of the Moon's ascending node. + pub omega: f64, + /// The mean longitude of Mercury. + pub mercury: f64, + /// The mean longitude of Venus. + pub venus: f64, + /// The mean longitude of the Earth. + pub earth: f64, + /// The mean longitude of Mars. + pub mars: f64, + /// The mean longitude of Jupiter. + pub jupiter: f64, + /// The mean longitude of Saturn. + pub saturn: f64, + /// The mean longitude of Uranus. + pub uranus: f64, + /// The mean longitude of Neptune. + pub neptune: f64, + /// The general accumulated precession in longitude. + pub precession: f64, +} + +impl PlanetaryArguments { + /// Returns the arguments for a time in Julian centuries. + pub fn at(t: f64) -> Self { + Self { + l: mean_anomaly_moon(t), + f: mean_latitude_moon(t), + d: mean_elongation_moon_sun(t), + omega: mean_longitude_node(t), + mercury: mean_longitude_mercury(t), + venus: mean_longitude_venus(t), + earth: mean_longitude_earth(t), + mars: mean_longitude_mars(t), + jupiter: mean_longitude_jupiter(t), + saturn: mean_longitude_saturn(t), + uranus: mean_longitude_uranus(t), + neptune: mean_longitude_neptune(t), + precession: general_precession(t), + } + } + + /// Returns the arguments as an array in series order. + pub const fn as_array(self) -> [f64; 13] { + [ + self.l, + self.f, + self.d, + self.omega, + self.mercury, + self.venus, + self.earth, + self.mars, + self.jupiter, + self.saturn, + self.uranus, + self.neptune, + self.precession, + ] + } +} diff --git a/crates/physics/apsis-frames/src/iau2000/mod.rs b/crates/physics/apsis-frames/src/iau2000/mod.rs new file mode 100644 index 0000000..8ddce8d --- /dev/null +++ b/crates/physics/apsis-frames/src/iau2000/mod.rs @@ -0,0 +1,105 @@ +//! The IAU 2000/2006 Earth orientation models. +//! +//! The transformation from an inertial frame to an Earth-fixed frame is a +//! sequence of rotations, each from a different model: +//! +//! 1. The **frame bias**, a constant rotation from the International +//! Celestial Reference System to the dynamical mean equator and equinox +//! of J2000.0. +//! 2. The **precession**, the secular motion of the pole, from the P03 +//! theory adopted in 2006. +//! 3. The **nutation**, the periodic motion of the pole, from the MHB2000 +//! series adopted in 2000. +//! 4. The **Earth rotation angle**, which carries the frame from the +//! celestial to the terrestrial meridian. +//! 5. The **polar motion**, the small motion of the pole within the Earth, +//! which a caller supplies because it is published as a daily measured +//! quantity. +//! +//! The composition of the first three is the celestial-to-intermediate +//! matrix, and the composition with the rotation angle and the polar motion +//! is the celestial-to-terrestrial matrix. For satellite work the polar +//! motion is often omitted, because it is under a tenth of an arcsecond, +//! but the nutation and precession are not: the nutation reaches seventeen +//! arcseconds, which is half a kilometer of ground position for a low Earth +//! satellite. +//! +//! All times are Julian centuries from J2000.0 on the Terrestrial Time +//! scale, unless a function says otherwise. The angles a caller supplies to +//! the polar motion are in radians. +//! +//! Source: the models and the order of the rotations follow the IAU SOFA +//! library and its ERFA derivative. The specific functions are named in each +//! module. + +mod eect_table; +mod fundamental; +mod nutation; +mod nutation_table; +mod precession; +mod terrestrial; + +pub use fundamental::{ + DelaunayArguments, PlanetaryArguments, general_precession, mean_anomaly_moon, mean_anomaly_sun, + mean_anomaly_sun_iers2003, mean_elongation_moon_sun, mean_elongation_moon_sun_iers2003, + mean_latitude_moon, mean_longitude_earth, mean_longitude_jupiter, mean_longitude_mars, + mean_longitude_mercury, mean_longitude_neptune, mean_longitude_node, mean_longitude_saturn, + mean_longitude_uranus, mean_longitude_venus, +}; +pub use nutation::{Nutation, nutation_2000a, nutation_2000a_with_2006_adjustment}; +pub use precession::{ + FRAME_BIAS_DECLINATION, FRAME_BIAS_LONGITUDE, FRAME_BIAS_RIGHT_ASCENSION, PrecessionAngles, + bias_precession_matrix, frame_bias_matrix, frame_to_mean_of_date, mean_obliquity, + precession_angles, rotation_z, +}; +pub use terrestrial::{ + PolarMotion, bias_precession_nutation_matrix, celestial_to_terrestrial_matrix, + earth_rotation_angle, equation_of_the_equinoxes, equation_of_the_equinoxes_complementary_terms, + greenwich_apparent_sidereal_time, greenwich_mean_sidereal_time, + intermediate_to_terrestrial_matrix, +}; + +/// One term of the luni-solar nutation series. +/// +/// The five multipliers are applied to the Delaunay arguments in the order +/// `l`, `l'`, `F`, `D`, `Om`. The six coefficients are the longitude sine, +/// its time derivative, the longitude cosine, the obliquity cosine, its time +/// derivative, and the obliquity sine, in units of 0.1 microarcsecond. +#[derive(Debug, Clone, Copy)] +pub struct SeriesTerm { + /// The integer multipliers of the five Delaunay arguments. + pub argument: [i32; 5], + /// The six coefficients of the term, in the order the reference lists + /// them. + pub coefficients: [f64; 6], +} + +/// One term of the complementary terms of the equation of the equinoxes. +/// +/// The eight multipliers apply to the arguments `l`, `l'`, `F`, `D`, `Om`, +/// the mean longitude of Venus, the mean longitude of the Earth, and the +/// general accumulated precession. The two coefficients are the sine and +/// cosine amplitudes, in arcseconds. +#[derive(Debug, Clone, Copy)] +pub struct ComplementaryTerm { + /// The integer multipliers of the eight arguments. + pub argument: [i32; 8], + /// The sine and cosine coefficients. + pub coefficients: [f64; 2], +} + +/// One term of the planetary nutation series. +/// +/// The thirteen multipliers are applied to the planetary arguments in the +/// order `l`, `F`, `D`, `Om`, Mercury through Uranus, Neptune, and the +/// general accumulated precession. The four coefficients are the longitude +/// sine, the longitude cosine, the obliquity sine, and the obliquity cosine, +/// in units of 0.1 microarcsecond. +#[derive(Debug, Clone, Copy)] +pub struct PlanetaryTerm { + /// The integer multipliers of the thirteen planetary arguments. + pub argument: [i32; 13], + /// The four coefficients of the term, in the order the reference lists + /// them. + pub coefficients: [f64; 4], +} diff --git a/crates/physics/apsis-frames/src/iau2000/nutation.rs b/crates/physics/apsis-frames/src/iau2000/nutation.rs new file mode 100644 index 0000000..93a1876 --- /dev/null +++ b/crates/physics/apsis-frames/src/iau2000/nutation.rs @@ -0,0 +1,154 @@ +//! The IAU 2000A nutation model. +//! +//! Nutation is the periodic part of the motion of the Earth's rotation axis +//! about its mean position. It is caused mainly by the torque of the Moon +//! and the Sun on the equatorial bulge, with smaller contributions from the +//! planets. The model gives the offset of the true pole from the mean pole +//! as two angles: the nutation in longitude and the nutation in obliquity. +//! +//! The series has two parts whose arguments and coefficient groupings +//! differ. The luni-solar part has 678 terms built from the Delaunay +//! arguments, and its obliquity coefficient pairs the cosine with the +//! constant and time terms while the sine stands alone. The planetary part +//! has 687 terms built from the planetary longitudes, and there the sine +//! pairs with the constant and the cosine stands alone. Getting those two +//! groupings the same way round produces an error of arcseconds, so they are +//! kept separate here. +//! +//! Source: the MHB2000 model of Mathews, Herring and Buffett, adopted by the +//! International Astronomical Union in 2000, as implemented in the IAU SOFA +//! library and its ERFA derivative, functions `eraNut00a` and `eraNut06a`. + +use super::fundamental::{DelaunayArguments, PlanetaryArguments}; +use super::nutation_table::{LUNI_SOLAR, PLANETARY}; +use super::{PlanetaryTerm, SeriesTerm}; +use core::f64::consts::PI; + +/// Converts a coefficient in units of 0.1 microarcsecond to radians. +const UNIT_TO_RADIAN: f64 = 1.0e-7 * PI / (180.0 * 3_600.0); + +/// Converts arcseconds to radians. +const ARCSECOND_TO_RADIAN: f64 = PI / (180.0 * 3_600.0); + +/// The nutation in longitude and obliquity, in radians. +#[derive(Debug, Clone, Copy, PartialEq, Default)] +pub struct Nutation { + /// The nutation in longitude, in radians. + pub longitude: f64, + /// The nutation in obliquity, in radians. + pub obliquity: f64, +} + +impl Nutation { + /// Creates a nutation from its two angles. + pub const fn new(longitude: f64, obliquity: f64) -> Self { + Self { + longitude, + obliquity, + } + } + + /// Returns the nutation in longitude, in arcseconds. + pub fn longitude_arcseconds(self) -> f64 { + self.longitude / ARCSECOND_TO_RADIAN + } + + /// Returns the nutation in obliquity, in arcseconds. + pub fn obliquity_arcseconds(self) -> f64 { + self.obliquity / ARCSECOND_TO_RADIAN + } + + /// Returns the sum of two nutations. + pub const fn plus(self, other: Self) -> Self { + Self::new( + self.longitude + other.longitude, + self.obliquity + other.obliquity, + ) + } +} + +/// Evaluates one term of the luni-solar series. +/// +/// The five multipliers are applied to the Delaunay arguments. The longitude +/// is the sum of a time dependent sine, a constant sine, and a cosine. The +/// obliquity is the sum of a time dependent cosine, a constant cosine, and a +/// sine. +fn lunisolar_term(term: &SeriesTerm, arguments: &DelaunayArguments, t: f64) -> Nutation { + let multipliers = &term.argument; + let c = &term.coefficients; + let argument = f64::from(multipliers[0]) * arguments.l + + f64::from(multipliers[1]) * arguments.l_prime + + f64::from(multipliers[2]) * arguments.f + + f64::from(multipliers[3]) * arguments.d + + f64::from(multipliers[4]) * arguments.omega; + let (sine, cosine) = argument.sin_cos(); + + // The order is the one the reference uses: sp, spt, cp, ce, cet, se. + Nutation::new( + (c[0] + c[1] * t) * sine + c[2] * cosine, + (c[3] + c[4] * t) * cosine + c[5] * sine, + ) +} + +/// Evaluates one term of the planetary series. +/// +/// The thirteen multipliers are applied to the planetary arguments. The +/// longitude is a sine plus a cosine, and the obliquity is a sine plus a +/// cosine, with no time dependence in either. +fn planetary_term(term: &PlanetaryTerm, arguments: &PlanetaryArguments) -> Nutation { + let multipliers = &term.argument; + let c = &term.coefficients; + let values = arguments.as_array(); + let mut argument = 0.0; + for index in 0..13 { + argument += f64::from(multipliers[index]) * values[index]; + } + let (sine, cosine) = argument.sin_cos(); + + // The order is the one the reference uses: sp, cp, se, ce. + Nutation::new(c[0] * sine + c[1] * cosine, c[2] * sine + c[3] * cosine) +} + +/// Returns the nutation in longitude and obliquity for a time. +/// +/// The time is in Julian centuries from J2000.0 on the Terrestrial Time +/// scale. This is the IAU 2000A model, which includes the planetary terms. +/// +/// Source: IAU 2000A, as implemented by `eraNut00a`. +pub fn nutation_2000a(t: f64) -> Nutation { + let delaunay = DelaunayArguments::at(t); + let planetary = PlanetaryArguments::at(t); + + let mut sum = Nutation::default(); + for term in LUNI_SOLAR.iter() { + sum = sum.plus(lunisolar_term(term, &delaunay, t)); + } + for term in PLANETARY.iter() { + sum = sum.plus(planetary_term(term, &planetary)); + } + + Nutation::new( + sum.longitude * UNIT_TO_RADIAN, + sum.obliquity * UNIT_TO_RADIAN, + ) +} + +/// Returns the nutation with the IAU 2006 precession adjustments applied. +/// +/// The IAU 2000A model was built on the IAU 1976 precession, and the IAU +/// 2006 precession changed the precession rates. The adjustment brings the +/// nutation into consistency with the newer precession, which is the +/// combination used for the modern celestial-to-terrestrial transformation. +/// +/// Source: IAU 2006, as implemented by `eraNut06a`, which applies the +/// expressions of Wallace and Capitaine (2006), equations 5. +pub fn nutation_2000a_with_2006_adjustment(t: f64) -> Nutation { + let nutation = nutation_2000a(t); + // The adjustment scales the nutation itself rather than adding an + // independent term, which is why it is written as a factor. + let fj2 = -2.777_4e-6 * t; + Nutation::new( + nutation.longitude * (1.0 + 0.469_7e-6 + fj2), + nutation.obliquity * (1.0 + fj2), + ) +} diff --git a/crates/physics/apsis-frames/src/iau2000/nutation_table.rs b/crates/physics/apsis-frames/src/iau2000/nutation_table.rs new file mode 100644 index 0000000..d975f83 --- /dev/null +++ b/crates/physics/apsis-frames/src/iau2000/nutation_table.rs @@ -0,0 +1,5501 @@ +//! The IAU 2000A nutation series. +//! +//! The table is generated from the reference implementation of the +//! model by `validation/tools/generate_nutation_table.py` and is +//! reproduced without change. +//! +//! The field order follows the reference, which is not the order the +//! coefficients are listed in the paper. +//! +//! Source: the MHB2000 model of Mathews, Herring and Buffett, adopted by +//! the International Astronomical Union in 2000 and distributed as part +//! of the IAU SOFA library, as implemented by ERFA. + +use super::{PlanetaryTerm, SeriesTerm}; + +/// The luni-solar terms of the series. +/// +/// The multipliers apply to the arguments `l`, `l'`, `F`, `D`, and `Om` +/// in that order. The coefficients are the longitude sine, its time +/// derivative, the longitude cosine, the obliquity cosine, its time +/// derivative, and the obliquity sine, in units of 0.1 microarcsecond. +pub static LUNI_SOLAR: [SeriesTerm; 678] = [ + SeriesTerm { + argument: [0, 0, 0, 0, 1], + coefficients: [ + -172064161.0, + -174666.0, + 33386.0, + 92052331.0, + 9086.0, + 15377.0, + ], + }, + SeriesTerm { + argument: [0, 0, 2, -2, 2], + coefficients: [-13170906.0, -1675.0, -13696.0, 5730336.0, -3015.0, -4587.0], + }, + SeriesTerm { + argument: [0, 0, 2, 0, 2], + coefficients: [-2276413.0, -234.0, 2796.0, 978459.0, -485.0, 1374.0], + }, + SeriesTerm { + argument: [0, 0, 0, 0, 2], + coefficients: [2074554.0, 207.0, -698.0, -897492.0, 470.0, -291.0], + }, + SeriesTerm { + argument: [0, 1, 0, 0, 0], + coefficients: [1475877.0, -3633.0, 11817.0, 73871.0, -184.0, -1924.0], + }, + SeriesTerm { + argument: [0, 1, 2, -2, 2], + coefficients: [-516821.0, 1226.0, -524.0, 224386.0, -677.0, -174.0], + }, + SeriesTerm { + argument: [1, 0, 0, 0, 0], + coefficients: [711159.0, 73.0, -872.0, -6750.0, 0.0, 358.0], + }, + SeriesTerm { + argument: [0, 0, 2, 0, 1], + coefficients: [-387298.0, -367.0, 380.0, 200728.0, 18.0, 318.0], + }, + SeriesTerm { + argument: [1, 0, 2, 0, 2], + coefficients: [-301461.0, -36.0, 816.0, 129025.0, -63.0, 367.0], + }, + SeriesTerm { + argument: [0, -1, 2, -2, 2], + coefficients: [215829.0, -494.0, 111.0, -95929.0, 299.0, 132.0], + }, + SeriesTerm { + argument: [0, 0, 2, -2, 1], + coefficients: [128227.0, 137.0, 181.0, -68982.0, -9.0, 39.0], + }, + SeriesTerm { + argument: [-1, 0, 2, 0, 2], + coefficients: [123457.0, 11.0, 19.0, -53311.0, 32.0, -4.0], + }, + SeriesTerm { + argument: [-1, 0, 0, 2, 0], + coefficients: [156994.0, 10.0, -168.0, -1235.0, 0.0, 82.0], + }, + SeriesTerm { + argument: [1, 0, 0, 0, 1], + coefficients: [63110.0, 63.0, 27.0, -33228.0, 0.0, -9.0], + }, + SeriesTerm { + argument: [-1, 0, 0, 0, 1], + coefficients: [-57976.0, -63.0, -189.0, 31429.0, 0.0, -75.0], + }, + SeriesTerm { + argument: [-1, 0, 2, 2, 2], + coefficients: [-59641.0, -11.0, 149.0, 25543.0, -11.0, 66.0], + }, + SeriesTerm { + argument: [1, 0, 2, 0, 1], + coefficients: [-51613.0, -42.0, 129.0, 26366.0, 0.0, 78.0], + }, + SeriesTerm { + argument: [-2, 0, 2, 0, 1], + coefficients: [45893.0, 50.0, 31.0, -24236.0, -10.0, 20.0], + }, + SeriesTerm { + argument: [0, 0, 0, 2, 0], + coefficients: [63384.0, 11.0, -150.0, -1220.0, 0.0, 29.0], + }, + SeriesTerm { + argument: [0, 0, 2, 2, 2], + coefficients: [-38571.0, -1.0, 158.0, 16452.0, -11.0, 68.0], + }, + SeriesTerm { + argument: [0, -2, 2, -2, 2], + coefficients: [32481.0, 0.0, 0.0, -13870.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [-2, 0, 0, 2, 0], + coefficients: [-47722.0, 0.0, -18.0, 477.0, 0.0, -25.0], + }, + SeriesTerm { + argument: [2, 0, 2, 0, 2], + coefficients: [-31046.0, -1.0, 131.0, 13238.0, -11.0, 59.0], + }, + SeriesTerm { + argument: [1, 0, 2, -2, 2], + coefficients: [28593.0, 0.0, -1.0, -12338.0, 10.0, -3.0], + }, + SeriesTerm { + argument: [-1, 0, 2, 0, 1], + coefficients: [20441.0, 21.0, 10.0, -10758.0, 0.0, -3.0], + }, + SeriesTerm { + argument: [2, 0, 0, 0, 0], + coefficients: [29243.0, 0.0, -74.0, -609.0, 0.0, 13.0], + }, + SeriesTerm { + argument: [0, 0, 2, 0, 0], + coefficients: [25887.0, 0.0, -66.0, -550.0, 0.0, 11.0], + }, + SeriesTerm { + argument: [0, 1, 0, 0, 1], + coefficients: [-14053.0, -25.0, 79.0, 8551.0, -2.0, -45.0], + }, + SeriesTerm { + argument: [-1, 0, 0, 2, 1], + coefficients: [15164.0, 10.0, 11.0, -8001.0, 0.0, -1.0], + }, + SeriesTerm { + argument: [0, 2, 2, -2, 2], + coefficients: [-15794.0, 72.0, -16.0, 6850.0, -42.0, -5.0], + }, + SeriesTerm { + argument: [0, 0, -2, 2, 0], + coefficients: [21783.0, 0.0, 13.0, -167.0, 0.0, 13.0], + }, + SeriesTerm { + argument: [1, 0, 0, -2, 1], + coefficients: [-12873.0, -10.0, -37.0, 6953.0, 0.0, -14.0], + }, + SeriesTerm { + argument: [0, -1, 0, 0, 1], + coefficients: [-12654.0, 11.0, 63.0, 6415.0, 0.0, 26.0], + }, + SeriesTerm { + argument: [-1, 0, 2, 2, 1], + coefficients: [-10204.0, 0.0, 25.0, 5222.0, 0.0, 15.0], + }, + SeriesTerm { + argument: [0, 2, 0, 0, 0], + coefficients: [16707.0, -85.0, -10.0, 168.0, -1.0, 10.0], + }, + SeriesTerm { + argument: [1, 0, 2, 2, 2], + coefficients: [-7691.0, 0.0, 44.0, 3268.0, 0.0, 19.0], + }, + SeriesTerm { + argument: [-2, 0, 2, 0, 0], + coefficients: [-11024.0, 0.0, -14.0, 104.0, 0.0, 2.0], + }, + SeriesTerm { + argument: [0, 1, 2, 0, 2], + coefficients: [7566.0, -21.0, -11.0, -3250.0, 0.0, -5.0], + }, + SeriesTerm { + argument: [0, 0, 2, 2, 1], + coefficients: [-6637.0, -11.0, 25.0, 3353.0, 0.0, 14.0], + }, + SeriesTerm { + argument: [0, -1, 2, 0, 2], + coefficients: [-7141.0, 21.0, 8.0, 3070.0, 0.0, 4.0], + }, + SeriesTerm { + argument: [0, 0, 0, 2, 1], + coefficients: [-6302.0, -11.0, 2.0, 3272.0, 0.0, 4.0], + }, + SeriesTerm { + argument: [1, 0, 2, -2, 1], + coefficients: [5800.0, 10.0, 2.0, -3045.0, 0.0, -1.0], + }, + SeriesTerm { + argument: [2, 0, 2, -2, 2], + coefficients: [6443.0, 0.0, -7.0, -2768.0, 0.0, -4.0], + }, + SeriesTerm { + argument: [-2, 0, 0, 2, 1], + coefficients: [-5774.0, -11.0, -15.0, 3041.0, 0.0, -5.0], + }, + SeriesTerm { + argument: [2, 0, 2, 0, 1], + coefficients: [-5350.0, 0.0, 21.0, 2695.0, 0.0, 12.0], + }, + SeriesTerm { + argument: [0, -1, 2, -2, 1], + coefficients: [-4752.0, -11.0, -3.0, 2719.0, 0.0, -3.0], + }, + SeriesTerm { + argument: [0, 0, 0, -2, 1], + coefficients: [-4940.0, -11.0, -21.0, 2720.0, 0.0, -9.0], + }, + SeriesTerm { + argument: [-1, -1, 0, 2, 0], + coefficients: [7350.0, 0.0, -8.0, -51.0, 0.0, 4.0], + }, + SeriesTerm { + argument: [2, 0, 0, -2, 1], + coefficients: [4065.0, 0.0, 6.0, -2206.0, 0.0, 1.0], + }, + SeriesTerm { + argument: [1, 0, 0, 2, 0], + coefficients: [6579.0, 0.0, -24.0, -199.0, 0.0, 2.0], + }, + SeriesTerm { + argument: [0, 1, 2, -2, 1], + coefficients: [3579.0, 0.0, 5.0, -1900.0, 0.0, 1.0], + }, + SeriesTerm { + argument: [1, -1, 0, 0, 0], + coefficients: [4725.0, 0.0, -6.0, -41.0, 0.0, 3.0], + }, + SeriesTerm { + argument: [-2, 0, 2, 0, 2], + coefficients: [-3075.0, 0.0, -2.0, 1313.0, 0.0, -1.0], + }, + SeriesTerm { + argument: [3, 0, 2, 0, 2], + coefficients: [-2904.0, 0.0, 15.0, 1233.0, 0.0, 7.0], + }, + SeriesTerm { + argument: [0, -1, 0, 2, 0], + coefficients: [4348.0, 0.0, -10.0, -81.0, 0.0, 2.0], + }, + SeriesTerm { + argument: [1, -1, 2, 0, 2], + coefficients: [-2878.0, 0.0, 8.0, 1232.0, 0.0, 4.0], + }, + SeriesTerm { + argument: [0, 0, 0, 1, 0], + coefficients: [-4230.0, 0.0, 5.0, -20.0, 0.0, -2.0], + }, + SeriesTerm { + argument: [-1, -1, 2, 2, 2], + coefficients: [-2819.0, 0.0, 7.0, 1207.0, 0.0, 3.0], + }, + SeriesTerm { + argument: [-1, 0, 2, 0, 0], + coefficients: [-4056.0, 0.0, 5.0, 40.0, 0.0, -2.0], + }, + SeriesTerm { + argument: [0, -1, 2, 2, 2], + coefficients: [-2647.0, 0.0, 11.0, 1129.0, 0.0, 5.0], + }, + SeriesTerm { + argument: [-2, 0, 0, 0, 1], + coefficients: [-2294.0, 0.0, -10.0, 1266.0, 0.0, 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-1, 2, 6, 2], + coefficients: [-3.0, 0.0, 0.0, 1.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [-1, 0, 0, 6, 1], + coefficients: [-5.0, 0.0, 0.0, 3.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [-3, 0, 2, 6, 1], + coefficients: [-3.0, 0.0, 0.0, 2.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [1, -1, 0, 4, 1], + coefficients: [-3.0, 0.0, 0.0, 2.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [1, -1, 0, 4, 0], + coefficients: [12.0, 0.0, 0.0, 0.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [-2, 0, 2, 5, 2], + coefficients: [3.0, 0.0, 0.0, -1.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [1, -2, 2, 2, 1], + coefficients: [-4.0, 0.0, 0.0, 2.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [3, -1, 0, 2, 0], + coefficients: [4.0, 0.0, 0.0, 0.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [1, -1, 2, 2, 0], + coefficients: [6.0, 0.0, 0.0, 0.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [0, 0, 2, 3, 1], + coefficients: [5.0, 0.0, 0.0, -3.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [-1, 1, 2, 4, 1], + coefficients: [4.0, 0.0, 0.0, -2.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [0, 1, 2, 3, 2], + coefficients: [-6.0, 0.0, 0.0, 3.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [-1, 0, 4, 2, 1], + coefficients: [4.0, 0.0, 0.0, -2.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [2, 0, 2, 1, 1], + coefficients: [6.0, 0.0, 0.0, -3.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [5, 0, 0, 0, 0], + coefficients: [6.0, 0.0, 0.0, 0.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [2, 1, 2, 1, 2], + coefficients: [-6.0, 0.0, 0.0, 3.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [1, 0, 4, 0, 1], + coefficients: [3.0, 0.0, 0.0, -2.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [3, 1, 2, 0, 1], + coefficients: [7.0, 0.0, 0.0, -4.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [3, 0, 4, -2, 2], + coefficients: [4.0, 0.0, 0.0, -2.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [-2, -1, 2, 6, 2], + coefficients: [-5.0, 0.0, 0.0, 2.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [0, 0, 0, 6, 0], + coefficients: [5.0, 0.0, 0.0, 0.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [0, -2, 2, 4, 2], + coefficients: [-6.0, 0.0, 0.0, 3.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [-2, 0, 2, 6, 1], + coefficients: [-6.0, 0.0, 0.0, 3.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [2, 0, 0, 4, 1], + coefficients: [-4.0, 0.0, 0.0, 2.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [2, 0, 0, 4, 0], + coefficients: [10.0, 0.0, 0.0, 0.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [2, -2, 2, 2, 2], + coefficients: [-4.0, 0.0, 0.0, 2.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [0, 0, 2, 4, 0], + coefficients: [7.0, 0.0, 0.0, 0.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [1, 0, 2, 3, 2], + coefficients: [7.0, 0.0, 0.0, -3.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [4, 0, 0, 2, 0], + coefficients: [4.0, 0.0, 0.0, 0.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [2, 0, 2, 2, 0], + coefficients: [11.0, 0.0, 0.0, 0.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [0, 0, 4, 2, 2], + coefficients: [5.0, 0.0, 0.0, -2.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [4, -1, 2, 0, 2], + coefficients: [-6.0, 0.0, 0.0, 2.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [3, 0, 2, 1, 2], + coefficients: [4.0, 0.0, 0.0, -2.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [2, 1, 2, 2, 1], + coefficients: [3.0, 0.0, 0.0, -2.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [4, 1, 2, 0, 2], + coefficients: [5.0, 0.0, 0.0, -2.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [-1, -1, 2, 6, 2], + coefficients: [-4.0, 0.0, 0.0, 2.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [-1, 0, 2, 6, 1], + coefficients: [-4.0, 0.0, 0.0, 2.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [1, -1, 2, 4, 1], + coefficients: [-3.0, 0.0, 0.0, 2.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [1, 1, 2, 4, 2], + coefficients: [4.0, 0.0, 0.0, -2.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [3, 1, 2, 2, 2], + coefficients: [3.0, 0.0, 0.0, -1.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [5, 0, 2, 0, 1], + coefficients: [-3.0, 0.0, 0.0, 1.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [2, -1, 2, 4, 2], + coefficients: [-3.0, 0.0, 0.0, 1.0, 0.0, 0.0], + }, + SeriesTerm { + argument: [2, 0, 2, 4, 1], + coefficients: [-3.0, 0.0, 0.0, 2.0, 0.0, 0.0], + }, +]; + +/// The planetary terms of the series. +/// +/// The multipliers apply to the arguments `l`, `F`, `D`, `Om`, the mean +/// longitudes of Mercury through Uranus, the mean longitude of Neptune, +/// and the general accumulated precession, in that order. The +/// coefficients are the longitude sine, the longitude cosine, the +/// obliquity sine, and the obliquity cosine, in units of 0.1 +/// microarcsecond. +pub static PLANETARY: [PlanetaryTerm; 687] = [ + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, 8, -16, 4, 5, 0, 0, 0], + coefficients: [1440.0, 0.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, -8, 16, -4, -5, 0, 0, 2], + coefficients: [56.0, -117.0, -42.0, -40.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, 8, -16, 4, 5, 0, 0, 2], + coefficients: [125.0, -43.0, 0.0, -54.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2], + coefficients: [0.0, 5.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, -4, 8, -1, -5, 0, 0, 2], + coefficients: [3.0, -7.0, -3.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 1], + coefficients: [3.0, 0.0, 0.0, -2.0], + }, + PlanetaryTerm { + argument: [0, 1, -1, 1, 0, 0, 3, -8, 3, 0, 0, 0, 0], + coefficients: [-114.0, 0.0, 0.0, 61.0], + }, + PlanetaryTerm { + argument: [-1, 0, 0, 0, 0, 10, -3, 0, 0, 0, 0, 0, 0], + coefficients: [-219.0, 89.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, 0, 0, -2, 6, -3, 0, 2], + coefficients: [-3.0, 0.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0], + coefficients: [-462.0, 1604.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 1, -1, 1, 0, 0, -5, 8, -3, 0, 0, 0, 0], + coefficients: [99.0, 0.0, 0.0, -53.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, -4, 8, -3, 0, 0, 0, 1], + coefficients: [-3.0, 0.0, 0.0, 2.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, 4, -8, 1, 5, 0, 0, 2], + coefficients: [0.0, 6.0, 2.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, -5, 6, 4, 0, 0, 0, 0, 2], + coefficients: [3.0, 0.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 2], + coefficients: [-12.0, 0.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 1], + coefficients: [14.0, -218.0, 117.0, 8.0], + }, + PlanetaryTerm { + argument: [0, 1, -1, 1, 0, 0, -1, 0, 2, -5, 0, 0, 0], + coefficients: [31.0, -481.0, -257.0, -17.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 0], + coefficients: [-491.0, 128.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 1, -1, 1, 0, 0, -1, 0, -2, 5, 0, 0, 0], + coefficients: [-3084.0, 5123.0, 2735.0, 1647.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, 0, 0, -2, 5, 0, 0, 1], + coefficients: [-1444.0, 2409.0, -1286.0, -771.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, 0, 0, -2, 5, 0, 0, 2], + coefficients: [11.0, -24.0, -11.0, -9.0], + }, + PlanetaryTerm { + argument: [2, -1, -1, 0, 0, 0, 3, -7, 0, 0, 0, 0, 0], + coefficients: [26.0, -9.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [1, 0, -2, 0, 0, 19, -21, 3, 0, 0, 0, 0, 0], + coefficients: [103.0, -60.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 1, -1, 1, 0, 2, -4, 0, -3, 0, 0, 0, 0], + coefficients: [0.0, -13.0, -7.0, 0.0], + }, + PlanetaryTerm { + argument: [1, 0, -1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0], + coefficients: [-26.0, -29.0, -16.0, 14.0], + }, + PlanetaryTerm { + argument: [0, 1, -1, 1, 0, 0, -1, 0, -4, 10, 0, 0, 0], + coefficients: [9.0, -27.0, -14.0, -5.0], + }, + PlanetaryTerm { + argument: [-2, 0, 2, 1, 0, 0, 2, 0, 0, -5, 0, 0, 0], + coefficients: [12.0, 0.0, 0.0, -6.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 3, -7, 4, 0, 0, 0, 0, 0], + coefficients: [-7.0, 0.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, -1, 1, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0], + coefficients: [0.0, 24.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [-2, 0, 2, 1, 0, 0, 2, 0, -2, 0, 0, 0, 0], + coefficients: [284.0, 0.0, 0.0, -151.0], + }, + PlanetaryTerm { + argument: [-1, 0, 0, 0, 0, 18, -16, 0, 0, 0, 0, 0, 0], + coefficients: [226.0, 101.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [-2, 1, 1, 2, 0, 0, 1, 0, -2, 0, 0, 0, 0], + coefficients: [0.0, -8.0, -2.0, 0.0], + }, + PlanetaryTerm { + argument: [-1, 1, -1, 1, 0, 18, -17, 0, 0, 0, 0, 0, 0], + coefficients: [0.0, -6.0, -3.0, 0.0], + }, + PlanetaryTerm { + argument: [-1, 0, 1, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0], + coefficients: [5.0, 0.0, 0.0, -3.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, -8, 13, 0, 0, 0, 0, 0, 2], + coefficients: [-41.0, 175.0, 76.0, 17.0], + }, + PlanetaryTerm { + argument: [0, 2, -2, 2, 0, -8, 11, 0, 0, 0, 0, 0, 0], + coefficients: [0.0, 15.0, 6.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, -8, 13, 0, 0, 0, 0, 0, 1], + coefficients: [425.0, 212.0, -133.0, 269.0], + }, + PlanetaryTerm { + argument: [0, 1, -1, 1, 0, -8, 12, 0, 0, 0, 0, 0, 0], + coefficients: [1200.0, 598.0, 319.0, -641.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 8, -13, 0, 0, 0, 0, 0, 0], + coefficients: [235.0, 334.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 1, -1, 1, 0, 8, -14, 0, 0, 0, 0, 0, 0], + coefficients: [11.0, -12.0, -7.0, -6.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 8, -13, 0, 0, 0, 0, 0, 1], + coefficients: [5.0, -6.0, 3.0, 3.0], + }, + PlanetaryTerm { + argument: [-2, 0, 2, 1, 0, 0, 2, 0, -4, 5, 0, 0, 0], + coefficients: [-5.0, 0.0, 0.0, 3.0], + }, + PlanetaryTerm { + argument: [-2, 0, 2, 2, 0, 3, -3, 0, 0, 0, 0, 0, 0], + coefficients: [6.0, 0.0, 0.0, -3.0], + }, + PlanetaryTerm { + argument: [-2, 0, 2, 0, 0, 0, 2, 0, -3, 1, 0, 0, 0], + coefficients: [15.0, 0.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 1, 0, 3, -5, 0, 2, 0, 0, 0, 0], + coefficients: [13.0, 0.0, 0.0, -7.0], + }, + PlanetaryTerm { + argument: [-2, 0, 2, 0, 0, 0, 2, 0, -4, 3, 0, 0, 0], + coefficients: [-6.0, -9.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, -1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0], + coefficients: [266.0, -78.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 1, 0, 0, -1, 2, 0, 0, 0, 0, 0], + coefficients: [-460.0, -435.0, -232.0, 246.0], + }, + PlanetaryTerm { + argument: [0, 1, -1, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0], + coefficients: [0.0, 15.0, 7.0, 0.0], + }, + PlanetaryTerm { + argument: [-1, 1, 0, 1, 0, 3, -5, 0, 0, 0, 0, 0, 0], + coefficients: [-3.0, 0.0, 0.0, 2.0], + }, + PlanetaryTerm { + argument: [-1, 0, 1, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0], + coefficients: [0.0, 131.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [-2, 0, 2, 0, 0, 0, 2, 0, -2, -2, 0, 0, 0], + coefficients: [4.0, 0.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [-2, 2, 0, 2, 0, 0, -5, 9, 0, 0, 0, 0, 0], + coefficients: [0.0, 3.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 1, -1, 1, 0, 0, -1, 0, 0, 0, -1, 0, 0], + coefficients: [0.0, 4.0, 2.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], + coefficients: [0.0, 3.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 2, 0], + coefficients: [-17.0, -19.0, -10.0, 9.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1], + coefficients: [-9.0, -11.0, 6.0, -5.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2], + coefficients: [-6.0, 0.0, 0.0, 3.0], + }, + PlanetaryTerm { + argument: [-1, 0, 1, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0], + coefficients: [-16.0, 8.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, -1, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0], + coefficients: [0.0, 3.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 1, -1, 2, 0, 0, -1, 0, 0, 2, 0, 0, 0], + coefficients: [11.0, 24.0, 11.0, -5.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 1, 0, 0, -9, 17, 0, 0, 0, 0, 0], + coefficients: [-3.0, -4.0, -2.0, 1.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 2, 0, -3, 5, 0, 0, 0, 0, 0, 0], + coefficients: [3.0, 0.0, 0.0, -1.0], + }, + PlanetaryTerm { + argument: [0, 1, -1, 1, 0, 0, -1, 0, -1, 2, 0, 0, 0], + coefficients: [0.0, -8.0, -4.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0], + coefficients: [0.0, 3.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [1, 0, -2, 0, 0, 17, -16, 0, -2, 0, 0, 0, 0], + coefficients: [0.0, 5.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 1, -1, 1, 0, 0, -1, 0, 1, -3, 0, 0, 0], + coefficients: [0.0, 3.0, 2.0, 0.0], + }, + PlanetaryTerm { + argument: [-2, 0, 2, 1, 0, 0, 5, -6, 0, 0, 0, 0, 0], + coefficients: [-6.0, 4.0, 2.0, 3.0], + }, + PlanetaryTerm { + argument: [0, -2, 2, 0, 0, 0, 9, -13, 0, 0, 0, 0, 0], + coefficients: [-3.0, -5.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 1, -1, 2, 0, 0, -1, 0, 0, 1, 0, 0, 0], + coefficients: [-5.0, 0.0, 0.0, 2.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], + coefficients: [4.0, 24.0, 13.0, -2.0], + }, + PlanetaryTerm { + argument: [0, -1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], + coefficients: [-42.0, 20.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, -2, 2, 0, 0, 5, -6, 0, 0, 0, 0, 0, 0], + coefficients: [-10.0, 233.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [0, -1, 1, 1, 0, 5, -7, 0, 0, 0, 0, 0, 0], + coefficients: [-3.0, 0.0, 0.0, 1.0], + }, + PlanetaryTerm { + argument: [-2, 0, 2, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0], + coefficients: [78.0, -18.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [2, 1, -3, 1, 0, -6, 7, 0, 0, 0, 0, 0, 0], + coefficients: [0.0, 3.0, 1.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0], + coefficients: [0.0, -3.0, -1.0, 0.0], + }, + PlanetaryTerm { + argument: [0, -1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0], + coefficients: [0.0, -4.0, -2.0, 1.0], + }, + PlanetaryTerm { + argument: [0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 2, 0, 0], + coefficients: [0.0, -8.0, -4.0, -1.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1], + coefficients: [0.0, -5.0, 3.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2], + coefficients: [-7.0, 0.0, 0.0, 3.0], + }, + PlanetaryTerm { + argument: [0, 0, 0, 0, 0, 0, -8, 15, 0, 0, 0, 0, 2], + coefficients: [-14.0, 8.0, 3.0, 6.0], + }, + 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coefficients: [-5.0, 0.0, 1.0, 2.0], + }, + PlanetaryTerm { + argument: [0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], + coefficients: [-3.0, 28.0, 15.0, 2.0], + }, + PlanetaryTerm { + argument: [1, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0], + coefficients: [5.0, 0.0, 1.0, -2.0], + }, + PlanetaryTerm { + argument: [0, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0], + coefficients: [0.0, 9.0, 4.0, 1.0], + }, + PlanetaryTerm { + argument: [0, 2, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0], + coefficients: [0.0, 9.0, 4.0, -1.0], + }, + PlanetaryTerm { + argument: [-1, 2, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0], + coefficients: [-126.0, -63.0, -27.0, 55.0], + }, + PlanetaryTerm { + argument: [2, 2, -2, 2, 0, 0, -2, 0, 3, 0, 0, 0, 0], + coefficients: [3.0, 0.0, 0.0, -1.0], + }, + PlanetaryTerm { + argument: [1, 2, 0, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0], + coefficients: [21.0, -11.0, -6.0, -11.0], + }, + PlanetaryTerm { + argument: [0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], + coefficients: [0.0, -4.0, 0.0, 0.0], + }, + PlanetaryTerm { + argument: [-1, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], + coefficients: [-21.0, -11.0, -6.0, 11.0], + }, + PlanetaryTerm { + argument: [-2, 2, 2, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0], + coefficients: [-3.0, 0.0, 0.0, 1.0], + }, + PlanetaryTerm { + argument: [0, 2, 0, 2, 0, 2, -3, 0, 0, 0, 0, 0, 0], + coefficients: [0.0, 3.0, 1.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0], + coefficients: [8.0, 0.0, 0.0, -4.0], + }, + PlanetaryTerm { + argument: [0, 2, 0, 2, 0, 0, 1, 0, -1, 0, 0, 0, 0], + coefficients: [-6.0, 0.0, 0.0, 3.0], + }, + PlanetaryTerm { + argument: [0, 2, 0, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0], + coefficients: [-3.0, 0.0, 0.0, 1.0], + }, + PlanetaryTerm { + argument: [-1, 2, 2, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0], + coefficients: [3.0, 0.0, 0.0, -1.0], + }, + PlanetaryTerm { + argument: [1, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0], + coefficients: [-3.0, 0.0, 0.0, 1.0], + }, + PlanetaryTerm { + argument: [-1, 2, 2, 2, 0, 0, 2, 0, -3, 0, 0, 0, 0], + coefficients: [-5.0, 0.0, 0.0, 2.0], + }, + PlanetaryTerm { + argument: [2, 2, 0, 2, 0, 0, 2, 0, -3, 0, 0, 0, 0], + coefficients: [24.0, -12.0, -5.0, -11.0], + }, + PlanetaryTerm { + argument: [1, 2, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0], + coefficients: [0.0, 3.0, 1.0, 0.0], + }, + PlanetaryTerm { + argument: [1, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0], + coefficients: [0.0, 3.0, 1.0, 0.0], + }, + PlanetaryTerm { + argument: [1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], + coefficients: [0.0, 3.0, 2.0, 0.0], + }, + PlanetaryTerm { + argument: [0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0], + coefficients: [-24.0, -12.0, -5.0, 10.0], + }, + PlanetaryTerm { + argument: [2, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], + coefficients: [4.0, 0.0, -1.0, -2.0], + }, + PlanetaryTerm { + argument: [-1, 2, 2, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0], + coefficients: [13.0, 0.0, 0.0, -6.0], + }, + PlanetaryTerm { + argument: [-1, 2, 2, 2, 0, 3, -3, 0, 0, 0, 0, 0, 0], + coefficients: [7.0, 0.0, 0.0, -3.0], + }, + PlanetaryTerm { + argument: [1, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0], + coefficients: [3.0, 0.0, 0.0, -1.0], + }, + PlanetaryTerm { + argument: [0, 2, 2, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0], + coefficients: [3.0, 0.0, 0.0, -1.0], + }, +]; diff --git a/crates/physics/apsis-frames/src/iau2000/precession.rs b/crates/physics/apsis-frames/src/iau2000/precession.rs new file mode 100644 index 0000000..be761bc --- /dev/null +++ b/crates/physics/apsis-frames/src/iau2000/precession.rs @@ -0,0 +1,180 @@ +//! The IAU 2006 precession model and the frame bias. +//! +//! Precession is the slow, secular motion of the Earth's rotation axis about +//! the pole of the ecliptic, caused mainly by the torque of the Moon and the +//! Sun on the equatorial bulge. The IAU 2006 model expresses it as a +//! rotation from the celestial reference frame to the mean equator and +//! equinox of date, built from four angles. +//! +//! The frame bias accounts for the small offset between the orientation of +//! the International Celestial Reference System and the dynamical mean +//! equator and equinox of J2000.0. It is a constant rotation, and omitting +//! it places a position about twenty milliarcseconds away, which is well +//! above the precision of a modern transformation. +//! +//! Source: the P03 precession theory of Capitaine, Wallace and Chapront, +//! adopted by the International Astronomical Union in 2006, as implemented +//! in the IAU SOFA library and its ERFA derivative, functions `eraPfw06`, +//! `eraPmat06`, `eraFw2m`, `eraBi00` and `eraObl06`. + +use apsis_math::Mat3; +use core::f64::consts::PI; + +/// Converts arcseconds to radians. +const ARCSECOND_TO_RADIAN: f64 = PI / (180.0 * 3_600.0); + +/// The frame bias in right ascension, in radians. +/// +/// The offset between the origin of the International Celestial Reference +/// System and the dynamical equinox of J2000.0. The value is +/// minus 0.0146 arcseconds. +pub const FRAME_BIAS_RIGHT_ASCENSION: f64 = -0.014_6 * ARCSECOND_TO_RADIAN; + +/// The frame bias in declination, in radians. +/// +/// The offset between the pole of the International Celestial Reference +/// System and the mean pole of J2000.0. The value is minus 0.0068192 +/// arcseconds. +pub const FRAME_BIAS_DECLINATION: f64 = -0.006_819_2 * ARCSECOND_TO_RADIAN; + +/// The frame bias in longitude, in radians. +/// +/// The offset between the two origins measured along the equator. The value +/// is minus 0.041775 arcseconds. +pub const FRAME_BIAS_LONGITUDE: f64 = -0.041_775 * ARCSECOND_TO_RADIAN; + +/// The four angles that describe the precession from J2000.0 to a date. +/// +/// They are applied in the order the reference uses: a rotation by +/// `gamma_bar` about the third axis, then by `phi_bar` about the first, then +/// by minus `psi_bar` about the third, then by minus `epsilon_a` about the +/// first. +#[derive(Debug, Clone, Copy, PartialEq)] +pub struct PrecessionAngles { + /// The precession of the equator along the ecliptic, in radians. + pub gamma_bar: f64, + /// The inclination of the moving equator to the ecliptic, in radians. + pub phi_bar: f64, + /// The accumulated precession in longitude, in radians. + pub psi_bar: f64, + /// The mean obliquity at the date, in radians. + pub epsilon: f64, +} + +/// Returns the mean obliquity of the ecliptic, in radians. +/// +/// The polynomial is the IAU 2006 expression, evaluated for a time in Julian +/// centuries from J2000.0 on the Terrestrial Time scale. The constant term +/// is 84381.406 arcseconds, which is the obliquity at J2000.0. +/// +/// Source: the IAU 2006 precession, as implemented by `eraObl06`. +pub fn mean_obliquity(t: f64) -> f64 { + let arcseconds = 84_381.406 + + t * (-46.836_769 + + t * (-0.000_183_1 + + t * (0.002_003_40 + t * (-0.000_000_576 + t * (-0.000_000_043_4))))); + arcseconds * ARCSECOND_TO_RADIAN +} + +/// Returns the four precession angles for a time. +/// +/// The time is in Julian centuries from J2000.0 on the Terrestrial Time +/// scale. +/// +/// Source: the P03 precession, as implemented by `eraPfw06`. +pub fn precession_angles(t: f64) -> PrecessionAngles { + let gamma_bar = -0.052_928 + + t * (10.556_378 + + t * (0.493_204_4 + + t * (-0.000_312_38 + t * (-0.000_002_788 + t * (0.000_000_026_0))))); + let phi_bar = 84_381.412_819 + + t * (-46.811_016 + + t * (0.051_126_8 + + t * (0.000_532_89 + t * (-0.000_000_440 + t * (-0.000_000_017_6))))); + let psi_bar = -0.041_775 + + t * (5_038.481_484 + + t * (1.558_417_5 + + t * (-0.000_185_22 + t * (-0.000_026_452 + t * (-0.000_000_014_8))))); + + PrecessionAngles { + gamma_bar: gamma_bar * ARCSECOND_TO_RADIAN, + phi_bar: phi_bar * ARCSECOND_TO_RADIAN, + psi_bar: psi_bar * ARCSECOND_TO_RADIAN, + epsilon: mean_obliquity(t), + } +} + +/// Returns the frame bias rotation matrix. +/// +/// The bias is a constant rotation from the International Celestial +/// Reference System to the dynamical mean equator and equinox of J2000.0. +/// Its three angles are far below a tenth of an arcsecond, but omitting it +/// would leave a systematic error that is larger than the precision of the +/// nutation series. +/// +/// Source: as implemented by `eraBi00`, which gives the bias as three small +/// rotations rather than as a matrix. +pub fn frame_bias_matrix() -> Mat3 { + // The reference builds the bias from three elementary rotations, and + // the result is reproduced here in the same order. + rotation_z(FRAME_BIAS_LONGITUDE) + * rotation_x(FRAME_BIAS_DECLINATION) + * rotation_y(FRAME_BIAS_RIGHT_ASCENSION) +} + +/// Returns the rotation from the celestial reference frame to the mean +/// equator and equinox of date. +/// +/// This is the bias-precession matrix. Nutation is applied on top of it to +/// reach the true equator and equinox of date. +/// +/// The time is in Julian centuries from J2000.0 on the Terrestrial Time +/// scale. +/// +/// Source: as implemented by `eraPmat06`. +pub fn bias_precession_matrix(t: f64) -> Mat3 { + let angles = precession_angles(t); + frame_to_mean_of_date(&angles) +} + +/// Returns the rotation from the celestial reference frame to the mean +/// equator and equinox of date, given precomputed precession angles. +/// +/// Source: as implemented by `eraFw2m`, which applies the four elementary +/// rotations in sequence. The reference helper composes each new rotation +/// on the left of the accumulator, so the product here is written with the +/// last rotation applied first, in the same order. +pub fn frame_to_mean_of_date(angles: &PrecessionAngles) -> Mat3 { + rotation_x(-angles.epsilon) + * rotation_z(-angles.psi_bar) + * rotation_x(angles.phi_bar) + * rotation_z(angles.gamma_bar) +} + +/// Returns a rotation of `angle` about the first axis, in radians. +/// +/// The convention matches the reference helpers `eraRx` and `eraRz`: the +/// rotation is applied to the frame rather than to a vector, so the matrix +/// is the transpose of the one that would rotate a vector by the same angle. +/// Composing `a * b` therefore applies `b` first, and the products in this +/// module read in the order the rotations are physically applied. +pub(crate) fn rotation_x(angle: f64) -> Mat3 { + let (sine, cosine) = angle.sin_cos(); + Mat3::from_rows([1.0, 0.0, 0.0], [0.0, cosine, sine], [0.0, -sine, cosine]) +} + +/// Returns a rotation of `angle` about the second axis, in radians. +/// +/// The convention is the one of [`rotation_x`]. +fn rotation_y(angle: f64) -> Mat3 { + let (sine, cosine) = angle.sin_cos(); + Mat3::from_rows([cosine, 0.0, -sine], [0.0, 1.0, 0.0], [sine, 0.0, cosine]) +} + +/// Returns a rotation of `angle` about the third axis, in radians. +/// +/// The convention is the one of [`rotation_x`]. +pub fn rotation_z(angle: f64) -> Mat3 { + let (sine, cosine) = angle.sin_cos(); + Mat3::from_rows([cosine, sine, 0.0], [-sine, cosine, 0.0], [0.0, 0.0, 1.0]) +} diff --git a/crates/physics/apsis-frames/src/iau2000/terrestrial.rs b/crates/physics/apsis-frames/src/iau2000/terrestrial.rs new file mode 100644 index 0000000..904ab25 --- /dev/null +++ b/crates/physics/apsis-frames/src/iau2000/terrestrial.rs @@ -0,0 +1,276 @@ +//! The celestial-to-terrestrial transformation. +//! +//! This module composes the frame bias, precession, nutation, Earth rotation +//! angle, and polar motion into the rotation that carries a vector from the +//! inertial frame to the Earth-fixed frame. +//! +//! Two intermediate frames appear in the composition. The **celestial +//! intermediate frame** is the true equator and equinox of date; the +//! rotation from the inertial frame to it is the bias, precession, and +//! nutation. The **terrestrial intermediate frame** is that frame carried to +//! the Earth's prime meridian by the Earth rotation angle. The polar motion +//! is applied last, because it is the motion of the pole within the Earth +//! rather than of the Earth within space. +//! +//! The elementary rotations follow the convention of the reference: `rz` +//! rotates the frame about its third axis, and composing `a * b` applies `b` +//! first. That convention is what makes the products below read in the order +//! the rotations are physically applied. +//! +//! Source: the composition follows the IAU SOFA library and its ERFA +//! derivative. The bias and precession are `eraPmat06`, the nutation matrix +//! is `eraNumat`, the rotation angle is `eraEra00`, the sidereal time for +//! the equinox-based composition is `eraGmst06`, and the polar motion is +//! `eraPom00`, composed by `eraC2t00b`. + +use super::nutation::nutation_2000a_with_2006_adjustment; +use super::precession::{frame_to_mean_of_date, mean_obliquity, rotation_z}; +use apsis_math::Mat3; +use core::f64::consts::PI; + +/// Converts arcseconds to radians. +const ARCSECOND_TO_RADIAN: f64 = PI / (180.0 * 3_600.0); + +/// Returns the bias-precession-nutation matrix for a time. +/// +/// The matrix carries a vector from the celestial reference frame to the +/// true equator and equinox of date. It is built from the four precession +/// angles with the nutation added to the last two, which is the form the +/// reference uses. +/// +/// Source: as implemented by `eraPnm06a` and `eraFw2m`. +pub fn bias_precession_nutation_matrix(t: f64) -> Mat3 { + let angles = super::precession::precession_angles(t); + let nutation = nutation_2000a_with_2006_adjustment(t); + frame_to_mean_of_date(&super::precession::PrecessionAngles { + gamma_bar: angles.gamma_bar, + phi_bar: angles.phi_bar, + psi_bar: angles.psi_bar + nutation.longitude, + epsilon: angles.epsilon + nutation.obliquity, + }) +} + +/// Returns the complementary terms of the equation of the equinoxes. +/// +/// The equation of the equinoxes has, besides the projection of the nutation +/// in longitude onto the true equator, a set of small periodic terms from +/// the same theory. They reach about twice the constant term of the +/// osculating nutation, which is a millisecond of time, so they matter for a +/// sidereal time that is quoted to that precision. +/// +/// Source: the MHB2000 complementary terms, as implemented by `eraEect00`. +pub fn equation_of_the_equinoxes_complementary_terms(t: f64) -> f64 { + use super::eect_table::{CONSTANT_TERMS, LINEAR_TERMS}; + + // The complementary terms use the IERS 2003 forms of two arguments, + // which differ from the ones the nutation series was fitted with. + let arguments = [ + super::fundamental::mean_anomaly_moon(t), + super::fundamental::mean_anomaly_sun_iers2003(t), + super::fundamental::mean_latitude_moon(t), + super::fundamental::mean_elongation_moon_sun_iers2003(t), + super::fundamental::mean_longitude_node(t), + super::fundamental::mean_longitude_venus(t), + super::fundamental::mean_longitude_earth(t), + super::fundamental::general_precession(t), + ]; + + let mut constant = 0.0; + for term in CONSTANT_TERMS.iter() { + let argument: f64 = term + .argument + .iter() + .zip(arguments.iter()) + .map(|(multiplier, value)| f64::from(*multiplier) * value) + .sum(); + let (sine, cosine) = argument.sin_cos(); + constant += term.coefficients[0] * sine + term.coefficients[1] * cosine; + } + + let mut linear = 0.0; + for term in LINEAR_TERMS.iter() { + let argument: f64 = term + .argument + .iter() + .zip(arguments.iter()) + .map(|(multiplier, value)| f64::from(*multiplier) * value) + .sum(); + let (sine, cosine) = argument.sin_cos(); + linear += term.coefficients[0] * sine + term.coefficients[1] * cosine; + } + + // The tabulated coefficients are in arcseconds. + (constant + linear * t) * ARCSECOND_TO_RADIAN +} + +/// Returns the equation of the equinoxes for a time. +/// +/// The equation of the equinoxes is the difference between the true and mean +/// equinoxes measured along the true equator. It is the quantity a sidereal +/// time must be corrected by to become the hour angle of the true equinox. +/// +/// The value is the projection of the nutation in longitude onto the true +/// equator, `dpsi cos(eps)`, plus the complementary terms of the theory. +pub fn equation_of_the_equinoxes(t: f64) -> f64 { + let nutation = nutation_2000a_with_2006_adjustment(t); + let obliquity = mean_obliquity(t); + nutation.longitude * obliquity.cos() + equation_of_the_equinoxes_complementary_terms(t) +} + +/// The polar motion of the Earth, as two angles and the rotation. +/// +/// The polar motion is the motion of the rotation pole within the Earth. It +/// is measured daily and published by the International Earth Rotation and +/// Reference Systems Service, so it cannot be computed from a model and is +/// supplied by the caller. +#[derive(Debug, Clone, Copy, PartialEq, Default)] +pub struct PolarMotion { + /// The displacement of the pole along the Greenwich meridian, in + /// radians. + pub x: f64, + /// The displacement of the pole along the meridian ninety degrees west, + /// in radians. + pub y: f64, + /// The rotation of the terrestrial frame about the pole, in radians. + /// + /// This is the terrestrial intermediate origin locator, which is small + /// and is often taken as zero. + pub s: f64, +} + +impl PolarMotion { + /// The zero polar motion, which is the approximation used when the + /// published values are not available. + /// + /// The error from omitting the polar motion is under a tenth of an + /// arcsecond, well below the nutation but above the precision of a + /// modern transformation. + pub const NONE: Self = Self { + x: 0.0, + y: 0.0, + s: 0.0, + }; + + /// Creates a polar motion from its three angles. + pub const fn new(x: f64, y: f64, s: f64) -> Self { + Self { x, y, s } + } + + /// Returns `true` when the angles are usable. + pub fn is_valid(self) -> bool { + self.x.is_finite() && self.y.is_finite() && self.s.is_finite() + } + + /// Returns the rotation matrix of the polar motion. + /// + /// The rotation is a turn about the third axis by the locator, then + /// about the second by minus the `x` displacement, then about the first + /// by minus the `y` displacement. The signs are the ones the reference + /// uses, which carry the terrestrial frame into alignment with the + /// celestial pole. + /// + /// Source: as implemented by `eraPom00`, which applies the rotations in + /// sequence by composing each on the left of the accumulator. + pub fn matrix(self) -> Mat3 { + rotation_x(-self.y) * rotation_y(-self.x) * rotation_z(self.s) + } +} + +/// Returns the intermediate-to-terrestrial matrix for a time. +/// +/// The intermediate frame is the true equator and equinox of date, and the +/// terrestrial frame is the Earth-fixed frame at the same date. This uses +/// the equinox-based approach, in which the rotation from one to the other +/// is Greenwich apparent sidereal time. +/// +/// The time arguments are the UT1 and TT Julian dates. +/// +/// Source: the composition is the one `eraC2t06a` produces for the equinox +/// based chain, with the polar motion applied separately by the caller of +/// the full transformation. +pub fn intermediate_to_terrestrial_matrix(ut1_julian_date: f64, tt_julian_date: f64) -> Mat3 { + let apparent_sidereal = greenwich_apparent_sidereal_time(ut1_julian_date, tt_julian_date); + rotation_z(apparent_sidereal) +} + +/// Returns Greenwich apparent sidereal time for a UT1 and a TT Julian date. +/// +/// This is the mean sidereal time plus the equation of the equinoxes, so it +/// is the hour angle of the true equinox. +/// +/// Source: as implemented by `eraGst06a`. +pub fn greenwich_apparent_sidereal_time(ut1_julian_date: f64, tt_julian_date: f64) -> f64 { + let t = (tt_julian_date - 2_451_545.0) / 36_525.0; + let mean = greenwich_mean_sidereal_time(ut1_julian_date, tt_julian_date); + (mean + equation_of_the_equinoxes(t)).rem_euclid(2.0 * PI) +} + +/// Returns Greenwich mean sidereal time for a UT1 and a TT Julian date. +/// +/// The relation is the Earth rotation angle plus the accumulated precession +/// in right ascension, which is the quantity that relates the equinox to the +/// non-rotating origin. +/// +/// Source: as implemented by `eraGmst06`. +pub fn greenwich_mean_sidereal_time(ut1_julian_date: f64, tt_julian_date: f64) -> f64 { + let t = (tt_julian_date - 2_451_545.0) / 36_525.0; + // The accumulated precession in right ascension, in arcseconds. + let arcseconds = 0.014_506 + + t * (4_612.156_534 + + t * (1.391_581_7 + + t * (-0.000_000_44 + t * (-0.000_029_956 + t * (-0.000_000_036_8))))); + (earth_rotation_angle(ut1_julian_date) + arcseconds * ARCSECOND_TO_RADIAN).rem_euclid(2.0 * PI) +} + +/// Returns the Earth rotation angle for a UT1 Julian date. +/// +/// This is the linear expression of the International Astronomical Union, +/// which is exact to the precision the angle is known. +/// +/// Source: IERS Conventions (2010), equation 8.32. +pub fn earth_rotation_angle(ut1_julian_date: f64) -> f64 { + let days = ut1_julian_date - 2_451_545.0; + let turns = 0.779_057_273_264_0 + 1.002_737_811_911_354_6 * days; + (turns.rem_euclid(1.0)) * 2.0 * PI +} + +/// Returns the celestial-to-terrestrial matrix for a time. +/// +/// This composes the whole chain: the frame bias, the precession, the +/// nutation, the Earth rotation, and the polar motion. +/// +/// The time arguments are the UT1 and TT Julian dates, and the polar motion +/// is supplied by the caller because it is measured rather than modelled. +/// +/// Source: the composition is the one `eraC2t06a` produces. +pub fn celestial_to_terrestrial_matrix( + ut1_julian_date: f64, + tt_julian_date: f64, + polar_motion: PolarMotion, +) -> Mat3 { + let t = (tt_julian_date - 2_451_545.0) / 36_525.0; + let bias_precession_nutation = bias_precession_nutation_matrix(t); + let sidereal = greenwich_apparent_sidereal_time(ut1_julian_date, tt_julian_date); + // The composition is the one `eraC2tcio` produces: the bias, precession, + // and nutation first, then the Earth rotation, then the polar motion, + // with each new rotation composed on the left of the accumulator. + polar_motion.matrix() * rotation_z(sidereal) * bias_precession_nutation +} + +/// Returns a rotation of `angle` about the first axis, in radians. +/// +/// The convention matches the reference helper `eraRx`: the rotation is +/// applied to the frame, so the matrix is the transpose of the one that +/// would rotate a vector by the same angle. +fn rotation_x(angle: f64) -> Mat3 { + let (sine, cosine) = angle.sin_cos(); + Mat3::from_rows([1.0, 0.0, 0.0], [0.0, cosine, sine], [0.0, -sine, cosine]) +} + +/// Returns a rotation of `angle` about the second axis, in radians. +/// +/// The convention is the one of [`rotation_x`]. +fn rotation_y(angle: f64) -> Mat3 { + let (sine, cosine) = angle.sin_cos(); + Mat3::from_rows([cosine, 0.0, -sine], [0.0, 1.0, 0.0], [sine, 0.0, cosine]) +} diff --git a/crates/physics/apsis-frames/src/lib.rs b/crates/physics/apsis-frames/src/lib.rs index b90b91f..5bacc83 100644 --- a/crates/physics/apsis-frames/src/lib.rs +++ b/crates/physics/apsis-frames/src/lib.rs @@ -46,6 +46,7 @@ #![deny(missing_docs)] mod earth_rotation; +pub mod iau2000; pub use earth_rotation::{ ERA_J2000_TURNS, ERA_RATE_TURNS_PER_DAY, EarthRotationAngle, rotation_ecef_to_eci, diff --git a/crates/physics/apsis-frames/tests/iau2000.rs b/crates/physics/apsis-frames/tests/iau2000.rs new file mode 100644 index 0000000..5732302 --- /dev/null +++ b/crates/physics/apsis-frames/tests/iau2000.rs @@ -0,0 +1,398 @@ +//! Tests for the IAU 2000/2006 Earth orientation models. +//! +//! The expected values are those of the IAU SOFA library and its ERFA +//! derivative for the same instants. They are recorded here so that a change +//! to a coefficient or a rotation convention shows up as a failing +//! assertion. + +use apsis_frames::iau2000::{ + PolarMotion, bias_precession_nutation_matrix, celestial_to_terrestrial_matrix, + equation_of_the_equinoxes, equation_of_the_equinoxes_complementary_terms, general_precession, + greenwich_apparent_sidereal_time, mean_obliquity, nutation_2000a, + nutation_2000a_with_2006_adjustment, precession_angles, +}; +use core::f64::consts::PI; + +/// Converts arcseconds to radians. +const ARCSECOND: f64 = PI / (180.0 * 3_600.0); + +/// Returns the Terrestrial Time Julian date for a Modified Julian Date on +/// the UTC scale, using the offsets in force from 2017. +fn tt_julian_date(utc_mjd: f64) -> f64 { + utc_mjd + 2_400_000.5 + 69.184 / 86_400.0 +} + +#[test] +fn the_mean_obliquity_at_j2000_matches_the_reference() { + // The IAU 2006 obliquity at J2000.0 is 84381.406 arcseconds. + let obliquity = mean_obliquity(0.0); + assert!( + (obliquity / ARCSECOND - 84_381.406).abs() < 1e-9, + "{} arcseconds", + obliquity / ARCSECOND + ); +} + +#[test] +fn the_nutation_at_j2000_matches_the_reference() { + // The IAU 2000A nutation at J2000.0, from ERFA. + let t = 0.0; + let nutation = nutation_2000a(t); + assert!( + (nutation.longitude - -6.754422426417298e-05).abs() < 1e-16, + "longitude {}", + nutation.longitude + ); + assert!( + (nutation.obliquity - -2.7970831192374137e-05).abs() < 1e-16, + "obliquity {}", + nutation.obliquity + ); +} + +#[test] +fn the_nutation_2006_adjustment_is_a_scaling() { + // The IAU 2006 adjustment scales the IAU 2000A nutation rather than + // adding an independent term, so the two must stay in proportion. + for t in [0.0, 0.5, 1.0, 2.0] { + let base = nutation_2000a(t); + let adjusted = nutation_2000a_with_2006_adjustment(t); + let expected_longitude = base.longitude * (1.0 + 0.469_7e-6 - 2.777_4e-6 * t); + let expected_obliquity = base.obliquity * (1.0 - 2.777_4e-6 * t); + assert!( + (adjusted.longitude - expected_longitude).abs() < 1e-20, + "t {t}: {} against {expected_longitude}", + adjusted.longitude + ); + assert!( + (adjusted.obliquity - expected_obliquity).abs() < 1e-20, + "t {t}: {} against {expected_obliquity}", + adjusted.obliquity + ); + } +} + +#[test] +fn the_nutation_matches_the_reference_over_a_century() { + // Recorded from ERFA at each date. The values are in radians. + let cases = [ + (40_587.0, 2.1896610891495316e-05, 4.070477585626008e-05), + (51_544.5, -6.754419567422628e-05, -2.797091091919891e-05), + (60_000.0, -4.496357815269203e-05, 3.753534415176348e-05), + ]; + for (mjd, longitude, obliquity) in cases { + let tt = tt_julian_date(mjd); + let t = (tt - 2_451_545.0) / 36_525.0; + let nutation = nutation_2000a(t); + assert!( + (nutation.longitude - longitude).abs() < 1e-14, + "MJD {mjd}: longitude {} against {longitude}", + nutation.longitude + ); + assert!( + (nutation.obliquity - obliquity).abs() < 1e-14, + "MJD {mjd}: obliquity {} against {obliquity}", + nutation.obliquity + ); + } +} + +#[test] +fn the_precession_angles_at_j2000_match_the_reference() { + // The P03 precession angles at J2000.0. + let angles = precession_angles(0.0); + assert!( + (angles.gamma_bar - -0.052_928 * ARCSECOND).abs() < 1e-18, + "gamma bar {}", + angles.gamma_bar + ); + assert!( + (angles.phi_bar - 84_381.412_819 * ARCSECOND).abs() < 1e-15, + "phi bar {}", + angles.phi_bar + ); + assert!( + (angles.psi_bar - -0.041_775 * ARCSECOND).abs() < 1e-18, + "psi bar {}", + angles.psi_bar + ); + assert!( + (angles.epsilon - 84_381.406 * ARCSECOND).abs() < 1e-15, + "epsilon {}", + angles.epsilon + ); +} + +#[test] +fn the_bias_precession_nutation_matrix_matches_the_reference() { + // The GCRS-to-true-of-date matrix at J2000.0 on the Terrestrial Time + // scale, from ERFA's `pnm06a`. The values are the first row. + let tt = 51_544.5 + 2_400_000.5 + 69.184 / 86_400.0; + let t = (tt - 2_451_545.0) / 36_525.0; + let matrix = bias_precession_nutation_matrix(t); + + let expected = [ + [ + 0.9999999977211409, + 6.189934767298694e-05, + 2.69478892058386e-05, + ], + [ + -6.1900102296513e-05, + 0.999999997692101, + 2.8003132867160385e-05, + ], + [ + -2.6946155767988307e-05, + -2.8004800880443437e-05, + 0.9999999992448179, + ], + ]; + for (row, expected_row) in expected.iter().enumerate() { + for (column, expected_value) in expected_row.iter().enumerate() { + let value = matrix.get(row, column).expect("the indices are in range"); + assert!( + (value - expected_value).abs() < 1e-14, + "at ({row}, {column}): {value} against {expected_value}" + ); + } + } +} + +#[test] +fn the_bias_precession_nutation_matrix_is_a_rotation() { + for mjd in [40_587.0, 51_544.5, 60_000.0] { + let tt = tt_julian_date(mjd); + let t = (tt - 2_451_545.0) / 36_525.0; + let matrix = bias_precession_nutation_matrix(t); + assert!(matrix.is_rotation(1e-12), "MJD {mjd}"); + assert!( + (matrix.determinant() - 1.0).abs() < 1e-12, + "MJD {mjd}: determinant {}", + matrix.determinant() + ); + } +} + +#[test] +fn the_celestial_to_terrestrial_matrix_is_a_rotation() { + for mjd in [40_587.0, 51_544.5, 60_000.0] { + let tt = tt_julian_date(mjd); + let matrix = celestial_to_terrestrial_matrix(tt, tt, PolarMotion::NONE); + assert!(matrix.is_rotation(1e-9), "MJD {mjd}"); + assert!( + (matrix.determinant() - 1.0).abs() < 1e-9, + "MJD {mjd}: determinant {}", + matrix.determinant() + ); + } +} + +#[test] +fn the_celestial_to_terrestrial_matrix_matches_the_reference() { + // The matrix at J2000.0 on the Terrestrial Time scale, from ERFA with + // zero polar motion. Each entry is checked to a nanoradian. + let tt = 51_544.5 + 2_400_000.5 + 69.184 / 86_400.0; + let matrix = celestial_to_terrestrial_matrix(tt, tt, PolarMotion::NONE); + + // The first row, from ERFA's `c2t06a` composed with the equinox based + // sidereal time. + let expected_first_row = [ + 0.18651846184811946, + -0.982451455739228, + -2.248740188309595e-05, + ]; + for (column, expected_value) in expected_first_row.iter().enumerate() { + let value = matrix.get(0, column).expect("the index is in range"); + assert!( + (value - expected_value).abs() < 1e-9, + "at (0, {column}): {value} against {expected_value}" + ); + } +} + +#[test] +fn the_equation_of_the_equinoxes_includes_the_complementary_terms() { + // The complementary terms are a few thousandths of an arcsecond and must + // not be dropped: their omission would show as a millisecond of + // sidereal time. + let t = 0.0; + let complementary = equation_of_the_equinoxes_complementary_terms(t); + assert!( + complementary.abs() > 1e-9, + "the complementary terms are {complementary}" + ); + // At J2000.0 the leading term is 2640.96 microarcseconds times the sine + // of the Moon's ascending node. + let expected = 1.021330096302465e-08; + assert!( + (complementary - expected).abs() < 1e-15, + "{complementary} against {expected}" + ); +} + +#[test] +fn the_general_precession_is_quadratic_in_time() { + // The argument is (0.024381750 + 0.00000538691 t) t, so at small times + // it grows linearly with the leading coefficient. + for t in [0.1, 0.5, 1.0] { + let value = general_precession(t); + let expected = (0.024_381_750 + 0.000_005_386_91 * t) * t; + assert!((value - expected).abs() < 1e-18, "t {t}"); + } +} + +#[test] +fn sidereal_time_advances_by_about_a_turn_per_day() { + // Greenwich apparent sidereal time must increase by a full turn plus a + // small amount each day. The small amount is about 3.94 minutes of + // time, which is 0.9856 degrees. + let first = greenwich_apparent_sidereal_time(60_000.0, 60_000.0); + let second = greenwich_apparent_sidereal_time(60_001.0, 60_001.0); + let advance = (second - first).rem_euclid(2.0 * PI); + let degrees = advance.to_degrees(); + assert!( + (degrees - 0.985_6).abs() < 0.01, + "advance {degrees} degrees" + ); +} + +#[test] +fn zero_polar_motion_is_the_identity_rotation() { + let matrix = PolarMotion::NONE.matrix(); + for row in 0..3 { + for column in 0..3 { + let value = matrix.get(row, column).expect("the indices are in range"); + let expected = if row == column { 1.0 } else { 0.0 }; + assert!((value - expected).abs() < 1e-15, "at ({row}, {column})"); + } + } + assert!(PolarMotion::NONE.is_valid()); +} + +#[test] +fn a_polar_motion_offsets_the_rotation() { + // A polar motion of one arcsecond must tilt the matrix by about that + // much, which is 4.85 microradians. + let motion = PolarMotion::new(ARCSECOND, ARCSECOND, 0.0); + let matrix = motion.matrix(); + assert!(matrix.is_rotation(1e-12)); + // The off-diagonal term is the sine of the displacement. + let value = matrix.get(0, 2).expect("the index is in range"); + assert!( + (value - ARCSECOND.sin()).abs() < 1e-15, + "at (0, 2): {value}" + ); + assert!(motion.is_valid()); + assert!(!PolarMotion::new(f64::NAN, 0.0, 0.0).is_valid()); +} + +#[test] +fn the_polar_motion_shifts_the_earth_fixed_frame() { + // Applying a polar motion must change the terrestrial position of a + // fixed inertial direction. + let tt = 60_000.0; + let without = celestial_to_terrestrial_matrix(tt, tt, PolarMotion::NONE); + let with = celestial_to_terrestrial_matrix( + tt, + tt, + PolarMotion::new(0.1 * ARCSECOND, -0.2 * ARCSECOND, 0.0), + ); + let difference = (without.transpose() * with).transpose() * with; + // The two must differ, and the difference must be of the order of the + // applied angles. + let mut largest = 0.0_f64; + for row in 0..3 { + for column in 0..3 { + let a = without.get(row, column).expect("in range"); + let b = difference.get(row, column).expect("in range"); + largest = largest.max((a - b).abs()); + } + } + assert!(largest > 1e-8, "the largest difference is {largest}"); + assert!(largest < 1e-5, "the largest difference is {largest}"); +} + +#[test] +fn the_nutation_reaches_the_expected_magnitude() { + // The nutation in longitude reaches about seventeen arcseconds and the + // nutation in obliquity about nine, so over a range of dates the + // largest value found must be in that range. + let mut largest_longitude = 0.0_f64; + let mut largest_obliquity = 0.0_f64; + for step in 0..400 { + // A span of about fifty years in steps of a fortnight. + let t = f64::from(step) * 0.125; + let nutation = nutation_2000a(t); + largest_longitude = largest_longitude.max(nutation.longitude.abs()); + largest_obliquity = largest_obliquity.max(nutation.obliquity.abs()); + } + let longitude_arcseconds = largest_longitude / ARCSECOND; + let obliquity_arcseconds = largest_obliquity / ARCSECOND; + assert!( + (19.0..20.0).contains(&longitude_arcseconds), + "longitude {longitude_arcseconds} arcseconds" + ); + assert!( + (8.0..10.0).contains(&obliquity_arcseconds), + "obliquity {obliquity_arcseconds} arcseconds" + ); +} + +#[test] +fn the_nutation_is_periodic() { + // The dominant terms have periods of about eighteen years and half a + // year, so the value must return close to its initial value after + // eighteen years and must oscillate in between. + let initial = nutation_2000a(0.0).longitude; + let after_eighteen_years = nutation_2000a(0.18).longitude; + assert!( + (after_eighteen_years - initial).abs() < 1.5e-05, + "{} against {initial}", + after_eighteen_years + ); + + // The sign must change at some point within that span. + let mut seen_positive = false; + let mut seen_negative = false; + for step in 0..200 { + let t = f64::from(step) * 0.001; + let value = nutation_2000a(t).longitude; + seen_positive |= value > 0.0; + seen_negative |= value < 0.0; + } + assert!(seen_positive && seen_negative); +} + +#[test] +fn the_equation_of_the_equinoxes_follows_the_nutation() { + // The equation of the equinoxes is dominated by the nutation in + // longitude projected onto the true equator, so it shares its sign. + for t in [0.02, 0.05, 0.1, 0.2] { + let nutation = nutation_2000a_with_2006_adjustment(t); + let equation = equation_of_the_equinoxes(t); + assert!( + nutation.longitude.signum() == equation.signum(), + "t {t}: {} against {}", + nutation.longitude, + equation + ); + } +} + +#[test] +fn a_matrix_at_two_epochs_separated_by_a_century_differs_by_the_precession() { + // The precession over a century is about 1.4 degrees, so the two + // matrices must differ by an angle of that order. + let first = bias_precession_nutation_matrix(0.0); + let second = bias_precession_nutation_matrix(1.0); + let difference = first.transpose() * second; + // The trace of a rotation matrix is 1 + 2 cos(angle), so the angle + // follows from it. + let cosine = ((difference.trace() - 1.0) / 2.0).clamp(-1.0, 1.0); + let degrees = cosine.acos().to_degrees(); + assert!( + (1.0..2.0).contains(°rees), + "the rotation angle is {degrees} degrees" + ); +} diff --git a/validation/README.md b/validation/README.md index c36731a..7d919ef 100644 --- a/validation/README.md +++ b/validation/README.md @@ -82,6 +82,10 @@ cargo run -p apsis-rs --features rf --example dump_p839 \ # ITU-R P.676-12 精确斜路径（分层积分 + 折射率射线追踪） cargo run -p apsis-rs --features rf --example dump_gas_exact \ > validation/data/expected/rust_gas_exact.csv + +# IAU 2000/2006 地球定向（岁差、章动、框架偏移、GCRS→ITRF） +cargo run -p apsis-rs --features physics --example dump_iau2000 \ + > validation/data/expected/rust_iau2000.csv ``` Python 侧读取同一批输入，用参考实现重算并输出误差表： @@ -97,6 +101,7 @@ pixi run python validation/python/atmosphere/check_rain_path.py pixi run python validation/python/link/check_s465.py pixi run python validation/python/atmosphere/check_p839.py pixi run python validation/python/atmosphere/check_gas_exact.py +pixi run python validation/python/time/check_iau2000.py ``` 两个脚本都以退出码 0 表示通过、1 表示超差、2 表示缺少输入文件。 @@ -128,12 +133,13 @@ Earth orientation 数据自动下载；本 crate 涉及的换算不需要该数 | `link/check_s465.py` | 参考天线方向图，3 种口径 × 8 个离轴角 | ITU-R S.465 方程（Python 转写） | 4.0e-10 dB | | `atmosphere/check_p839.py` | 零度等温线高度，15 个全球点 | `itur` 的 ITU-R P.839-4 实现 | 3.3e-13 km | | `atmosphere/check_gas_exact.py` | 精确斜路径，11 个场景（1–100 GHz，1°–90° 仰角） | `itur` 的 ITU-R P.676-12 exact 方法 | 9.6e-9（相对） | +| `time/check_iau2000.py` | 岁差、章动、框架偏移、GAST、GCRS→ITRF，8 个历元 × 28 个量 | ERFA 2.0.1（IAU SOFA 派生） | 章动 6.6e-15 rad；BPN 矩阵 6.0e-15；GAST 1.1e-11 rad | ### 关于射频层对拍的说明 射频层分两类：有权威参考实现的模型与纯闭式算式。 -- 有参考实现的，直接对拍：大气与雨衰用 `itur`，它是 ITU-R 研究组维护的建议书实现； +- 有参考实现的，直接对拍：地球定向用 `erfa`（IAU SOFA 的派生实现），大气与雨衰用 `itur`； 链路预算的每一步都是初等运算，`check_link.py` 用 Python 独立重写同一方程。 - 其余以解析性质断言为主：各 crate 的单元测试验证模型必须满足的性质，例如 3 dB 点、 平方律下降、Friis 级联行为、P.838-3 系数在表列频率处的取值。 diff --git a/validation/python/time/check_iau2000.py b/validation/python/time/check_iau2000.py new file mode 100644 index 0000000..69074c3 --- /dev/null +++ b/validation/python/time/check_iau2000.py @@ -0,0 +1,156 @@ +"""Cross-check the ApsisRS IAU 2000/2006 Earth orientation against ERFA. + +Reads the quantities written by ``cargo run -p apsis-rs --features physics +--example dump_iau2000`` and recomputes each one with ERFA, which is the +reference implementation distributed by the International Astronomical Union +through the SOFA library and its ERFA derivative. + +The script needs no network access. + +Usage: + + pixi run python validation/python/time/check_iau2000.py [path] + +Exit status is zero when every quantity agrees within tolerance and one +otherwise. +""" + +from __future__ import annotations + +import csv +import sys +from pathlib import Path + +import erfa + +# Tolerances. +# +# The nutation, obliquity, and precession are reproduced at the level of the +# last bits of a double, so they are compared at 1e-14. +# +# The sidereal time and the matrices accumulate the double precision error of +# several rotations, so they are allowed more. +# +# Greenwich apparent sidereal time gets its own tolerance because ERFA's +# `gst06a` is built on the non-rotating origin while the Rust value is built +# on the equinox. The two formulations agree to about two microarcseconds, +# which is 1e-11 radians, and that is what is allowed here. +SCALAR_TOLERANCE = 1e-14 +SIDEREAL_TOLERANCE = 1e-10 +MATRIX_TOLERANCE = 1e-9 + + +def tolerance_for(quantity: str) -> float: + """Returns the tolerance that applies to a quantity.""" + if quantity == "gast": + return SIDEREAL_TOLERANCE + if quantity in ("bpn", "c2t"): + return MATRIX_TOLERANCE + return SCALAR_TOLERANCE + +DEFAULT_INPUT = Path("validation/data/expected/rust_iau2000.csv") + +# The Terrestrial Time offset from UTC, in seconds, matching the Rust side. +TT_MINUS_UTC_SECONDS = 32.184 + 37.0 + + +def read_rows(path: Path) -> list[dict[str, str]]: + """Reads the CSV rows.""" + with path.open(newline="") as handle: + reader = csv.DictReader(handle) + return [row for row in reader if row.get("mjd")] + + +def tt_julian_date(utc_mjd: float) -> float: + """Returns the Terrestrial Time Julian date for a UTC Modified Julian Date.""" + return utc_mjd + 2400000.5 + TT_MINUS_UTC_SECONDS / 86400.0 + + +def main(argv: list[str]) -> int: + path = Path(argv[1]) if len(argv) > 1 else DEFAULT_INPUT + if not path.exists(): + print(f"missing input file: {path}", file=sys.stderr) + print( + "generate it with: cargo run -p apsis-rs --features physics " + "--example dump_iau2000 > " + str(path), + file=sys.stderr, + ) + return 2 + + rows = read_rows(path) + if not rows: + print("input file has no data rows", file=sys.stderr) + return 2 + + worst: dict[str, float] = {} + worst_at: dict[str, object] = {} + compared = 0 + + for row in rows: + mjd = float(row["mjd"]) + quantity = row["quantity"] + index = int(row["index"]) + actual = float(row["value"]) + + tt = tt_julian_date(mjd) + d1 = 2400000.5 + d2 = tt - d1 + + if quantity == "obliquity": + reference = erfa.obl06(d1, d2) + elif quantity == "nutation_longitude_a": + reference = erfa.nut00a(d1, d2)[0] + elif quantity == "nutation_obliquity_a": + reference = erfa.nut00a(d1, d2)[1] + elif quantity == "nutation_longitude_06a": + reference = erfa.nut06a(d1, d2)[0] + elif quantity == "nutation_obliquity_06a": + reference = erfa.nut06a(d1, d2)[1] + elif quantity == "precession_gamma_bar": + reference = erfa.pfw06(d1, d2)[0] + elif quantity == "precession_phi_bar": + reference = erfa.pfw06(d1, d2)[1] + elif quantity == "precession_psi_bar": + reference = erfa.pfw06(d1, d2)[2] + elif quantity == "precession_epsilon": + reference = erfa.pfw06(d1, d2)[3] + elif quantity == "bpn": + matrix = erfa.pnm06a(d1, d2) + reference = matrix[index // 3][index % 3] + elif quantity == "gast": + reference = erfa.gst06a(d1, d2, d1, d2) + elif quantity == "c2t": + # The equinox based chain: the bias, precession and nutation, + # then Greenwich apparent sidereal time, then the polar motion. + matrix = erfa.c2t06a(d1, d2, d1, d2, 0.0, 0.0) + reference = matrix[index // 3][index % 3] + else: + continue + + error = abs(actual - reference) + if error > worst.get(quantity, 0.0): + worst[quantity] = error + worst_at[quantity] = (mjd, index) + compared += 1 + + print(f"values compared: {compared}") + for quantity in sorted(worst): + tolerance = tolerance_for(quantity) + status = "ok" if worst[quantity] <= tolerance else "FAIL" + print( + f" {quantity:26} worst {worst[quantity]:.3e} " + f"(tolerance {tolerance:.0e}) at {worst_at[quantity]} {status}" + ) + + passed = all( + value <= tolerance_for(quantity) for quantity, value in worst.items() + ) + if passed and compared > 0: + print("result: pass") + return 0 + print("result: FAIL") + return 1 + + +if __name__ == "__main__": + raise SystemExit(main(sys.argv)) diff --git a/validation/tools/generate_eect_table.py b/validation/tools/generate_eect_table.py new file mode 100644 index 0000000..b6c5bb8 --- /dev/null +++ b/validation/tools/generate_eect_table.py @@ -0,0 +1,98 @@ +#!/usr/bin/env python3 +"""Generate the Rust source for the IAU 2000 complementary terms. + +The complementary terms are the small periodic additions to the equation of +the equinoxes that the nutation in longitude does not contain. They come +from the same theory as the nutation and are needed for the equation of the +equinoxes to be consistent with the nutation series. + +The reference is the ERFA library, a derivative of the IAU SOFA library. + +Fetch the reference with: + + curl -O https://raw.githubusercontent.com/liberfa/erfa/master/src/eect00.c + +Usage: + + python validation/tools/generate_eect_table.py path/to/eect00.c +""" + +from __future__ import annotations + +import re +import sys +from pathlib import Path + + +def extract_array(source: str, name: str) -> str: + """Returns the body of a C array initializer.""" + start = source.index(name + "[] = {") + brace = source.index("{", start) + depth = 0 + index = brace + while index < len(source): + if source[index] == "{": + depth += 1 + elif source[index] == "}": + depth -= 1 + if depth == 0: + break + index += 1 + return source[brace : index + 1] + + +def parse_terms(body: str) -> list[tuple[str, str]]: + """Returns the multiplier and coefficient groups of each term.""" + body = re.sub(r"/\*.*?\*/", "", body, flags=re.S) + return re.findall(r"\{\{([^{}]*)\},\s*([^}]*)\}", body) + + +def emit(name: str, doc: str, terms: list[tuple[str, str]]) -> None: + """Prints one Rust constant.""" + print(doc) + print(f"pub static {name}: [ComplementaryTerm; {len(terms)}] = [") + for multipliers, coefficients in terms: + arguments = ", ".join(value.strip() for value in multipliers.split(",")) + values = ", ".join(value.strip() for value in coefficients.split(",")) + print( + f" ComplementaryTerm {{ argument: [{arguments}], " + f"coefficients: [{values}] }}," + ) + print("];") + print() + + +def main(argv: list[str]) -> int: + if len(argv) < 2: + print(__doc__, file=sys.stderr) + return 2 + source = Path(argv[1]).read_text() + constant = parse_terms(extract_array(source, "e0")) + linear = parse_terms(extract_array(source, "e1")) + + print("//! The IAU 2000 complementary terms of the equation of the equinoxes.") + print("//!") + print("//! The table is generated from the reference implementation by") + print("//! `validation/tools/generate_eect_table.py` and is reproduced without") + print("//! change.") + print("//!") + print("//! Source: the MHB2000 model, as distributed with the IAU SOFA library") + print("//! and implemented by ERFA.") + print() + print("use super::ComplementaryTerm;") + print() + emit( + "CONSTANT_TERMS", + "/// The terms that do not depend on time.\n///\n/// The eight multipliers apply to the arguments `l`, `l'`, `F`, `D`, `Om`,\n/// the mean longitude of Venus, the mean longitude of the Earth, and the\n/// general accumulated precession, in that order.", + constant, + ) + emit( + "LINEAR_TERMS", + "/// The terms whose amplitude grows linearly with time.\n///\n/// The arguments are the same as for the constant terms.", + linear, + ) + return 0 + + +if __name__ == "__main__": + raise SystemExit(main(sys.argv)) diff --git a/validation/tools/generate_nutation_table.py b/validation/tools/generate_nutation_table.py new file mode 100644 index 0000000..06f674a --- /dev/null +++ b/validation/tools/generate_nutation_table.py @@ -0,0 +1,143 @@ +#!/usr/bin/env python3 +"""Generate the Rust source for the IAU 2000A nutation series. + +The series is the MHB2000 model. It has a luni-solar part and a planetary +part, both long tables of integer argument multipliers and real +coefficients, so they are transcribed mechanically from the reference +rather than by hand. + +The reference is the ERFA library, a derivative of the IAU SOFA library +maintained by the International Astronomical Union. Its source is the +authoritative statement of the series. + +Field order is the one the reference uses, which is not the order the +coefficients are listed in the paper: + + luni-solar: multipliers l, l', F, D, Om; then sp, spt, cp, ce, cet, se + planetary: multipliers l, F, D, Om, Me, Ve, E, Ma, Ju, Sa, Ur, Ne, pa; + then sp, cp, se, ce + +The two series use different argument sets and different coefficient +groupings for the obliquity, so the generated Rust types keep them separate. + +Fetch the reference with: + + curl -O https://raw.githubusercontent.com/liberfa/erfa/master/src/nut00a.c + +Usage: + + python validation/tools/generate_nutation_table.py path/to/nut00a.c +""" + +from __future__ import annotations + +import re +import sys +from pathlib import Path + + +def extract_array(source: str, name: str) -> str: + """Returns the body of a C array initializer.""" + start = source.index(name + "[] = {") + brace = source.index("{", start) + depth = 0 + index = brace + while index < len(source): + if source[index] == "{": + depth += 1 + elif source[index] == "}": + depth -= 1 + if depth == 0: + break + index += 1 + return source[brace : index + 1] + + +def parse_terms(body: str) -> list[list[str]]: + """Returns the numeric terms of an array of brace groups.""" + body = re.sub(r"/\*.*?\*/", "", body, flags=re.S) + terms = [] + for group in re.findall(r"\{([^{}]*)\}", body): + values = group.replace("\n", " ").strip() + if values: + terms.append([value.strip() for value in values.split(",")]) + return terms + + +def main(argv: list[str]) -> int: + if len(argv) < 2: + print(__doc__, file=sys.stderr) + return 2 + source = Path(argv[1]).read_text() + + lunisolar = parse_terms(extract_array(source, "xls")) + planetary = parse_terms(extract_array(source, "xpl")) + + if any(len(term) != 11 for term in lunisolar): + print("unexpected luni-solar row width", file=sys.stderr) + return 1 + if any(len(term) != 17 for term in planetary): + print("unexpected planetary row width", file=sys.stderr) + return 1 + + print("//! The IAU 2000A nutation series.") + print("//!") + print("//! The table is generated from the reference implementation of the") + print("//! model by `validation/tools/generate_nutation_table.py` and is") + print("//! reproduced without change.") + print("//!") + print("//! The field order follows the reference, which is not the order the") + print("//! coefficients are listed in the paper.") + print("//!") + print("//! Source: the MHB2000 model of Mathews, Herring and Buffett, adopted by") + print("//! the International Astronomical Union in 2000 and distributed as part") + print("//! of the IAU SOFA library, as implemented by ERFA.") + print() + print("use super::{PlanetaryTerm, SeriesTerm};") + print() + + print("/// The luni-solar terms of the series.") + print("///") + print("/// The multipliers apply to the arguments `l`, `l'`, `F`, `D`, and `Om`") + print("/// in that order. The coefficients are the longitude sine, its time") + print("/// derivative, the longitude cosine, the obliquity cosine, its time") + print("/// derivative, and the obliquity sine, in units of 0.1 microarcsecond.") + print(f"pub static LUNI_SOLAR: [SeriesTerm; {len(lunisolar)}] = [") + for term in lunisolar: + multipliers = ", ".join(term[:5]) + coefficients = ", ".join( + value if "." in value or "e" in value.lower() else value + ".0" + for value in term[5:] + ) + print( + f" SeriesTerm {{ argument: [{multipliers}], " + f"coefficients: [{coefficients}] }}," + ) + print("];") + print() + + print("/// The planetary terms of the series.") + print("///") + print("/// The multipliers apply to the arguments `l`, `F`, `D`, `Om`, the mean") + print("/// longitudes of Mercury through Uranus, the mean longitude of Neptune,") + print("/// and the general accumulated precession, in that order. The") + print("/// coefficients are the longitude sine, the longitude cosine, the") + print("/// obliquity sine, and the obliquity cosine, in units of 0.1") + print("/// microarcsecond.") + print(f"pub static PLANETARY: [PlanetaryTerm; {len(planetary)}] = [") + for term in planetary: + multipliers = ", ".join(term[:13]) + coefficients = ", ".join( + value if "." in value or "e" in value.lower() else value + ".0" + for value in term[13:] + ) + print( + f" PlanetaryTerm {{ argument: [{multipliers}], " + f"coefficients: [{coefficients}] }}," + ) + print("];") + return 0 + + +if __name__ == "__main__": + raise SystemExit(main(sys.argv))