diff --git a/crates/physics/apsis-frames/src/earth_rotation.rs b/crates/physics/apsis-frames/src/earth_rotation.rs
index 31eec1b..8ac9334 100644
--- a/crates/physics/apsis-frames/src/earth_rotation.rs
+++ b/crates/physics/apsis-frames/src/earth_rotation.rs
@@ -9,6 +9,11 @@ use core::f64::consts::PI;
 /// The epoch value is zero by the definition of the angle: the International
 /// Astronomical Union defines the Earth Rotation Angle to be zero at
 /// 2000-01-01T12:00:00 UT1.
+///
+/// J2000.0 历元处的地球自转角，以周计。
+///
+/// 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
+/// 处的地球自转角定义为零。
 pub const ERA_J2000_TURNS: f64 = 0.0;
 
 /// The rate of change of the Earth Rotation Angle, in turns per day of UT1.
@@ -18,6 +23,13 @@ pub const ERA_J2000_TURNS: f64 = 0.0;
 /// in a sidereal day, which is shorter than a solar day.
 ///
 /// Source: IERS Conventions (2010), equation 8.32.
+///
+/// 地球自转角的变化率，以每 UT1 日的周数计。
+///
+/// 该值为 `1.002 737 811 911 354 6`，即每天 `360.985 612 288 088` 度。它
+/// 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。
+///
+/// 出处：IERS Conventions（2010），式 8.32。
 pub const ERA_RATE_TURNS_PER_DAY: f64 = 1.002_737_811_911_354_6;
 
 /// The number of days from the J2000.0 epoch to the given Julian Date on the
@@ -25,6 +37,10 @@ pub const ERA_RATE_TURNS_PER_DAY: f64 = 1.002_737_811_911_354_6;
 ///
 /// The J2000.0 epoch is Julian Date 2451545.0, which is noon on
 /// 2000-01-01.
+///
+/// 从 J2000.0 历元到给定 UT1 时标儒略日的天数。
+///
+/// J2000.0 历元是儒略日 2451545.0，即 2000-01-01 的正午。
 pub fn ut1_days_from_j2000(ut1_julian_date: f64) -> f64 {
     ut1_julian_date - 2_451_545.0
 }
@@ -40,6 +56,14 @@ pub fn ut1_days_from_j2000(ut1_julian_date: f64) -> f64 {
 /// is periodic with a period of one. The value returned is not reduced to
 /// any interval, so differences between two angles are meaningful even when
 /// the interval is longer than a day.
+///
+/// 某瞬时的地球自转角。
+///
+/// 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
+/// 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。
+///
+/// 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
+/// 区间，故即便区间长于一日，两角之差仍有意义。
 #[derive(Debug, Clone, Copy, PartialEq, PartialOrd)]
 pub struct EarthRotationAngle {
     turns: f64,
@@ -47,11 +71,15 @@ pub struct EarthRotationAngle {
 
 impl EarthRotationAngle {
     /// Creates an angle from a value in turns.
+    ///
+    /// 由以周表示的值创建角。
     pub const fn from_turns(turns: f64) -> Self {
         Self { turns }
     }
 
     /// Creates an angle from a value in radians.
+    ///
+    /// 由以弧度表示的值创建角。
     pub fn from_radians(radians: f64) -> Self {
         Self {
             turns: radians / (2.0 * PI),
@@ -59,6 +87,8 @@ impl EarthRotationAngle {
     }
 
     /// Returns the angle for a Julian Date on the UT1 scale.
+    ///
+    /// 返回 UT1 时标上某儒略日对应的角。
     pub fn from_ut1_julian_date(ut1_julian_date: f64) -> Self {
         Self::from_ut1_days(ut1_days_from_j2000(ut1_julian_date))
     }
@@ -72,6 +102,14 @@ impl EarthRotationAngle {
     /// about 280.46 degrees.
     ///
     /// Source: IERS Conventions (2010), equation 8.32.
+    ///
+    /// 返回自 J2000.0 历元起的若干 UT1 天对应的角。
+    ///
+    /// 该式为线性：`theta = 0.779 057 273 2640 + 1.002 737 909 350 795 * d`，
+    /// 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，
+    /// 约为 280.46 度。
+    ///
+    /// 出处：IERS Conventions（2010），式 8.32。
     pub fn from_ut1_days(days_since_j2000: f64) -> Self {
         const EPOCH_TURNS: f64 = 0.779_057_273_264_0;
         Self {
@@ -82,11 +120,17 @@ impl EarthRotationAngle {
     /// Returns the angle in turns.
     ///
     /// The value is not reduced to `[0, 1)`.
+    ///
+    /// 返回以周表示的角。
+    ///
+    /// 该值不归约到 `[0, 1)`。
     pub const fn turns(self) -> f64 {
         self.turns
     }
 
     /// Returns the angle in turns, reduced to `[0, 1)`.
+    ///
+    /// 返回以周表示的角，归约到 `[0, 1)`。
     pub fn turns_positive(self) -> f64 {
         self.turns.rem_euclid(1.0)
     }
@@ -94,11 +138,17 @@ impl EarthRotationAngle {
     /// Returns the angle in radians.
     ///
     /// The value is not reduced to `[0, 2 pi)`.
+    ///
+    /// 返回以弧度表示的角。
+    ///
+    /// 该值不归约到 `[0, 2 pi)`。
     pub fn radians(self) -> f64 {
         self.turns * 2.0 * PI
     }
 
     /// Returns the angle in radians, reduced to `[0, 2 pi)`.
+    ///
+    /// 返回以弧度表示的角，归约到 `[0, 2 pi)`。
     pub fn radians_positive(self) -> f64 {
         self.turns_positive() * 2.0 * PI
     }
@@ -111,6 +161,12 @@ impl EarthRotationAngle {
 /// Rotation Angle. Applying it to an inertial vector yields the Earth-fixed
 /// vector, so a vector that is fixed in inertial space acquires a negative
 /// rotation as the Earth turns beneath it.
+///
+/// 返回把惯性系中的矢量映射到地固系的转动。
+///
+/// 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
+/// 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
+/// 转动。
 pub fn rotation_eci_to_ecef(angle: EarthRotationAngle) -> Mat3 {
     let (sin, cos) = angle.radians_positive().sin_cos();
     Mat3::from_rows([cos, sin, 0.0], [-sin, cos, 0.0], [0.0, 0.0, 1.0])
@@ -121,6 +177,10 @@ pub fn rotation_eci_to_ecef(angle: EarthRotationAngle) -> Mat3 {
 ///
 /// This is the transpose of [`rotation_eci_to_ecef`], which for a rotation
 /// matrix is also its inverse.
+///
+/// 返回把地固系中的矢量映射到惯性系的转动。
+///
+/// 它是 [`rotation_eci_to_ecef`] 的转置，对旋转矩阵而言也是其逆。
 pub fn rotation_ecef_to_eci(angle: EarthRotationAngle) -> Mat3 {
     rotation_eci_to_ecef(angle).transpose()
 }
diff --git a/crates/physics/apsis-frames/src/iau2000/eect_table.rs b/crates/physics/apsis-frames/src/iau2000/eect_table.rs
index 663bd2d..e8ea266 100644
--- a/crates/physics/apsis-frames/src/iau2000/eect_table.rs
+++ b/crates/physics/apsis-frames/src/iau2000/eect_table.rs
@@ -14,6 +14,11 @@ use super::ComplementaryTerm;
 /// 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.
+///
+/// 不依赖时间的各项。
+///
+/// 八个乘数按 `l`、`l'`、`F`、`D`、`Om`、金星的平黄经、地球的平黄经，以及
+/// 一般累积岁差的次序施加于这些参数。
 pub static CONSTANT_TERMS: [ComplementaryTerm; 33] = [
     ComplementaryTerm {
         argument: [0, 0, 0, 0, 1, 0, 0, 0],
@@ -152,6 +157,10 @@ pub static CONSTANT_TERMS: [ComplementaryTerm; 33] = [
 /// The terms whose amplitude grows linearly with time.
 ///
 /// The arguments are the same as for the constant terms.
+///
+/// 幅度随时间线性增长的各项。
+///
+/// 参数与常数项相同。
 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
index 7ba8fd0..63f6cae 100644
--- a/crates/physics/apsis-frames/src/iau2000/fundamental.rs
+++ b/crates/physics/apsis-frames/src/iau2000/fundamental.rs
@@ -298,12 +298,20 @@ impl DelaunayArguments {
 #[derive(Debug, Clone, Copy, PartialEq)]
 pub struct PlanetaryArguments {
     /// The mean anomaly of the Moon.
+    ///
+    /// 月球的平近点角。
     pub l: f64,
     /// The mean argument of latitude of the Moon.
+    ///
+    /// 月球的平纬度参数。
     pub f: f64,
     /// The mean elongation of the Moon from the Sun.
+    ///
+    /// 月球相对太阳的平距角。
     pub d: f64,
     /// The mean longitude of the Moon's ascending node.
+    ///
+    /// 月球升交点的平黄经。
     pub omega: f64,
     /// The mean longitude of Mercury.
     ///
@@ -366,6 +374,8 @@ impl PlanetaryArguments {
     }
 
     /// Returns the arguments as an array in series order.
+    ///
+    /// 按级数次序把各参数作为数组返回。
     pub const fn as_array(self) -> [f64; 13] {
         [
             self.l,
diff --git a/crates/physics/apsis-frames/src/iau2000/mod.rs b/crates/physics/apsis-frames/src/iau2000/mod.rs
index 76e7dbb..a96196a 100644
--- a/crates/physics/apsis-frames/src/iau2000/mod.rs
+++ b/crates/physics/apsis-frames/src/iau2000/mod.rs
@@ -67,12 +67,22 @@ pub use terrestrial::{
 /// `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.
+///
+/// 日月章动级数的一项。
+///
+/// 五个乘数按 `l`、`l'`、`F`、`D`、`Om` 的次序施加于 Delaunay 参数。六个
+/// 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。
 #[derive(Debug, Clone, Copy)]
 pub struct SeriesTerm {
     /// The integer multipliers of the five Delaunay arguments.
+    ///
+    /// 五个 Delaunay 参数的整数乘数。
     pub argument: [i32; 5],
     /// The six coefficients of the term, in the order the reference lists
     /// them.
+    ///
+    /// 该项的六个系数，按参考实现列出的次序。
     pub coefficients: [f64; 6],
 }
 
@@ -82,11 +92,20 @@ pub struct SeriesTerm {
 /// 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.
+///
+/// 分点方程式补充项的一项。
+///
+/// 八个乘数施加于参数 `l`、`l'`、`F`、`D`、`Om`、金星的平黄经、地球的平
+/// 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。
 #[derive(Debug, Clone, Copy)]
 pub struct ComplementaryTerm {
     /// The integer multipliers of the eight arguments.
+    ///
+    /// 八个参数的整数乘数。
     pub argument: [i32; 8],
     /// The sine and cosine coefficients.
+    ///
+    /// 正弦与余弦系数。
     pub coefficients: [f64; 2],
 }
 
@@ -97,11 +116,21 @@ pub struct ComplementaryTerm {
 /// 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.
+///
+/// 行星章动级数的一项。
+///
+/// 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
+/// 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
+/// 正弦与黄赤交角余弦，单位为 0.1 微角秒。
 #[derive(Debug, Clone, Copy)]
 pub struct PlanetaryTerm {
     /// The integer multipliers of the thirteen planetary arguments.
+    ///
+    /// 十三个行星参数的整数乘数。
     pub argument: [i32; 13],
     /// The four coefficients of the term, in the order the reference lists
     /// them.
+    ///
+    /// 该项的四个系数，按参考实现列出的次序。
     pub coefficients: [f64; 4],
 }
diff --git a/crates/physics/apsis-frames/src/iau2000/nutation.rs b/crates/physics/apsis-frames/src/iau2000/nutation.rs
index 4187d51..68cc6d1 100644
--- a/crates/physics/apsis-frames/src/iau2000/nutation.rs
+++ b/crates/physics/apsis-frames/src/iau2000/nutation.rs
@@ -25,6 +25,8 @@ use super::{PlanetaryTerm, SeriesTerm};
 use core::f64::consts::PI;
 
 /// Converts a coefficient in units of 0.1 microarcsecond to radians.
+///
+/// 把以 0.1 微角秒为单位的系数换算为弧度。
 const UNIT_TO_RADIAN: f64 = 1.0e-7 * PI / (180.0 * 3_600.0);
 
 /// Converts arcseconds to radians.
@@ -33,16 +35,24 @@ const UNIT_TO_RADIAN: f64 = 1.0e-7 * PI / (180.0 * 3_600.0);
 const ARCSECOND_TO_RADIAN: f64 = PI / (180.0 * 3_600.0);
 
 /// The nutation in longitude and obliquity, in radians.
+///
+/// 黄经与黄赤交角方向的章动，单位为弧度。
 #[derive(Debug, Clone, Copy, PartialEq, Default)]
 pub struct Nutation {
     /// The nutation in longitude, in radians.
+    ///
+    /// 黄经方向的章动，单位为弧度。
     pub longitude: f64,
     /// The nutation in obliquity, in radians.
+    ///
+    /// 黄赤交角方向的章动，单位为弧度。
     pub obliquity: f64,
 }
 
 impl Nutation {
     /// Creates a nutation from its two angles.
+    ///
+    /// 由其两个角创建章动。
     pub const fn new(longitude: f64, obliquity: f64) -> Self {
         Self {
             longitude,
@@ -51,16 +61,22 @@ impl Nutation {
     }
 
     /// Returns the nutation in longitude, in arcseconds.
+    ///
+    /// 返回黄经方向的章动，单位为角秒。
     pub fn longitude_arcseconds(self) -> f64 {
         self.longitude / ARCSECOND_TO_RADIAN
     }
 
     /// Returns the nutation in obliquity, in arcseconds.
+    ///
+    /// 返回黄赤交角方向的章动，单位为角秒。
     pub fn obliquity_arcseconds(self) -> f64 {
         self.obliquity / ARCSECOND_TO_RADIAN
     }
 
     /// Returns the sum of two nutations.
+    ///
+    /// 返回两个章动之和。
     pub const fn plus(self, other: Self) -> Self {
         Self::new(
             self.longitude + other.longitude,
@@ -75,6 +91,12 @@ impl Nutation {
 /// 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.
+///
+/// 求日月级数的一项。
+///
+/// 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
+/// 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
+/// 一个正弦之和。
 fn lunisolar_term(term: &SeriesTerm, arguments: &DelaunayArguments, t: f64) -> Nutation {
     let multipliers = &term.argument;
     let c = &term.coefficients;
@@ -86,6 +108,7 @@ fn lunisolar_term(term: &SeriesTerm, arguments: &DelaunayArguments, t: f64) -> N
     let (sine, cosine) = argument.sin_cos();
 
     // The order is the one the reference uses: sp, spt, cp, ce, cet, se.
+    // 次序即参考实现所用者：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,
@@ -97,6 +120,11 @@ fn lunisolar_term(term: &SeriesTerm, arguments: &DelaunayArguments, t: f64) -> N
 /// 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.
+///
+/// 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),
diff --git a/crates/physics/apsis-frames/src/iau2000/nutation_table.rs b/crates/physics/apsis-frames/src/iau2000/nutation_table.rs
index d975f83..4d1d8b0 100644
--- a/crates/physics/apsis-frames/src/iau2000/nutation_table.rs
+++ b/crates/physics/apsis-frames/src/iau2000/nutation_table.rs
@@ -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],
diff --git a/crates/physics/apsis-frames/src/iau2000/precession.rs b/crates/physics/apsis-frames/src/iau2000/precession.rs
index 1d2a02c..e0d0276 100644
--- a/crates/physics/apsis-frames/src/iau2000/precession.rs
+++ b/crates/physics/apsis-frames/src/iau2000/precession.rs
@@ -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])
diff --git a/crates/physics/apsis-frames/src/iau2000/teme.rs b/crates/physics/apsis-frames/src/iau2000/teme.rs
index eb3c363..7e8994a 100644
--- a/crates/physics/apsis-frames/src/iau2000/teme.rs
+++ b/crates/physics/apsis-frames/src/iau2000/teme.rs
@@ -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)
 }
diff --git a/crates/physics/apsis-frames/src/iau2000/terrestrial.rs b/crates/physics/apsis-frames/src/iau2000/terrestrial.rs
index 2c4054d..04ef78d 100644
--- a/crates/physics/apsis-frames/src/iau2000/terrestrial.rs
+++ b/crates/physics/apsis-frames/src/iau2000/terrestrial.rs
@@ -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])