astro 2.0.0

/*
Copyright (c) 2015, 2016 Saurav Sachidanand

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
*/

//! The Earth's moon

use angle;
use coords;
use time;

/**
Computes the equatorial horizontal parallax of the Moon

# Returns

* `eq_hz_parllx`: Equatorial horizontal parallax of the
                  Moon *| in radians*

# Arguments

* `earth_moon_dist`: Earth-Moon distance *| in kilometers*
**/
#[inline]
pub fn eq_hz_parllx(earth_moon_dist: f64) -> f64 {

    (6378.14 / earth_moon_dist).asin()

}

/**
Computes the equatorial semidiameter of the Moon

# Returns

* `eq_semidiameter`: Geocentric equatorial semidiameter
                     *| in radians per kilometers*

# Arguments

* `earth_moon_dist`: Earth-Moon distance *| in kilometers*
**/
#[inline]
pub fn semidiameter(earth_moon_dist: f64) -> f64 {

    0.272481 * eq_hz_parllx(earth_moon_dist).sin()

}

/**
Computes the inclination of the mean lunar equator with the
ecliptic

# Returns

* `inc`: Inclination of the mean lunar equator with the
         ecliptic *| in radians*
**/
#[inline]
pub fn inc_of_mn_lunar_eq() -> f64 {

    angle::deg_frm_dms(1, 32, 32.7).to_radians()

}

#[inline]
fn A (

    mn_geocent_moon_long   : f64,
    app_geocent_moon_lat   : f64,
    long_of_mn_ascent_node : f64

) -> f64 {

    let I = inc_of_mn_lunar_eq();
    let W = mn_geocent_moon_long - long_of_mn_ascent_node;

    (
        W.sin() * app_geocent_moon_lat.cos() * I.cos()
      - app_geocent_moon_lat.sin() * I.sin()
    ).atan2(W.cos() * app_geocent_moon_lat.cos())

}

#[inline]
fn F(JC: f64) -> f64 {

    angle::limit_to_360(
        Horner_eval!(
            JC,
            93.272095,
            483202.0175233,
           -0.0036539,
           -1.0 / 3526000.0,
            1.0 / 863310000.0
         )
    ).to_radians()

}

#[inline]
fn E(JC: f64) -> f64 {

    1.0 - JC*(0.002_516 + JC*0.000_0074)

}

#[inline]
fn DMM1(JC: f64) -> (f64, f64, f64) {

    let D = angle::limit_to_360(
        Horner_eval!(
            JC,
            297.8501921,
            445267.1114034,
           -0.0018819,
            1.0 / 545868.0,
           -1.0 / 113065000.0
       )
   ).to_radians();

    let M = angle::limit_to_360(
        Horner_eval!(
            JC,
            357.5291092,
            35999.0502909,
           -0.0001536,
            1.0 / 24490000.0
         )
    ).to_radians();

    let M1 = angle::limit_to_360(
        Horner_eval!(
            JC,
            134.9633964,
            477198.8675055,
            0.0087414,
            1.0 / 69699.0,
           -1.0 / 14712000.0
        )
    ).to_radians();

    (D, M, M1)

}

#[inline]
fn rho_sig(D: f64, M1: f64, F: f64) -> (f64, f64) {

    let x2F = 2.0 * F;
    let x2F2D = x2F - 2.0*D;

    (
        (
          - 0.02752 * M1.cos()
          - 0.02245 * F.sin()
          + 0.00684 * (M1 - x2F).cos()
          - 0.00293 * (x2F).cos()
          - 0.00085 * (x2F2D).cos()
          - 0.00054 * (M1 - 2.0*D).cos()
          - 0.00020 * (
                (M1 + F).sin()
              + (M1 + x2F).cos()
              + (M1 - F).cos()
            )
          + 0.00014 * (M1 + x2F2D).cos()
        ).to_radians(),

        (
          - 0.02816 * M1.sin()
          + 0.02244 * F.cos()
          - 0.00682 * (M1 - x2F).sin()
          - 0.00279 * (x2F).sin()
          - 0.00083 * (x2F2D).sin()
          + 0.00069 * (M1 - 2.0*D).sin()
          + 0.0004  * (M1 + F).cos()
          - 0.00025 * (2.0 * M1).sin()
          - 0.00023 * (M1 + x2F).sin()
          + 0.0002  * (M1 - F).cos()
          + 0.00019 * (M1 - F).sin()
          + 0.00013 * (M1 + x2F2D).sin()
          - 0.0001  * (M1 - 3.0*F).cos()
        ).to_radians()
    )

}

/**
Computes the optical librations of the Moon in longitude and
latitude

# Returns

`(optical_libr_in_long, optical_libr_in_lat)`

* `optical_libr_in_long`: The optical libration in
                          longitude *| in radians*
* `optical_libr_in_lat` : The optical libration in
                          latitude *| in radians*

# Arguments

* `JD`                 : Julian (Ephemeris) day
* `mn_ecl_long_moon`   : The mean ecliptic longitude of the
                         Moon *| in radians*, i.e, *without* the correction for
                         nutation
* `apprnt_ecl_lat_moon`: The apparent ecliptic latitude of the
                         Moon *| in radians*, i.e, *with* the correction for
                         nutation
**/
pub fn optical_libr (

    JD                  : f64,
    mn_ecl_long_moon    : f64,
    apprnt_ecl_lat_moon : f64,

) -> (f64, f64) {

    let JC = time::julian_cent(JD);
    let F = F(JC);
    let I = inc_of_mn_lunar_eq();

    let long_of_mn_ascend_node = mn_ascend_node(JC);
    let W = mn_ecl_long_moon - long_of_mn_ascend_node;

    let A = A (
        mn_ecl_long_moon, apprnt_ecl_lat_moon, long_of_mn_ascend_node
    );

    let b1 = (
       -W.sin() * apprnt_ecl_lat_moon.cos() * I.sin()
      - apprnt_ecl_lat_moon.sin() * I.cos()
    ).asin();

    (angle::limit_to_two_PI(A - F), b1)

}

/**
Computes the physical librations of the Moon in longitude and
latitude

# Returns

`(physical_libr_in_long, physical_libr_in_lat)`

* `physical_libr_in_long`: The physical libration in
                           longitude *| in radians*
* `physical_libr_in_lat`: The physical libration in
                          latitude *| in radians*

# Arguments

* `JD`                 : Julian (Ephemeris) day
* `mn_ecl_long_moon`   : The mean ecliptic longitude of the
                         Moon *| in radians*, i.e, *without* the correction
                         for nutation
* `apprnt_ecl_lat_moon`: The apparent ecliptic latitude of the
                         Moon *| in radians*, i.e, *with* the correction for
                         nutation
* `optical_lib_lat`    : The optical libration in latitude *| in radians*
**/
pub fn physical_libr (

    JD                  : f64,
    mn_ecl_long_moon    : f64,
    apprnt_ecl_lat_moon : f64,
    optical_lib_lat     : f64

) -> (f64, f64) {

    let JC = time::julian_cent(JD);
    let K1 = (119.75 + 131.849*JC).to_radians();
    let K2 = (72.560 + 20.186*JC).to_radians();

    let long_of_mn_ascend_node = mn_ascend_node(JC);
    let (D, M, M1) = DMM1(JC);
    let F = F(JC);
    let E = E(JC);

    let x2F = 2.0 * F;
    let x2D = 2.0 * D;
    let x2F2D = x2F - x2D;

    let (rho, sig) = rho_sig(D, M1, F);
    let tau = (
        0.02520 * E * M.sin()
      + 0.00473 * (2.0*M1 - x2F).sin()
      - 0.00467 * M1.sin()
      + 0.00396 * K1.sin()
      + 0.00276 * (2.0*M1 - x2D).sin()
      + 0.00196 * long_of_mn_ascend_node.sin()
      - 0.00183 * (M1 - F).cos()
      + 0.00115 * (M1 - x2D).sin()
      - 0.00096 * (M1 - D).sin()
      + 0.00046 * (x2F2D).sin()
      - 0.00039 * (M1 - F).sin()
      - 0.00032 * (M1 - M - D).sin()
      + 0.00027 * (2.0*M1 - M - x2D).sin()
      + 0.00023 * K2.sin()
      - 0.00014 * (
            x2D.sin()
          - (2.0*M1 - x2F).cos()
        )
      - 0.00012 * (
            (M1 - x2F).sin()
          + (2.0 * M1).sin()
        )
      + 0.00011 * (2.0 * (M1 - M - D)).sin()
    ).to_radians();

    let A = A (
        mn_ecl_long_moon, apprnt_ecl_lat_moon, long_of_mn_ascend_node
    );

    (
        optical_lib_lat.tan() * (rho*A.cos() + sig*A.sin()) - tau,
        sig*A.cos() - rho*A.sin()
    )

}

/**
Computes the total librations of the Moon in longitude and
latitude

# Returns

`(total_libr_in_long, total_libr_in_lat)`

* `total_libr_in_long`: The total libration in longitude *| in radians*
* `total_libr_in_lat` : The total libration in latitude *| in radians*

# Arguments

* `JD`                 : Julian (Ephemeris) day
* `mn_ecl_long_moon`   : The mean ecliptic longitude of the
                         Moon *| in radians*, i.e, *without* the correction
                         for nutation
* `apprnt_ecl_lat_moon`: The apparent ecliptic latitude of the
                         Moon *| in radians*, i.e, *with* the correction for
                         nutation
**/
pub fn total_libr (

    JD                  : f64,
    mn_ecl_long_moon    : f64,
    apprnt_ecl_lat_moon : f64

) -> (f64, f64) {

    let (opt_long, opt_lat) = optical_libr (
        mn_ecl_long_moon, apprnt_ecl_lat_moon, JD
    );
    let (phys_long, phys_lat) = physical_libr (
        mn_ecl_long_moon, apprnt_ecl_lat_moon, JD, opt_lat
    );

    (opt_long + phys_long, opt_lat + phys_lat)

}

/**
Computes the position angle of the axis of rotation of the Moon

# Returns

* `pos_angl_of_axis_of_rot`: The position angle of the axis
                             of rotation of the Moon *| in radians*

# Arguments

* `JD`                 : Julian (Ephemeris) day
* `mn_ascent_node_long`: Longitude of the mean ascending node of the
                         Moon *| in radians*
* `total_lib_lat`      : Total libration of the Moon in
                         latitude *| in radians*
* `nut_in_long`        : Nutation correction for longitude *| in radians*
* `true_oblq`          : True obliquity of the ecliptic *| in radians*
* `apprnt_moon_asc`    : Apparent geocentric right ascension of the
                         Moon *| in radians*
**/
#[allow(unused_variables)]
pub fn pos_angl_of_axis_of_rot (

    JD                  : f64,
    mn_ascent_node_long : f64,
    total_lib_lat       : f64,
    nut_in_long         : f64,
    true_oblq           : f64,
    apprnt_moon_asc     : f64

) -> f64 {

    let JC = time::julian_cent(JD);
    let (D, M, M1) = DMM1(JC);
    let F = F(JC);
    let (rho, sig) = rho_sig(D, M1, F);

    let I = inc_of_mn_lunar_eq();
    let V = mn_ascent_node_long + nut_in_long + sig/I.sin();
    let X = (I + rho).sin() * V.sin();
    let Y =
        (I + rho).sin()*V.cos()*true_oblq.cos()
      - (I + rho).cos()*true_oblq.sin();
    let w = X.atan2(Y);

    (
        (X*X + Y*Y).sqrt() * (apprnt_moon_asc - w).cos() / total_lib_lat.cos()
    ).asin()

}

/**
Computes the topocentric librations of the Moon

# Returns

`(topocent_libr_in_long, topocent_libr_in_lat, topocent_libr_in_P)`

* `topocent_libr_in_long`: Topocentric libration in longitude *| in radians*
* `topocent_libr_in_lat` : Topocentric libration in latitude *| in radians*
* `topocent_libr_in_P`   : Topocentric libration in position angle of the axis
                           of rotation *| in radians*

# Arguments

* `observer_lat`          : Latitude of the observer *| in radians*
* `geocent_dec_moon`      : Geocentric decation of the Moon *| in radians*
* `local_hour_angl`       : Local hour angle of the Moon *| in radians*
* `geocent_hz_parllx_moon`: Geocentric equatorial horizontal parallax of the
                            Moon *| in radians*
* `pos_angl_axis_of_rot`  : Position angle of the axis of rotation of the
                            Moon *| in radians*
* `total_lib_lat`         : Total libration of the Moon in
                            latitude *| in radians*
**/
pub fn topocent_libr_by_diff_corrections (

    observer_lat           : f64,
    geocent_dec_moon       : f64,
    local_hour_angl        : f64,
    geocent_hz_parllx_moon : f64,
    pos_angl_axis_of_rot   : f64,
    total_lib_lat          : f64

) -> (f64, f64, f64) {

    let Q = (observer_lat.cos() * local_hour_angl.sin()).atan2 (
        geocent_dec_moon.cos() * observer_lat.sin()
      - geocent_dec_moon.sin() * observer_lat.cos() * local_hour_angl.cos()
    );
    let z = (
        geocent_dec_moon.sin() * observer_lat.sin()
      + geocent_dec_moon.cos() * observer_lat.cos() * local_hour_angl.cos()
    ).acos();
    let pi1 = geocent_hz_parllx_moon * (z.sin() + 0.0084*(2.0 * z).sin());

    let delta_l = -pi1 * (Q - pos_angl_axis_of_rot).sin() / total_lib_lat.cos();
    let delta_b = -pi1 * (Q - pos_angl_axis_of_rot).cos();
    let delta_P =
        delta_l * (total_lib_lat + delta_b).sin()
      - pi1 * Q.sin() * geocent_dec_moon.tan();

    (delta_l, delta_b, delta_P)

}

/**
Computes the geocentric ecliptic position of the Moon,
referred to the mean equinox of the date

# Returns

`(moon_ecl_point, rad_vec)`

* `moon_ecl_point`: Ecliptic point of the Moon *| in radians*
* `rad_vec`: Moon-Earth distance *| in kilometers*

This function uses the partial Chapront ELP-2000/82
lunar theory, so the accruacy of:

* `moon_ecl_point.long`: is `10` arcseconds
* `moon_ecl_point.lat`: is `4` arcseconds

# Arguments

* `JD`: Julian (Ephemeris) day
**/
pub fn geocent_ecl_pos(JD: f64) -> (coords::EclPoint, f64) {

    let JC = time::julian_cent(JD);
    let (D, M, M1) = DMM1(JC);
    let F = F(JC);
    let E = E(JC);
    let L1 = angle::limit_to_360(
        Horner_eval!(
            JC,
            218.3164477,
            481267.88123421,
           -0.0015786,
            1.0 / 538841.0,
           -1.0 / 65194000.0
        )
    ).to_radians();

    let A1 = angle::limit_to_360(119.75 + 131.849*JC).to_radians();
    let A2 = angle::limit_to_360(53.090 + 479264.29*JC).to_radians();
    let A3 = angle::limit_to_360(313.45 + 481266.484*JC).to_radians();

    struct lrterms(i8, i8, i8, i8, i32, i32);
    let terms_for_lr = [
        lrterms(0,  0,  1,  0,  6288774, -20905355),
        lrterms(2,  0, -1,  0,  1274027, -3699111),
        lrterms(2,  0,  0,  0,  658314,  -2955968),
        lrterms(0,  0,  2,  0,  213618,  -569925),
        lrterms(0,  1,  0,  0, -185116,   48888),
        lrterms(0,  0,  0,  2, -114332,  -3149),
        lrterms(2,  0, -2,  0,  58793,    246158),
        lrterms(2, -1, -1,  0,  57066,   -152138),
        lrterms(2,  0,  1,  0,  53322,   -170733),
        lrterms(2, -1,  0,  0,  45758,   -204586),
        lrterms(0,  1, -1,  0, -40923,   -129620),
        lrterms(1,  0,  0,  0, -34720,    108743),
        lrterms(0,  1,  1,  0, -30383,    104755),
        lrterms(2,  0,  0, -2,  15327,    10321),
        lrterms(0,  0,  1,  2, -12528,    0),
        lrterms(0,  0,  1, -2,  10980,    79661),
        lrterms(4,  0, -1,  0,  10675,   -34782),
        lrterms(0,  0,  3,  0,  10034,   -23210),
        lrterms(4,  0, -2,  0,  8548,    -21636),
        lrterms(2,  1, -1,  0, -7888,     24208),
        lrterms(2,  1,  0,  0, -6766,     30824),
        lrterms(1,  0, -1,  0, -5163,    -8379),
        lrterms(1,  1,  0,  0,  4987,    -16675),
        lrterms(2, -1,  1,  0,  4036,    -12831),
        lrterms(2,  0,  2,  0,  3994,    -10445),
        lrterms(4,  0,  0,  0,  3861,    -11650),
        lrterms(2,  0, -3,  0,  3665,     14403),
        lrterms(0,  1, -2,  0, -2689,    -7003),
        lrterms(2,  0, -1,  2, -2602,     0),
        lrterms(2, -1, -2,  0,  2390,     10056),
        lrterms(1,  0,  1,  0, -2348,     6322),
        lrterms(2, -2,  0,  0,  2236,    -9884),
        lrterms(0,  1,  2,  0, -2120,     5751),
        lrterms(0,  2,  0,  0, -2069,     0),
        lrterms(2, -2, -1,  0,  2048,    -4950),
        lrterms(2,  0,  1, -2, -1773,     4130),
        lrterms(2,  0,  0,  2, -1595,     0),
        lrterms(4, -1, -1,  0,  1215,    -3958),
        lrterms(0,  0,  2,  2, -1110,     0),
        lrterms(3,  0, -1,  0, -892,      3258),
        lrterms(2,  1,  1,  0, -810,      2616),
        lrterms(4, -1, -2,  0,  759,     -1897),
        lrterms(0,  2, -1,  0, -713,     -2117),
        lrterms(2,  2, -1,  0, -700,      2354),
        lrterms(2,  1, -2,  0,  691,      0),
        lrterms(2, -1,  0, -2,  596,      0),
        lrterms(4,  0,  1,  0,  549,     -1423),
        lrterms(0,  0,  4,  0,  537,     -1117),
        lrterms(4, -1,  0,  0,  520,     -1571),
        lrterms(1,  0, -2,  0, -487,     -1739),
        lrterms(2,  1,  0, -2, -399,      0),
        lrterms(0,  0,  2, -2, -381,     -4421),
        lrterms(1,  1,  1,  0,  351,      0),
        lrterms(3,  0, -2,  0, -340,      0),
        lrterms(4,  0, -3,  0,  330,      0),
        lrterms(2, -1,  2,  0,  327,      0),
        lrterms(0,  2,  1,  0, -323,      1165),
        lrterms(1,  1, -1,  0,  299,      0),
        lrterms(2,  0,  3,  0,  294,      0),
        lrterms(2,  0, -1, -2,  0,        8752),
    ];
    struct bterms(i8, i8, i8, i8, i32);
    let terms_for_b = [
        bterms(0,  0,  0,  1,  5128122),
    	bterms(0,  0,  1,  1,  280602),
    	bterms(0,  0,  1, -1,  277693),
    	bterms(2,  0,  0, -1,  173237),
    	bterms(2,  0, -1,  1,  55413),
    	bterms(2,  0, -1, -1,  46271),
    	bterms(2,  0,  0,  1,  32573),
    	bterms(0,  0,  2,  1,  17198),
    	bterms(2,  0,  1, -1,  9266),
    	bterms(0,  0,  2, -1,  8822),
    	bterms(2, -1,  0, -1,  8216),
    	bterms(2,  0, -2, -1,  4324),
    	bterms(2,  0,  1,  1,  4200),
    	bterms(2,  1,  0, -1, -3359),
    	bterms(2, -1, -1,  1,  2463),
    	bterms(2, -1,  0,  1,  2211),
    	bterms(2, -1, -1, -1,  2065),
    	bterms(0,  1, -1, -1, -1870),
    	bterms(4,  0, -1, -1,  1828),
    	bterms(0,  1,  0,  1, -1794),
    	bterms(0,  0,  0,  3, -1749),
    	bterms(0,  1, -1,  1, -1565),
    	bterms(1,  0,  0,  1, -1491),
    	bterms(0,  1,  1,  1, -1475),
    	bterms(0,  1,  1, -1, -1410),
    	bterms(0,  1,  0, -1, -1344),
    	bterms(1,  0,  0, -1, -1335),
    	bterms(0,  0,  3,  1,  1107),
    	bterms(4,  0,  0, -1,  1021),
    	bterms(4,  0, -1,  1,  833),
    	bterms(0,  0,  1, -3,  777),
    	bterms(4,  0, -2,  1,  671),
    	bterms(2,  0,  0, -3,  607),
    	bterms(2,  0,  2, -1,  596),
    	bterms(2, -1,  1, -1,  491),
    	bterms(2,  0, -2,  1, -451),
    	bterms(0,  0,  3, -1,  439),
    	bterms(2,  0,  2,  1,  422),
    	bterms(2,  0, -3, -1,  421),
    	bterms(2,  1, -1,  1, -366),
    	bterms(2,  1,  0,  1, -351),
    	bterms(4,  0,  0,  1,  331),
    	bterms(2, -1,  1,  1,  315),
    	bterms(2, -2,  0, -1,  302),
    	bterms(0,  0,  1,  3, -283),
    	bterms(2,  1,  1, -1, -229),
    	bterms(1,  1,  0, -1,  223),
    	bterms(1,  1,  0,  1,  223),
    	bterms(0,  1, -2, -1, -220),
    	bterms(2,  1, -1, -1, -220),
    	bterms(1,  0,  1,  1, -185),
    	bterms(2, -1, -2, -1,  181),
    	bterms(0,  1,  2,  1, -177),
    	bterms(4,  0, -2, -1,  176),
    	bterms(4, -1, -1, -1,  166),
    	bterms(1,  0,  1, -1, -164),
    	bterms(4,  0,  1, -1,  132),
    	bterms(1,  0, -1, -1, -119),
    	bterms(4, -1,  0, -1,  115),
    	bterms(2, -2,  0,  1,  107),
    ];

    let mut l = 0.0;
    let mut r = 0.0;
    let mut b = 0.0;

    for x in terms_for_lr.iter() {
        let arg =
            (x.0 as f64) * D
          + (x.1 as f64) * M
          + (x.2 as f64) * M1
          + (x.3 as f64) * F;

        let t = if      (x.1).abs() == 1 { E }
                else if (x.1).abs() == 2 { E * E }
                else                     { 1.0 };

        l += (x.4 as f64) * t * arg.sin();
        r += (x.5 as f64) * t * arg.cos();
    }

    for x in terms_for_b.iter() {
        let arg =
            (x.0 as f64) * D
          + (x.1 as f64) * M
          + (x.2 as f64) * M1
          + (x.3 as f64) * F;
        let mut t = (x.4 as f64) * arg.sin();

        t *= if      (x.1).abs() == 1 { E }
             else if (x.1).abs() == 2 { E * E }
             else                     { 1.0 };

        b += t;
    }

    l +=
        3958.0 * A1.sin()
      + 1962.0 * (L1 - F).sin()
      + 318.0  * A2.sin();

    b +=
      - 2235.0 * L1.sin()
      + 382.0  * A3.sin()
      + 175.0  * (
            (A1 - F).sin()
          + (A1 + F).sin()
        )
      + 127.0  * (L1 - M1).sin()
      - 115.0  * (L1 + M1).sin();

    l = l.to_radians();
    b = b.to_radians();

    let ecl_point = coords::EclPoint {
        long: L1 + l/1000000.0,
        lat:  b/1000000.0
    };

    let rad_vec = 385000.56 + r/1000.0;

    (ecl_point, rad_vec)

}

/**
Computes the longitude of the mean ascending node of the Moon

# Returns

* `long_mn_ascend_node`: Longitude of the mean ascending
                         node *| in radians*

# Arguments

* `JC`: Julian century
**/
pub fn mn_ascend_node(JC: f64) -> f64 {

    angle::limit_to_360(
        Horner_eval!(
            JC,
            125.0445479,
           -1934.1362891,
            0.0020754,
            1.0 / 467441.0,
           -1.0 / 60616000.0
        )
    ).to_radians()

}

/**
Computes the longitude of the true ascending node of the Moon

# Returns

* `long_true_ascend_node`: Longitude of the true ascending
                           node *| in radians*

# Arguments

* `JC`: Julian century
**/
pub fn true_ascend_node(JC: f64) -> f64 {

    let (D, M, M1) = DMM1(JC);
    let F = F(JC);

    mn_ascend_node(JC) + (
      - 1.4979 * (2.0 * (D - F)).sin()
      - 0.1500 * M.sin()
      - 0.1226 * (2.0 * D).sin()
      + 0.1176 * (2.0 * F).sin()
      - 0.0801 * (2.0 * (M1 - F)).sin()
    ).to_radians()

}

/**
Computes the longitude of the mean perigee of the Moon

# Returns

* `long_mn_perigee`: Longitude of mean perigee
                     *| in radians*

# Arguments

* `JC`: Julian century
**/
pub fn mn_perigee(JC: f64) -> f64 {

    angle::limit_to_360(
        Horner_eval!(
            JC,
            83.3532465,
            4069.0137287,
           -0.01032,
           -1.0 / 80053.0,
            1.0 / 18999000.0
        )
    ).to_radians()

}

/**
Computes the position angle of the Moon's bright limb

# Returns

* `pos_angl_of_bright_limb` The position angle of the midpoint
                            of the illuminated limb of the Moon
                            *| in radians*

# Arguments

* `sun_eq_point`: Equatorial coordinate of the Sun *| in radians*
* `moon_eq_point`: Equatorial coordinate of the Moon *| in radians*
**/
pub fn bright_limb (

    sun_eq_point  : coords::EqPoint,
    moon_eq_point : coords::EqPoint

) -> f64 {

    let a = sun_eq_point.dec.cos();
    let n = a * (sun_eq_point.asc - moon_eq_point.asc).sin();
    let d =
        sun_eq_point.dec.sin() * moon_eq_point.dec.cos()
      - moon_eq_point.dec.sin() * (
            sun_eq_point.asc - moon_eq_point.asc
        ).cos() * a;

    n.atan2(d)

}

/**
Computes the illuminated fraction of the lunar disk, using equatorial
coordinates

# Arguments

* `sun_eq_point`   : Equatorial coordinate of the Sun *| in radians*
* `moon_eq_point`  : Equatorial coordinate of the Moon *| in radians*
* `earth_moon_dist`: Earth-Moon distance (in any unit, but same as
                     that of `earth_sun_dist`)
* `earth_sun_dist` : Earth-Sun distance (in any unit, but same as
                     that of `earth_moon_dist`)
**/
pub fn illum_frac_frm_eq_coords (

    sun_eq_point    : &coords::EqPoint,
    moon_eq_point   : &coords::EqPoint,
    earth_moon_dist : f64,
    earth_sun_dist  : f64

) -> f64 {

    illuminated_frac (
        sun_eq_point.anglr_sepr(&moon_eq_point).acos(),
        earth_moon_dist,
        earth_sun_dist
    )

}

/**
Computes the illuminated fraction of the lunar disk, using eclipctic
coordinates

# Arguments

* `moon_long`      : Eclipctic longitude of the Moon *| in radians*
* `moon_lat`       : Eclipctic latitude of the Moon *| in radians*
* `sun_long`       : Eclipctic longitude of the Sun *| in radians*
* `earth_moon_dist`: Earth-Moon distance (in any unit, but same as
                     that of `earth_sun_dist`)
* `earth_sun_dist` : Earth-Sun distance (in any unit, but same as
                     that of `earth_moon_dist`)
**/
pub fn illum_frac_frm_ecl_coords (

    moon_long       : f64,
    moon_lat        : f64,
    sun_long        : f64,
    earth_moon_dist : f64,
    earth_sun_dist  : f64

) -> f64 {

    illuminated_frac(
        (moon_lat.cos() * (moon_long - sun_long).cos()).acos(),
        earth_moon_dist,
        earth_sun_dist
    )

}

#[inline]
fn illuminated_frac (

    moon_geocent_elong : f64,
    earth_moon_dist    : f64,
    earth_sun_dist     : f64

) -> f64 {

    let i = (earth_sun_dist * moon_geocent_elong.sin()).atan2 (
        earth_moon_dist - earth_sun_dist*moon_geocent_elong.cos()
    );

    (1.0 + i.cos()) / 2.0

}

/**
Computes the times of passage of the Moon through the ascending and
descending nodes, close to a given date

# Returns

`(time_of_ascend_node, time_of_descend_node)`

* `time_of_ascend_node` : Time of passage through the ascending node
* `time_of_descend_node`: Time of passage through the descending node

# Arguments

`date`: The Date
**/
#[inline]
pub fn time_of_passage_through_nodes(date: &time::Date) -> (f64, f64) {

    let k = 13.4223 * (time::decimal_year(&date) - 2000.05);
    let T = k / 1342.23;
    let k1 = (k as i32) as f64;
    let k2 = (k1 as f64) + 0.5;

    (time_of_passage_through_node(k1, T), time_of_passage_through_node(k2, T))

}

fn time_of_passage_through_node(k: f64, T: f64) -> f64 {

    let D = (
        183.638
      + 331.73735682*k
      + T * T * (
            0.0014852
          + T * (0.00000209 - T*0.00000001)
        )
    ).to_radians();
    let D_times_2 = 2.0 * D;
    let M = (17.4006 + 26.8203725*k + T*T*(0.0001186 + T*0.00000006)).to_radians();
    let M1 = (38.3776 + 355.52747313*k + T*T*(0.0123499 + T*(0.000014627 - T*0.000000069))).to_radians();
    let sigma = (123.9767 - 1.44098956*k + T*T*(0.0020608 + T*(0.00000214 - T*0.000000016))).to_radians();
    let P = sigma + (272.75 - T*2.3).to_radians();
    let V = (299.75 + T*(132.85 - T*0.009173)).to_radians();

    (
        2451565.1619
      + 27.212220817 * k
      + T * T * (
            0.0002762
          + T * (0.000000021 - T*0.000000000088)
        )
      - 0.4721 * M1.sin()
      - 0.1649 * D_times_2.sin()
      - 0.0868 * (D_times_2 - M1).sin()
      + 0.0084 * (D_times_2 + M1).sin()
      - 0.0083 * (D_times_2 - M).sin()
      - 0.0039 * (D_times_2 - M - M1).sin()
      + 0.0034 * (2.0 * M1).sin()
      - 0.0031 * (2.0 * (D - M1)).sin()
      + 0.0030 * (D_times_2 + M).sin()
      + 0.0028 * (M - M1).sin()
      + 0.0026 * M.sin()
      + 0.0025 * (2.0 * D_times_2).sin()
      + 0.0024 * D.sin()
      + 0.0022 * (M + M1).sin()
      + 0.0017 * sigma.sin()
      + 0.0014 * (2.0*D_times_2 - M1).sin()
      + 0.0005 * (D_times_2 + M - M1).sin()
      + 0.0004 * (D_times_2 - M + M1).sin()
      + 0.0003 * (
            (2.0 * (M - D)).sin()
          + (2.0*D_times_2 - M).sin()
          + V.sin()
          + P.sin()
        )
    )

}

/// Represents a phase of the Moon
pub enum Phase {
    /// New Moon
    New,
    /// First Quarter
    First,
    /// Full Moon
    Full,
    /// Last Quarter
    Last
}

/**
Computes the Julian day corresponding to one of the four phases
of the Moon

# Returns

* `JD`: Julian day corresponding to the exact time of the phase
        that is closest to `date`

*Meeus* says the mean error in `JD` for phases between 1980 AD
and mid-2020 AD is 3.8 seconds.

# Arguments

* `date` : Date of interest, close to the phase
* `phase`: The [Phase](./enum.Phase.html)
**/
pub fn time_of_phase(date: &time::Date, phase: &Phase) -> f64 {

    let mut K = 12.3685 * (time::decimal_year(&date) - 2000.0);
    K = (K as i64) as f64;

    let k = match phase {
        &Phase::New   => K,
        &Phase::First => K + 0.25,
        &Phase::Full  => K + 0.5,
        &Phase::Last  => K + 0.75,
    };

    let T = k / 1236.85;

    let mut JD =
        2451550.09766
      + k * 29.530588861
      + T * Horner_eval!(
            T,
            0.0,
            0.00015437,
           -0.00000015,
            0.00000000073
        );

    let E = E(T);

    let M = (
        2.5534
      + k * 29.1053567
      + T * Horner_eval!(
            T,
            0.0,
           -0.0000014,
           -0.00000011
        )
    ).to_radians();

    let M1 = (
        201.5643
      + k * 385.81693528
      + T * Horner_eval!(
            T,
            0.0,
            0.0107582,
            0.00001238,
           -0.000000058
        )
    ).to_radians();

    let F = (
        160.7108
        + k * 390.67050284
        + T * Horner_eval!(
              T,
              0.0,
             -0.0016118,
             -0.00000227,
              0.000000011
        )
    ).to_radians();

    let omega = (
        124.7746
      - k * 1.56375588
      + T * Horner_eval!(
            T,
            0.0,
            0.0020672,
            0.00000215
        )
    ).to_radians();

    let A1  = (299.77 + 0.107408*k - 0.009173*T*T).to_radians();
    let A2  = (251.88 + 0.016321*k).to_radians();
    let A3  = (251.83 + 26.651886*k).to_radians();
    let A4  = (349.42 + 36.412478*k).to_radians();
    let A5  = (84.66  + 18.206239*k).to_radians();
    let A6  = (141.74 + 53.303771*k).to_radians();
    let A7  = (207.14 + 2.453732*k).to_radians();
    let A8  = (154.84 + 7.306860*k).to_radians();
    let A9  = (34.52  + 27.261239*k).to_radians();
    let A10 = (207.19 + 0.121824*k).to_radians();
    let A11 = (291.34 + 1.844379*k).to_radians();
    let A12 = (161.72 + 24.198154*k).to_radians();
    let A13 = (239.56 + 25.513099*k).to_radians();
    let A14 = (331.55 + 3.592518*k).to_radians();

    let is_quarter = match phase {
        &Phase::Last | &Phase::First  => true,
        &_  => false,
    };

    if is_quarter {
        let W =
            0.00306
          - 0.00038 * E * M.cos()
          + 0.00026 * M1.cos();
          - 0.00002 * ((M1 - M).cos() - (M1 + M).cos() - (2.0 * F).cos());

        JD += match phase {
            &Phase::Last  => -W,
            &Phase::First =>  W,
            &_  => 0.0,
        };

        let corrections = [
            [-0.62801,         M1],
            [ 0.17172 * E,     M],
            [-0.01183 * E,     M1 + M],
            [ 0.00862,         2.0 * M1],
            [ 0.00804,         2.0 * F],
            [ 0.00454 * E,     M1 - M],
            [ 0.00204 * E * E, 2.0 * M],
            [-0.0018,          M1 - 2.0*F],
            [-0.0007,          M1 + 2.0*F],
            [-0.0004,          3.0 * M1],
            [-0.00034,         2.0*M1 - M],
            [ 0.00032 * E,     M + 2.0*F],
            [ 0.00032 * E,     M - 2.0*F],
            [-0.00028 * E * E, M1 + 2.0*M],
            [ 0.00027 * E,     2.0*M1 + M],
            [-0.00017,         omega],
            [-0.00005,         M1 - M - 2.0*F],
            [ 0.00004,         2.0 * (M1 + F)],
            [-0.00004,         M1 + M + 2.0*F],
            [ 0.00004,         M1 - 2.0*M],
            [ 0.00003,         M1 + M - 2.0*F],
            [ 0.00003,         3.0 * M],
            [ 0.00002,         2.0 * (M1 - F)],
            [ 0.00002,         M1 - M + 2.0*F],
            [-0.00002,         3.0*M1 + M],
        ];

        for &x in corrections.iter() {
            JD += x[0] * x[1].sin();
        }
    }
    else {
        let is_new = match phase {
            &Phase::New => true,
            &_ => false,
        };

        let sine_arguments = [
            M1,
            M,
            2.0 * M1,
            2.0 * F,
            M1 - M,
            M1 + M,
            2.0 * M,
            M1 - 2.0*F,
            M1 + 2.0*F,
            2.0*M1 + M,
            3.0 * M1,
            M + 2.0*F,
            M - 2.0*F,
            2.0*M1 - M,
            omega,
            M1 + 2.0*M,
            2.0 * (M1 - F),
            3.0 * M,
            M1 + M - 2.0*F,
            2.0 * (M1 + F),
            M1 + M + 2.0*F,
            M1 - M + 2.0*F,
            M1 - M - 2.0*F,
            3.0*M1 + M,
            4.0 * M1
        ];

        let multipliers = if is_new {[

           -0.4072,
            0.17241 * E,
            0.01608,
            0.01039,
            0.00739 * E,
           -0.00514 * E,
            0.00208 * E * E,
           -0.00111,
           -0.00057,
            0.00056 * E,
           -0.00042,
            0.00042 * E,
            0.00038 * E,
           -0.00024 * E,
           -0.00017,
           -0.00007,
            0.00004,
            0.00004,
            0.00003,
            0.00003,
           -0.00003,
            0.00003,
           -0.00002,
           -0.00002,
            0.00002

        ]} else {[

           -0.40614,
            0.17302 * E,
            0.01614,
            0.01043,
            0.00734 * E,
           -0.00515 * E,
            0.00209 * E * E,
           -0.00111,
           -0.00057,
            0.00056 * E,
           -0.00042,
            0.00042 * E,
            0.00038 * E,
           -0.00024 * E,
           -0.00017,
           -0.00007,
            0.00004,
            0.00004,
            0.00003,
            0.00003,
           -0.00003,
            0.00003,
           -0.00002,
           -0.00002,
            0.00002

        ]};

        for mx in multipliers.iter().zip(sine_arguments.iter()) {
            JD += mx.0 * (mx.1).sin();
        }
    }

    let additional_corrections = [
        [0.000_325, A1],
        [0.000_165, A2],
        [0.000_164, A3],
        [0.000_126, A4],
        [0.000_110, A5],
        [0.000_062, A6],
        [0.000_06,  A7],
        [0.000_056, A8],
        [0.000_047, A9],
        [0.000_042, A10],
        [0.000_04,  A11],
        [0.000_037, A12],
        [0.000_035, A13],
        [0.000_023, A14],
    ];
    for &x in additional_corrections.iter() {
        JD += x[0] * x[1].sin();
    }

    JD

}