docs: bilingual comments for the IAU 2000 frames and Earth rotation
The Delaunay and planetary arguments, the precession, nutation, polar motion and Earth rotation angles, and the TEME and terrestrial matrices. This completes the bilingual sweep: every comment block in the workspace now carries its Chinese counterpart.
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@ -9,6 +9,11 @@ use core::f64::consts::PI;
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/// The epoch value is zero by the definition of the angle: the International
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/// Astronomical Union defines the Earth Rotation Angle to be zero at
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/// 2000-01-01T12:00:00 UT1.
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///
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/// J2000.0 历元处的地球自转角，以周计。
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///
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/// 按该角的定义，历元值就是零：国际天文学联合会把 2000-01-01T12:00:00 UT1
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/// 处的地球自转角定义为零。
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pub const ERA_J2000_TURNS: f64 = 0.0;
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/// The rate of change of the Earth Rotation Angle, in turns per day of UT1.
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@ -18,6 +23,13 @@ pub const ERA_J2000_TURNS: f64 = 0.0;
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/// in a sidereal day, which is shorter than a solar day.
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///
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/// Source: IERS Conventions (2010), equation 8.32.
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///
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/// 地球自转角的变化率，以每 UT1 日的周数计。
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///
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/// 该值为 `1.002 737 811 911 354 6`，即每天 `360.985 612 288 088` 度。它
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/// 超过每天一周，因为地球在一个恒星日内转一周，而恒星日短于太阳日。
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///
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/// 出处：IERS Conventions（2010），式 8.32。
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pub const ERA_RATE_TURNS_PER_DAY: f64 = 1.002_737_811_911_354_6;
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/// The number of days from the J2000.0 epoch to the given Julian Date on the
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@ -25,6 +37,10 @@ pub const ERA_RATE_TURNS_PER_DAY: f64 = 1.002_737_811_911_354_6;
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///
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/// The J2000.0 epoch is Julian Date 2451545.0, which is noon on
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/// 2000-01-01.
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///
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/// 从 J2000.0 历元到给定 UT1 时标儒略日的天数。
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///
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/// J2000.0 历元是儒略日 2451545.0，即 2000-01-01 的正午。
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pub fn ut1_days_from_j2000(ut1_julian_date: f64) -> f64 {
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ut1_julian_date - 2_451_545.0
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}
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@ -40,6 +56,14 @@ pub fn ut1_days_from_j2000(ut1_julian_date: f64) -> f64 {
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/// is periodic with a period of one. The value returned is not reduced to
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/// any interval, so differences between two angles are meaningful even when
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/// the interval is longer than a day.
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///
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/// 某瞬时的地球自转角。
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///
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/// 该角是从天球中间原点到地球中间原点的转动，绕天球中间极量取。它在现代
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/// 实践中取代格林尼治平恒星时，且与恒星时不同，它是 UT1 的线性函数。
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///
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/// 该值以周保存。一周即一整圈，故该角以 1 为周期。所返回的值不归约到任何
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/// 区间，故即便区间长于一日，两角之差仍有意义。
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#[derive(Debug, Clone, Copy, PartialEq, PartialOrd)]
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pub struct EarthRotationAngle {
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turns: f64,
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@ -47,11 +71,15 @@ pub struct EarthRotationAngle {
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impl EarthRotationAngle {
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/// Creates an angle from a value in turns.
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///
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/// 由以周表示的值创建角。
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pub const fn from_turns(turns: f64) -> Self {
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Self { turns }
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}
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/// Creates an angle from a value in radians.
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///
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/// 由以弧度表示的值创建角。
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pub fn from_radians(radians: f64) -> Self {
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Self {
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turns: radians / (2.0 * PI),
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@ -59,6 +87,8 @@ impl EarthRotationAngle {
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}
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/// Returns the angle for a Julian Date on the UT1 scale.
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///
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/// 返回 UT1 时标上某儒略日对应的角。
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pub fn from_ut1_julian_date(ut1_julian_date: f64) -> Self {
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Self::from_ut1_days(ut1_days_from_j2000(ut1_julian_date))
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}
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@ -72,6 +102,14 @@ impl EarthRotationAngle {
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/// about 280.46 degrees.
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///
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/// Source: IERS Conventions (2010), equation 8.32.
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///
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/// 返回自 J2000.0 历元起的若干 UT1 天对应的角。
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///
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/// 该式为线性：`theta = 0.779 057 273 2640 + 1.002 737 909 350 795 * d`，
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/// 其中 `d` 是以天计的间隔。`0.779 057` 周的常数项是历元本身的角，
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/// 约为 280.46 度。
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///
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/// 出处：IERS Conventions（2010），式 8.32。
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pub fn from_ut1_days(days_since_j2000: f64) -> Self {
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const EPOCH_TURNS: f64 = 0.779_057_273_264_0;
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Self {
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@ -82,11 +120,17 @@ impl EarthRotationAngle {
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/// Returns the angle in turns.
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///
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/// The value is not reduced to `[0, 1)`.
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///
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/// 返回以周表示的角。
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///
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/// 该值不归约到 `[0, 1)`。
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pub const fn turns(self) -> f64 {
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self.turns
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}
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/// Returns the angle in turns, reduced to `[0, 1)`.
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///
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/// 返回以周表示的角，归约到 `[0, 1)`。
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pub fn turns_positive(self) -> f64 {
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self.turns.rem_euclid(1.0)
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}
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@ -94,11 +138,17 @@ impl EarthRotationAngle {
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/// Returns the angle in radians.
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///
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/// The value is not reduced to `[0, 2 pi)`.
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///
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/// 返回以弧度表示的角。
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///
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/// 该值不归约到 `[0, 2 pi)`。
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pub fn radians(self) -> f64 {
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self.turns * 2.0 * PI
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}
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/// Returns the angle in radians, reduced to `[0, 2 pi)`.
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///
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/// 返回以弧度表示的角，归约到 `[0, 2 pi)`。
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pub fn radians_positive(self) -> f64 {
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self.turns_positive() * 2.0 * PI
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}
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@ -111,6 +161,12 @@ impl EarthRotationAngle {
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/// Rotation Angle. Applying it to an inertial vector yields the Earth-fixed
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/// vector, so a vector that is fixed in inertial space acquires a negative
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/// rotation as the Earth turns beneath it.
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///
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/// 返回把惯性系中的矢量映射到地固系的转动。
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///
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/// 该转动是绕第三轴按地球自转角作顺时针转。把它施加于惯性矢量即得地固
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/// 矢量，故在惯性空间固定的矢量会随地球在其下方转动而获得一个负的
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/// 转动。
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pub fn rotation_eci_to_ecef(angle: EarthRotationAngle) -> Mat3 {
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let (sin, cos) = angle.radians_positive().sin_cos();
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Mat3::from_rows([cos, sin, 0.0], [-sin, cos, 0.0], [0.0, 0.0, 1.0])
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@ -121,6 +177,10 @@ pub fn rotation_eci_to_ecef(angle: EarthRotationAngle) -> Mat3 {
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///
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/// This is the transpose of [`rotation_eci_to_ecef`], which for a rotation
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/// matrix is also its inverse.
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///
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/// 返回把地固系中的矢量映射到惯性系的转动。
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///
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/// 它是 [`rotation_eci_to_ecef`] 的转置，对旋转矩阵而言也是其逆。
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pub fn rotation_ecef_to_eci(angle: EarthRotationAngle) -> Mat3 {
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rotation_eci_to_ecef(angle).transpose()
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}
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@ -14,6 +14,11 @@ use super::ComplementaryTerm;
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/// The eight multipliers apply to the arguments `l`, `l'`, `F`, `D`, `Om`,
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/// the mean longitude of Venus, the mean longitude of the Earth, and the
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/// general accumulated precession, in that order.
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///
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/// 不依赖时间的各项。
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///
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/// 八个乘数按 `l`、`l'`、`F`、`D`、`Om`、金星的平黄经、地球的平黄经，以及
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/// 一般累积岁差的次序施加于这些参数。
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pub static CONSTANT_TERMS: [ComplementaryTerm; 33] = [
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ComplementaryTerm {
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argument: [0, 0, 0, 0, 1, 0, 0, 0],
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@ -152,6 +157,10 @@ pub static CONSTANT_TERMS: [ComplementaryTerm; 33] = [
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/// The terms whose amplitude grows linearly with time.
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///
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/// The arguments are the same as for the constant terms.
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///
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/// 幅度随时间线性增长的各项。
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///
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/// 参数与常数项相同。
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pub static LINEAR_TERMS: [ComplementaryTerm; 1] = [ComplementaryTerm {
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argument: [0, 0, 0, 0, 1, 0, 0, 0],
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coefficients: [-0.87e-6, 0.00e-6],
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@ -298,12 +298,20 @@ impl DelaunayArguments {
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#[derive(Debug, Clone, Copy, PartialEq)]
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pub struct PlanetaryArguments {
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/// The mean anomaly of the Moon.
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///
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/// 月球的平近点角。
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pub l: f64,
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/// The mean argument of latitude of the Moon.
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///
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/// 月球的平纬度参数。
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pub f: f64,
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/// The mean elongation of the Moon from the Sun.
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///
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/// 月球相对太阳的平距角。
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pub d: f64,
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/// The mean longitude of the Moon's ascending node.
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///
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/// 月球升交点的平黄经。
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pub omega: f64,
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/// The mean longitude of Mercury.
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///
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@ -366,6 +374,8 @@ impl PlanetaryArguments {
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}
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/// Returns the arguments as an array in series order.
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///
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/// 按级数次序把各参数作为数组返回。
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pub const fn as_array(self) -> [f64; 13] {
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[
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self.l,
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@ -67,12 +67,22 @@ pub use terrestrial::{
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/// `l`, `l'`, `F`, `D`, `Om`. The six coefficients are the longitude sine,
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/// its time derivative, the longitude cosine, the obliquity cosine, its time
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/// derivative, and the obliquity sine, in units of 0.1 microarcsecond.
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///
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/// 日月章动级数的一项。
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///
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/// 五个乘数按 `l`、`l'`、`F`、`D`、`Om` 的次序施加于 Delaunay 参数。六个
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/// 系数依次是黄经正弦、其时间导数、黄经余弦、黄赤交角余弦、其时间导数，
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/// 以及黄赤交角正弦，单位为 0.1 微角秒。
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#[derive(Debug, Clone, Copy)]
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pub struct SeriesTerm {
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/// The integer multipliers of the five Delaunay arguments.
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///
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/// 五个 Delaunay 参数的整数乘数。
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pub argument: [i32; 5],
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/// The six coefficients of the term, in the order the reference lists
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/// them.
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///
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/// 该项的六个系数，按参考实现列出的次序。
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pub coefficients: [f64; 6],
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}
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@ -82,11 +92,20 @@ pub struct SeriesTerm {
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/// the mean longitude of Venus, the mean longitude of the Earth, and the
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/// general accumulated precession. The two coefficients are the sine and
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/// cosine amplitudes, in arcseconds.
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///
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/// 分点方程式补充项的一项。
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///
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/// 八个乘数施加于参数 `l`、`l'`、`F`、`D`、`Om`、金星的平黄经、地球的平
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/// 黄经，以及一般累积岁差。两个系数是正弦与余弦幅度，单位为角秒。
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#[derive(Debug, Clone, Copy)]
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pub struct ComplementaryTerm {
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/// The integer multipliers of the eight arguments.
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///
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/// 八个参数的整数乘数。
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pub argument: [i32; 8],
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/// The sine and cosine coefficients.
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///
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/// 正弦与余弦系数。
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pub coefficients: [f64; 2],
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}
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@ -97,11 +116,21 @@ pub struct ComplementaryTerm {
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/// general accumulated precession. The four coefficients are the longitude
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/// sine, the longitude cosine, the obliquity sine, and the obliquity cosine,
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/// in units of 0.1 microarcsecond.
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///
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/// 行星章动级数的一项。
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///
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/// 十三个乘数按 `l`、`F`、`D`、`Om`、水星到天王星、海王星，以及一般累积
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/// 岁差的次序施加于行星参数。四个系数依次是黄经正弦、黄经余弦、黄赤交角
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/// 正弦与黄赤交角余弦，单位为 0.1 微角秒。
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#[derive(Debug, Clone, Copy)]
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pub struct PlanetaryTerm {
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/// The integer multipliers of the thirteen planetary arguments.
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///
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/// 十三个行星参数的整数乘数。
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pub argument: [i32; 13],
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/// The four coefficients of the term, in the order the reference lists
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/// them.
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///
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/// 该项的四个系数，按参考实现列出的次序。
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pub coefficients: [f64; 4],
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}
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@ -25,6 +25,8 @@ use super::{PlanetaryTerm, SeriesTerm};
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use core::f64::consts::PI;
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/// Converts a coefficient in units of 0.1 microarcsecond to radians.
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///
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/// 把以 0.1 微角秒为单位的系数换算为弧度。
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const UNIT_TO_RADIAN: f64 = 1.0e-7 * PI / (180.0 * 3_600.0);
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/// Converts arcseconds to radians.
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@ -33,16 +35,24 @@ const UNIT_TO_RADIAN: f64 = 1.0e-7 * PI / (180.0 * 3_600.0);
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const ARCSECOND_TO_RADIAN: f64 = PI / (180.0 * 3_600.0);
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/// The nutation in longitude and obliquity, in radians.
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///
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/// 黄经与黄赤交角方向的章动，单位为弧度。
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#[derive(Debug, Clone, Copy, PartialEq, Default)]
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pub struct Nutation {
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/// The nutation in longitude, in radians.
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///
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/// 黄经方向的章动，单位为弧度。
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pub longitude: f64,
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/// The nutation in obliquity, in radians.
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///
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/// 黄赤交角方向的章动，单位为弧度。
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pub obliquity: f64,
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}
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impl Nutation {
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/// Creates a nutation from its two angles.
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///
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/// 由其两个角创建章动。
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pub const fn new(longitude: f64, obliquity: f64) -> Self {
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Self {
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longitude,
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}
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/// Returns the nutation in longitude, in arcseconds.
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///
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/// 返回黄经方向的章动，单位为角秒。
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pub fn longitude_arcseconds(self) -> f64 {
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self.longitude / ARCSECOND_TO_RADIAN
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}
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/// Returns the nutation in obliquity, in arcseconds.
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///
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/// 返回黄赤交角方向的章动，单位为角秒。
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pub fn obliquity_arcseconds(self) -> f64 {
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self.obliquity / ARCSECOND_TO_RADIAN
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}
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/// Returns the sum of two nutations.
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///
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/// 返回两个章动之和。
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pub const fn plus(self, other: Self) -> Self {
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Self::new(
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self.longitude + other.longitude,
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@ -75,6 +91,12 @@ impl Nutation {
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/// is the sum of a time dependent sine, a constant sine, and a cosine. The
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/// obliquity is the sum of a time dependent cosine, a constant cosine, and a
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/// sine.
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///
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/// 求日月级数的一项。
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///
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/// 五个乘数施加于 Delaunay 参数。黄经是一个随时间变化的正弦、一个常数
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/// 正弦与一个余弦之和。黄赤交角是一个随时间变化的余弦、一个常数余弦与
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/// 一个正弦之和。
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fn lunisolar_term(term: &SeriesTerm, arguments: &DelaunayArguments, t: f64) -> Nutation {
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let multipliers = &term.argument;
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let c = &term.coefficients;
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@ -86,6 +108,7 @@ fn lunisolar_term(term: &SeriesTerm, arguments: &DelaunayArguments, t: f64) -> N
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let (sine, cosine) = argument.sin_cos();
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// The order is the one the reference uses: sp, spt, cp, ce, cet, se.
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// 次序即参考实现所用者：sp、spt、cp、ce、cet、se。
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Nutation::new(
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(c[0] + c[1] * t) * sine + c[2] * cosine,
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(c[3] + c[4] * t) * cosine + c[5] * sine,
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@ -97,6 +120,11 @@ fn lunisolar_term(term: &SeriesTerm, arguments: &DelaunayArguments, t: f64) -> N
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/// The thirteen multipliers are applied to the planetary arguments. The
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/// longitude is a sine plus a cosine, and the obliquity is a sine plus a
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/// cosine, with no time dependence in either.
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///
|
||||
/// 求行星级数的一项。
|
||||
///
|
||||
/// 十三个乘数施加于行星参数。黄经是一个正弦加一个余弦，黄赤交角也是一个
|
||||
/// 正弦加一个余弦，二者都不含时间依赖。
|
||||
fn planetary_term(term: &PlanetaryTerm, arguments: &PlanetaryArguments) -> Nutation {
|
||||
let multipliers = &term.argument;
|
||||
let c = &term.coefficients;
|
||||
|
|
@ -108,6 +136,7 @@ fn planetary_term(term: &PlanetaryTerm, arguments: &PlanetaryArguments) -> Nutat
|
|||
let (sine, cosine) = argument.sin_cos();
|
||||
|
||||
// The order is the one the reference uses: sp, cp, se, ce.
|
||||
// 次序即参考实现所用者：sp、cp、se、ce。
|
||||
Nutation::new(c[0] * sine + c[1] * cosine, c[2] * sine + c[3] * cosine)
|
||||
}
|
||||
|
||||
|
|
@ -146,10 +175,20 @@ pub fn nutation_2000a(t: f64) -> Nutation {
|
|||
///
|
||||
/// Source: IAU 2006, as implemented by `eraNut06a`, which applies the
|
||||
/// expressions of Wallace and Capitaine (2006), equations 5.
|
||||
///
|
||||
/// 返回施加 IAU 2006 岁差调整后的章动。
|
||||
///
|
||||
/// IAU 2000A 模型建立在 IAU 1976 岁差之上，而 IAU 2006 岁差改变了岁差
|
||||
/// 速率。该调整使章动与较新的岁差一致，这一组合正是现代天球到地球转换
|
||||
/// 所用的。
|
||||
///
|
||||
/// 出处：IAU 2006，按 `eraNut06a` 所实现，它施加 Wallace 与
|
||||
/// Capitaine（2006）式 5 的表达式。
|
||||
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.
|
||||
// 该调整是对章动本身缩放，而非加上一个独立项，故它被写成一个因子。
|
||||
let fj2 = -2.777_4e-6 * t;
|
||||
Nutation::new(
|
||||
nutation.longitude * (1.0 + 0.469_7e-6 + fj2),
|
||||
|
|
|
|||
|
|
@ -19,6 +19,12 @@ use super::{PlanetaryTerm, SeriesTerm};
|
|||
/// 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.
|
||||
///
|
||||
/// 级数中的日月各项。
|
||||
///
|
||||
/// 各乘数按 `l`、`l'`、`F`、`D`、`Om` 的次序施加于这些参数。各系数依次是
|
||||
/// 黄经正弦、其时间导数、黄经余弦、黄赤交角余弦、其时间导数，以及黄赤交角
|
||||
/// 正弦，单位为 0.1 微角秒。
|
||||
pub static LUNI_SOLAR: [SeriesTerm; 678] = [
|
||||
SeriesTerm {
|
||||
argument: [0, 0, 0, 0, 1],
|
||||
|
|
@ -2749,6 +2755,12 @@ pub static LUNI_SOLAR: [SeriesTerm; 678] = [
|
|||
/// coefficients are the longitude sine, the longitude cosine, the
|
||||
/// obliquity sine, and the obliquity cosine, in units of 0.1
|
||||
/// microarcsecond.
|
||||
///
|
||||
/// 级数中的行星各项。
|
||||
///
|
||||
/// 各乘数按 `l`、`F`、`D`、`Om`、水星到天王星的平黄经、海王星的平黄经，
|
||||
/// 以及一般累积岁差的次序施加于这些参数。各系数依次是黄经正弦、黄经余弦、
|
||||
/// 黄赤交角正弦与黄赤交角余弦，单位为 0.1 微角秒。
|
||||
pub static PLANETARY: [PlanetaryTerm; 687] = [
|
||||
PlanetaryTerm {
|
||||
argument: [0, 0, 0, 0, 0, 0, 8, -16, 4, 5, 0, 0, 0],
|
||||
|
|
|
|||
|
|
@ -30,6 +30,11 @@ const ARCSECOND_TO_RADIAN: f64 = PI / (180.0 * 3_600.0);
|
|||
/// 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.
|
||||
///
|
||||
/// 赤经方向的坐标架偏差，单位为弧度。
|
||||
///
|
||||
/// 国际天球参考系原点与 J2000.0 动力学春分点之间的偏移。该值为负
|
||||
/// 0.0146 角秒。
|
||||
pub const FRAME_BIAS_RIGHT_ASCENSION: f64 = -0.014_6 * ARCSECOND_TO_RADIAN;
|
||||
|
||||
/// The frame bias in declination, in radians.
|
||||
|
|
@ -37,12 +42,21 @@ pub const FRAME_BIAS_RIGHT_ASCENSION: f64 = -0.014_6 * ARCSECOND_TO_RADIAN;
|
|||
/// 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.
|
||||
///
|
||||
/// 赤纬方向的坐标架偏差，单位为弧度。
|
||||
///
|
||||
/// 国际天球参考系极与 J2000.0 平极之间的偏移。该值为负 0.0068192
|
||||
/// 角秒。
|
||||
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.
|
||||
///
|
||||
/// 黄经方向的坐标架偏差，单位为弧度。
|
||||
///
|
||||
/// 沿赤道量得的两个原点之间的偏移。该值为负 0.041775 角秒。
|
||||
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.
|
||||
|
|
@ -51,15 +65,29 @@ pub const FRAME_BIAS_LONGITUDE: f64 = -0.041_775 * ARCSECOND_TO_RADIAN;
|
|||
/// `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.
|
||||
///
|
||||
/// 描述从 J2000.0 到某日岁差的四个角。
|
||||
///
|
||||
/// 它们按参考实现所用的次序施加：绕第三轴转 `gamma_bar`，再绕第一轴转
|
||||
/// `phi_bar`，再绕第三轴转负的 `psi_bar`，再绕第一轴转负的
|
||||
/// `epsilon_a`。
|
||||
#[derive(Debug, Clone, Copy, PartialEq)]
|
||||
pub struct PrecessionAngles {
|
||||
/// The precession of the equator along the ecliptic, in radians.
|
||||
///
|
||||
/// 赤道沿黄道的岁差，单位为弧度。
|
||||
pub gamma_bar: f64,
|
||||
/// The inclination of the moving equator to the ecliptic, in radians.
|
||||
///
|
||||
/// 运动赤道相对黄道的倾角，单位为弧度。
|
||||
pub phi_bar: f64,
|
||||
/// The accumulated precession in longitude, in radians.
|
||||
///
|
||||
/// 黄经上的累积岁差，单位为弧度。
|
||||
pub psi_bar: f64,
|
||||
/// The mean obliquity at the date, in radians.
|
||||
///
|
||||
/// 该日的平黄赤交角，单位为弧度。
|
||||
pub epsilon: f64,
|
||||
}
|
||||
|
||||
|
|
@ -70,6 +98,13 @@ pub struct PrecessionAngles {
|
|||
/// is 84381.406 arcseconds, which is the obliquity at J2000.0.
|
||||
///
|
||||
/// Source: the IAU 2006 precession, as implemented by `eraObl06`.
|
||||
///
|
||||
/// 返回黄道的平黄赤交角，单位为弧度。
|
||||
///
|
||||
/// 该多项式是 IAU 2006 表达式，按地球时标、自 J2000.0 起的儒略世纪求值。
|
||||
/// 常数项为 84381.406 角秒，即 J2000.0 处的黄赤交角。
|
||||
///
|
||||
/// 出处：IAU 2006 岁差，按 `eraObl06` 所实现。
|
||||
pub fn mean_obliquity(t: f64) -> f64 {
|
||||
let arcseconds = 84_381.406
|
||||
+ t * (-46.836_769
|
||||
|
|
@ -118,9 +153,18 @@ pub fn precession_angles(t: f64) -> PrecessionAngles {
|
|||
///
|
||||
/// Source: as implemented by `eraBi00`, which gives the bias as three small
|
||||
/// rotations rather than as a matrix.
|
||||
///
|
||||
/// 返回坐标架偏差旋转矩阵。
|
||||
///
|
||||
/// 该偏差是从国际天球参考系到 J2000.0 动力学平赤道与平春分点的常值
|
||||
/// 转动。其三个角远小于十分之一角秒，但略去它会留下大于章动级数精度
|
||||
/// 的系统误差。
|
||||
///
|
||||
/// 出处：按 `eraBi00` 所实现，它把偏差给出为三个小转动而非一个矩阵。
|
||||
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.
|
||||
// 参考实现由三个基本转动构建该偏差，此处按同一次序再现结果。
|
||||
rotation_z(FRAME_BIAS_LONGITUDE)
|
||||
* rotation_x(FRAME_BIAS_DECLINATION)
|
||||
* rotation_y(FRAME_BIAS_RIGHT_ASCENSION)
|
||||
|
|
@ -150,6 +194,13 @@ pub fn bias_precession_matrix(t: f64) -> Mat3 {
|
|||
/// 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.
|
||||
///
|
||||
/// 在给定预先算出的岁差角时，返回从天球参考系到该日平赤道与平春分点的
|
||||
/// 转动。
|
||||
///
|
||||
/// 出处：按 `eraFw2m` 所实现，它依次施加四个基本转动。参考辅助函数把
|
||||
/// 每个新转动合成到累加器的左侧，故此处的乘积按最后施加的转动写在最前，
|
||||
/// 次序一致。
|
||||
pub fn frame_to_mean_of_date(angles: &PrecessionAngles) -> Mat3 {
|
||||
rotation_x(-angles.epsilon)
|
||||
* rotation_z(-angles.psi_bar)
|
||||
|
|
@ -164,6 +215,12 @@ pub fn frame_to_mean_of_date(angles: &PrecessionAngles) -> Mat3 {
|
|||
/// 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.
|
||||
///
|
||||
/// 返回绕第一轴转 `angle` 的旋转，单位为弧度。
|
||||
///
|
||||
/// 该约定与参考辅助函数 `eraRx` 与 `eraRz` 一致：转动施加于坐标系而非
|
||||
/// 矢量，故该矩阵是把矢量转同一角度的矩阵的转置。因此合成 `a * b` 时先
|
||||
/// 施加 `b`，本模块中的各乘积按各转动实际施加的次序阅读。
|
||||
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])
|
||||
|
|
@ -172,6 +229,10 @@ pub(crate) fn rotation_x(angle: f64) -> Mat3 {
|
|||
/// Returns a rotation of `angle` about the second axis, in radians.
|
||||
///
|
||||
/// The sign convention matches the other axis rotations in this module.
|
||||
///
|
||||
/// 返回绕第二轴转 `angle` 的旋转，单位为弧度。
|
||||
///
|
||||
/// 符号约定与本模块中其余各轴转动一致。
|
||||
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])
|
||||
|
|
@ -180,6 +241,10 @@ fn rotation_y(angle: f64) -> Mat3 {
|
|||
/// Returns a rotation of `angle` about the third axis, in radians.
|
||||
///
|
||||
/// The sign convention matches the other axis rotations in this module.
|
||||
///
|
||||
/// 返回绕第三轴转 `angle` 的旋转，单位为弧度。
|
||||
///
|
||||
/// 符号约定与本模块中其余各轴转动一致。
|
||||
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])
|
||||
|
|
|
|||
|
|
@ -27,6 +27,8 @@ use apsis_math::Mat3;
|
|||
use core::f64::consts::PI;
|
||||
|
||||
/// The number of seconds in a day.
|
||||
///
|
||||
/// 一日的秒数。
|
||||
const SECONDS_PER_DAY: f64 = 86_400.0;
|
||||
|
||||
/// Converts seconds of time to radians.
|
||||
|
|
@ -34,6 +36,11 @@ const SECONDS_PER_DAY: f64 = 86_400.0;
|
|||
/// A full turn is 86 400 seconds of time, so one second of time is
|
||||
/// `2 pi / 86400` radians. Sidereal time is quoted in seconds of time, not in
|
||||
/// arcseconds, and the two differ by a factor of fifteen.
|
||||
///
|
||||
/// 把时间秒换算为弧度。
|
||||
///
|
||||
/// 一整圈是 86 400 时间秒，故一时间秒是 `2 pi / 86400` 弧度。恒星时以时间
|
||||
/// 秒而非角秒给出，二者相差十五倍。
|
||||
const SECONDS_OF_TIME_TO_RADIAN: f64 = 2.0 * PI / SECONDS_PER_DAY;
|
||||
|
||||
/// Returns Greenwich mean sidereal time from the 1982 expression, in
|
||||
|
|
@ -54,9 +61,22 @@ const SECONDS_OF_TIME_TO_RADIAN: f64 = 2.0 * PI / SECONDS_PER_DAY;
|
|||
/// part preserves more of the fraction.
|
||||
///
|
||||
/// Source: as implemented by `eraGmst82`.
|
||||
///
|
||||
/// 返回 1982 表达式给出的格林尼治平恒星时，单位为弧度。
|
||||
///
|
||||
/// 该表达式是自 J2000.0 起儒略世纪数加上当日以时间秒计的零头所构成的多项
|
||||
/// 式。它是 SGP4 理论所拟合的恒星时，故此处用它而非现代表达式：根数集与
|
||||
/// 它一致。
|
||||
///
|
||||
/// 儒略日按两部分取，一为整数天数、一为零头，因为接近 2 461 000 的单个
|
||||
/// `f64` 分辨率约为 40 微秒，而所要求的恒星时优于该值。只有一个值的调用
|
||||
/// 方可以分别传入整数部分与零头，或把同一个值传两次：`(jd, 0.0)`、
|
||||
/// `(2400000.5, mjd)` 与 `(jd - 0.5, 0.5)` 都可接受，但整数部分更小的
|
||||
/// 拆分能保留更多零头。
|
||||
pub fn greenwich_mean_sidereal_time_1982(day: f64, fraction: f64) -> f64 {
|
||||
// The constant absorbs the half day between the start of the Julian
|
||||
// date and the start of the day.
|
||||
// 该常数吸收了儒略日起点与当日起点之间的半日。
|
||||
let a = 24_110.548_41 - SECONDS_PER_DAY / 2.0;
|
||||
let b = 8_640_184.812_866;
|
||||
let c = 0.093_104;
|
||||
|
|
@ -64,6 +84,7 @@ pub fn greenwich_mean_sidereal_time_1982(day: f64, fraction: f64) -> f64 {
|
|||
|
||||
// The reference orders the two parts so that the smaller is the first,
|
||||
// which is the arrangement that preserves the most precision.
|
||||
// 参考实现把两部分排序使较小者在前，这是最能保留精度的安排。
|
||||
let (first, second) = if day < fraction {
|
||||
(day, fraction)
|
||||
} else {
|
||||
|
|
@ -85,6 +106,13 @@ pub fn greenwich_mean_sidereal_time_1982(day: f64, fraction: f64) -> f64 {
|
|||
///
|
||||
/// This is the transformation to apply to the position and velocity that
|
||||
/// `apsis-sgp4` produces.
|
||||
///
|
||||
/// 返回从真赤道平春分点坐标系到地固系的转动。
|
||||
///
|
||||
/// 参数是 UT1 儒略日，因为该转动即地球自转；极移由调用方提供，因为它是
|
||||
/// 实测而非建模的。
|
||||
///
|
||||
/// 这是施加于 `apsis-sgp4` 所产生的位置与速度的变换。
|
||||
pub fn teme_to_terrestrial_matrix(
|
||||
ut1_day: f64,
|
||||
ut1_fraction: f64,
|
||||
|
|
@ -93,6 +121,7 @@ pub fn teme_to_terrestrial_matrix(
|
|||
let sidereal = greenwich_mean_sidereal_time_1982(ut1_day, ut1_fraction);
|
||||
// The composition applies the Earth rotation first and the polar motion
|
||||
// last, with each new rotation on the left of the accumulator.
|
||||
// 该合成先施加地球自转、最后施加极移，每个新转动都在累加器的左侧。
|
||||
polar_motion.matrix() * rotation_z(sidereal)
|
||||
}
|
||||
|
||||
|
|
@ -100,6 +129,11 @@ pub fn teme_to_terrestrial_matrix(
|
|||
///
|
||||
/// The convention is the one the reference helpers use: the rotation is
|
||||
/// applied to the frame, so composing `a * b` applies `b` first.
|
||||
///
|
||||
/// 返回绕第三轴转 `angle` 的旋转，单位为弧度。
|
||||
///
|
||||
/// 约定即各参考辅助函数所用者：转动施加于坐标系，故合成 `a * b` 时先施加
|
||||
/// `b`。
|
||||
fn rotation_z(angle: f64) -> Mat3 {
|
||||
super::precession::rotation_z(angle)
|
||||
}
|
||||
|
|
|
|||
|
|
@ -41,6 +41,13 @@ const ARCSECOND_TO_RADIAN: f64 = PI / (180.0 * 3_600.0);
|
|||
/// reference uses.
|
||||
///
|
||||
/// Source: as implemented by `eraPnm06a` and `eraFw2m`.
|
||||
///
|
||||
/// 返回某时刻的偏差-岁差-章动矩阵。
|
||||
///
|
||||
/// 该矩阵把矢量从天球参考系带到该日的真赤道与真春分点。它由四个岁差角
|
||||
/// 构成，其中最后两个角加上章动，这正是参考实现所用的形式。
|
||||
///
|
||||
/// 出处：按 `eraPnm06a` 与 `eraFw2m` 所实现。
|
||||
pub fn bias_precession_nutation_matrix(t: f64) -> Mat3 {
|
||||
let angles = super::precession::precession_angles(t);
|
||||
let nutation = nutation_2000a_with_2006_adjustment(t);
|
||||
|
|
@ -61,11 +68,20 @@ pub fn bias_precession_nutation_matrix(t: f64) -> Mat3 {
|
|||
/// sidereal time that is quoted to that precision.
|
||||
///
|
||||
/// Source: the MHB2000 complementary terms, as implemented by `eraEect00`.
|
||||
///
|
||||
/// 返回分点方程式的补充项。
|
||||
///
|
||||
/// 分点方程式除黄经章动在真赤道上的投影外，还有来自同一理论的一组小
|
||||
/// 周期项。它们达到密切章动常数项的两倍左右，即一毫秒的时间，故对以该
|
||||
/// 精度给出的恒星时是重要的。
|
||||
///
|
||||
/// 出处：MHB2000 补充项，按 `eraEect00` 所实现。
|
||||
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.
|
||||
// 补充项使用两个参数的 IERS 2003 形式，它们与章动级数所拟合的有所不同。
|
||||
let arguments = [
|
||||
super::fundamental::mean_anomaly_moon(t),
|
||||
super::fundamental::mean_anomaly_sun_iers2003(t),
|
||||
|
|
@ -102,6 +118,7 @@ pub fn equation_of_the_equinoxes_complementary_terms(t: f64) -> f64 {
|
|||
}
|
||||
|
||||
// The tabulated coefficients are in arcseconds.
|
||||
// 所列系数以角秒计。
|
||||
(constant + linear * t) * ARCSECOND_TO_RADIAN
|
||||
}
|
||||
|
||||
|
|
@ -113,6 +130,13 @@ pub fn equation_of_the_equinoxes_complementary_terms(t: f64) -> f64 {
|
|||
///
|
||||
/// The value is the projection of the nutation in longitude onto the true
|
||||
/// equator, `dpsi cos(eps)`, plus the complementary terms of the theory.
|
||||
///
|
||||
/// 返回某时刻的分点方程式。
|
||||
///
|
||||
/// 分点方程式是沿真赤道量得的真春分点与平春分点之差。它是恒星时须用以
|
||||
/// 改正才能成为真春分点时角的量。
|
||||
///
|
||||
/// 该值是黄经章动在真赤道上的投影 `dpsi cos(eps)`，加上该理论的补充项。
|
||||
pub fn equation_of_the_equinoxes(t: f64) -> f64 {
|
||||
let nutation = nutation_2000a_with_2006_adjustment(t);
|
||||
let obliquity = mean_obliquity(t);
|
||||
|
|
@ -125,18 +149,31 @@ pub fn equation_of_the_equinoxes(t: f64) -> f64 {
|
|||
/// 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.
|
||||
///
|
||||
/// 地球的极移，以两个角与转动表示。
|
||||
///
|
||||
/// 极移是自转极在地球内部的运动。它由国际地球自转与参考系服务每日测量
|
||||
/// 并发布，故无法由模型算出，而由调用方提供。
|
||||
#[derive(Debug, Clone, Copy, PartialEq, Default)]
|
||||
pub struct PolarMotion {
|
||||
/// The displacement of the pole along the Greenwich meridian, in
|
||||
/// radians.
|
||||
///
|
||||
/// 极点沿格林尼治子午线的位移，单位为弧度。
|
||||
pub x: f64,
|
||||
/// The displacement of the pole along the meridian ninety degrees west,
|
||||
/// in radians.
|
||||
///
|
||||
/// 极点沿西经九十度子午线的位移，单位为弧度。
|
||||
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.
|
||||
///
|
||||
/// 地球坐标系绕极点的转动，单位为弧度。
|
||||
///
|
||||
/// 这是地球中间原点定位角，它很小，常取为零。
|
||||
pub s: f64,
|
||||
}
|
||||
|
||||
|
|
@ -147,6 +184,11 @@ impl PolarMotion {
|
|||
/// 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.
|
||||
///
|
||||
/// 零极移，即无法获得已发布值时所采用的近似。
|
||||
///
|
||||
/// 略去极移的误差不到十分之一角秒，远低于章动，但高于现代转换的
|
||||
/// 精度。
|
||||
pub const NONE: Self = Self {
|
||||
x: 0.0,
|
||||
y: 0.0,
|
||||
|
|
@ -154,11 +196,15 @@ impl PolarMotion {
|
|||
};
|
||||
|
||||
/// Creates a polar motion from its three angles.
|
||||
///
|
||||
/// 由其三个角创建极移。
|
||||
pub const fn new(x: f64, y: f64, s: f64) -> Self {
|
||||
Self { x, y, s }
|
||||
}
|
||||
|
||||
/// Returns `true` when the angles are usable.
|
||||
///
|
||||
/// 当各角可用时返回 `true`。
|
||||
pub fn is_valid(self) -> bool {
|
||||
self.x.is_finite() && self.y.is_finite() && self.s.is_finite()
|
||||
}
|
||||
|
|
@ -173,6 +219,15 @@ impl PolarMotion {
|
|||
///
|
||||
/// Source: as implemented by `eraPom00`, which applies the rotations in
|
||||
/// sequence by composing each on the left of the accumulator.
|
||||
///
|
||||
/// 返回极移的旋转矩阵。
|
||||
///
|
||||
/// 该转动是绕第三轴转定位角，再绕第二轴转负的 `x` 位移，再绕第一轴
|
||||
/// 转负的 `y` 位移。符号是参考实现所用者，它们把地球坐标系带到与
|
||||
/// 天极对齐。
|
||||
///
|
||||
/// 出处：按 `eraPom00` 所实现，它依次施加各转动，每次都把新转动合成
|
||||
/// 到累加器的左侧。
|
||||
pub fn matrix(self) -> Mat3 {
|
||||
rotation_x(-self.y) * rotation_y(-self.x) * rotation_z(self.s)
|
||||
}
|
||||
|
|
@ -190,6 +245,16 @@ impl PolarMotion {
|
|||
/// 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.
|
||||
///
|
||||
/// 返回某时刻的中间坐标系到地球坐标系的矩阵。
|
||||
///
|
||||
/// 中间坐标系是该日的真赤道与真春分点，地球坐标系是同一日的地固系。这里
|
||||
/// 用基于春分点的方法，其中从一个到另一个的转动是格林尼治视恒星时。
|
||||
///
|
||||
/// 时间参数为 UT1 与 TT 儒略日。
|
||||
///
|
||||
/// 出处：该合成即 `eraC2t06a` 对基于春分点的链条所产生者，极移由完整
|
||||
/// 变换的调用方单独施加。
|
||||
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)
|
||||
|
|
@ -201,6 +266,12 @@ pub fn intermediate_to_terrestrial_matrix(ut1_julian_date: f64, tt_julian_date:
|
|||
/// is the hour angle of the true equinox.
|
||||
///
|
||||
/// Source: as implemented by `eraGst06a`.
|
||||
///
|
||||
/// 返回某 UT1 与 TT 儒略日的格林尼治视恒星时。
|
||||
///
|
||||
/// 它是平恒星时加分点方程式，故即真春分点的时角。
|
||||
///
|
||||
/// 出处：按 `eraGst06a` 所实现。
|
||||
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);
|
||||
|
|
@ -214,9 +285,17 @@ pub fn greenwich_apparent_sidereal_time(ut1_julian_date: f64, tt_julian_date: f6
|
|||
/// non-rotating origin.
|
||||
///
|
||||
/// Source: as implemented by `eraGmst06`.
|
||||
///
|
||||
/// 返回某 UT1 与 TT 儒略日的格林尼治平恒星时。
|
||||
///
|
||||
/// 关系为地球自转角加上赤经上的累积岁差，后者是联系春分点与非旋转原点
|
||||
/// 的量。
|
||||
///
|
||||
/// 出处：按 `eraGmst06` 所实现。
|
||||
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.
|
||||
// 赤经上的累积岁差，单位为角秒。
|
||||
let arcseconds = 0.014_506
|
||||
+ t * (4_612.156_534
|
||||
+ t * (1.391_581_7
|
||||
|
|
@ -230,6 +309,12 @@ pub fn greenwich_mean_sidereal_time(ut1_julian_date: f64, tt_julian_date: f64) -
|
|||
/// which is exact to the precision the angle is known.
|
||||
///
|
||||
/// Source: IERS Conventions (2010), equation 8.32.
|
||||
///
|
||||
/// 返回某 UT1 儒略日的地球自转角。
|
||||
///
|
||||
/// 这是国际天文学联合会的线性表达式，它在该角已知的精度内是精确的。
|
||||
///
|
||||
/// 出处：IERS Conventions（2010），式 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;
|
||||
|
|
@ -245,6 +330,15 @@ pub fn earth_rotation_angle(ut1_julian_date: f64) -> f64 {
|
|||
/// is supplied by the caller because it is measured rather than modelled.
|
||||
///
|
||||
/// Source: the composition is the one `eraC2t06a` produces.
|
||||
///
|
||||
/// 返回某时刻的天球到地球坐标系矩阵。
|
||||
///
|
||||
/// 它合成整条链：坐标架偏差、岁差、章动、地球自转与极移。
|
||||
///
|
||||
/// 时间参数为 UT1 与 TT 儒略日，极移由调用方提供，因为它是实测而非建模
|
||||
/// 的。
|
||||
///
|
||||
/// 出处：该合成即 `eraC2t06a` 所产生者。
|
||||
pub fn celestial_to_terrestrial_matrix(
|
||||
ut1_julian_date: f64,
|
||||
tt_julian_date: f64,
|
||||
|
|
@ -256,6 +350,8 @@ pub fn celestial_to_terrestrial_matrix(
|
|||
// 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.
|
||||
// 该合成即 `eraC2tcio` 所产生者：先是偏差、岁差与章动，然后是地球
|
||||
// 自转，再是极移，每个新转动都合成到累加器的左侧。
|
||||
polar_motion.matrix() * rotation_z(sidereal) * bias_precession_nutation
|
||||
}
|
||||
|
||||
|
|
@ -264,6 +360,11 @@ pub fn celestial_to_terrestrial_matrix(
|
|||
/// 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.
|
||||
///
|
||||
/// 返回绕第一轴转 `angle` 的旋转，单位为弧度。
|
||||
///
|
||||
/// 该约定与参考辅助函数 `eraRx` 一致：转动施加于坐标系，故该矩阵是把
|
||||
/// 矢量转同一角度的矩阵的转置。
|
||||
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])
|
||||
|
|
@ -272,6 +373,10 @@ fn rotation_x(angle: f64) -> Mat3 {
|
|||
/// Returns a rotation of `angle` about the second axis, in radians.
|
||||
///
|
||||
/// The convention is the one of [`rotation_x`].
|
||||
///
|
||||
/// 返回绕第二轴转 `angle` 的旋转，单位为弧度。
|
||||
///
|
||||
/// 约定与 [`rotation_x`] 相同。
|
||||
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])
|
||||
|
|
|
|||
Loading…
Reference in New Issue