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Moon ecliptic coordinates (#73)
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This introduces the new body `Astronoby::Moon` and an entire algorithm to compute its ecliptic coordinates.

The algorithm is based on the Lunar theory called "Éphéméride Lunaire Parisienne" by Jean Chapront and Michelle Chapront-Touzé, and used by Jean Meeus's formulae in Astronomical Algorithms.

```rb
time = Time.utc(2015, 1, 1)
moon = Astronoby::Moon.new(time: time)

coordinates = moon.apparent_ecliptic_coordinates

coordinates.latitude.str(:dms)
# => "-2° 53′ 58.1867″"

coordinates.longitude.str(:dms)
# => "+50° 37′ 3.5842″"
```
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@rhannequin
rhannequin authored May 22, 2024
1 parent a1bed12 commit d7abcef
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2 changes: 2 additions & 0 deletions lib/astronoby.rb
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require "astronoby/angles/dms"
require "astronoby/angles/hms"
require "astronoby/epoch"
require "astronoby/astronomical_models/ephemeride_lunaire_parisienne"
require "astronoby/bodies/moon"
require "astronoby/bodies/sun"
require "astronoby/coordinates/ecliptic"
require "astronoby/coordinates/equatorial"
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143 changes: 143 additions & 0 deletions lib/astronoby/astronomical_models/ephemeride_lunaire_parisienne.rb
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# frozen_string_literal: true

module Astronoby
class EphemerideLunaireParisienne
# Lunar theory: Éphéméride Lunaire Parisienne
# By Jean Chapront, Michelle Chapront-Touzé
# https://en.wikipedia.org/wiki/Ephemeride_Lunaire_Parisienne

DEGREES_UNIT = 10**-6

# @return [Array] Periodic terms for the Moon's longitude and distance
def self.periodic_terms_for_moon_longitude_and_distance
[
[0, 0, 1, 0, 6288774, -20905355],
[2, 0, -1, 0, 1274027, -3699111],
[2, 0, 0, 0, 658314, -2955968],
[0, 0, 2, 0, 213618, -569925],
[0, 1, 0, 0, -185116, 48888],
[0, 0, 0, 2, -114332, -3149],
[2, 0, -2, 0, 58793, 246158],
[2, -1, -1, 0, 57066, -152138],
[2, 0, 1, 0, 53322, -170733],
[2, -1, 0, 0, 45758, -204586],
[0, 1, -1, 0, -40923, -129620],
[1, 0, 0, 0, -34720, 108743],
[0, 1, 1, 0, -30383, 104755],
[2, 0, 0, -2, 15327, 10321],
[0, 0, 1, 2, -12528, 0],
[0, 0, 1, -2, 10980, 79661],
[4, 0, -1, 0, 10675, -34782],
[0, 0, 3, 0, 10034, -23210],
[4, 0, -2, 0, 8548, -21636],
[2, 1, -1, 0, -7888, 24208],
[2, 1, 0, 0, -6766, 30824],
[1, 0, -1, 0, -5163, -8379],
[1, 1, 0, 0, 4987, -16675],
[2, -1, 1, 0, 4036, -12831],
[2, 0, 2, 0, 3994, -10445],
[4, 0, 0, 0, 3861, -11650],
[2, 0, -3, 0, 3665, 14403],
[0, 1, -2, 0, -2689, -7003],
[2, 0, -1, 2, -2602, 0],
[2, -1, -2, 0, 2390, 10056],
[1, 0, 1, 0, -2348, 6322],
[2, -2, 0, 0, 2236, -9884],
[0, 1, 2, 0, -2120, 5751],
[0, 2, 0, 0, -2069, 0],
[2, -2, -1, 0, 2048, -4950],
[2, 0, 1, -2, -1773, 4130],
[2, 0, 0, 2, -1595, 0],
[4, -1, -1, 0, 1215, -3958],
[0, 0, 2, 2, -1110, 0],
[3, 0, -1, 0, -892, 3258],
[2, 1, 1, 0, -810, 2616],
[4, -1, -2, 0, 759, -1897],
[0, 2, -1, 0, -713, -2117],
[2, 2, -1, 0, -700, 2354],
[2, 1, -2, 0, 691, 0],
[2, -1, 0, -2, 596, 0],
[4, 0, 1, 0, 549, -1423],
[0, 0, 4, 0, 537, -1117],
[4, -1, 0, 0, 520, -1571],
[1, 0, -2, 0, -487, -1739],
[2, 1, 0, -2, -399, 0],
[0, 0, 2, -2, -381, -4421],
[1, 1, 1, 0, 351, 0],
[3, 0, -2, 0, -340, 0],
[4, 0, -3, 0, 330, 0],
[2, -1, 2, 0, 327, 0],
[0, 2, 1, 0, -323, 1165],
[1, 1, -1, 0, 299, 0],
[2, 0, 3, 0, 294, 0],
[2, 0, -1, -2, 0, 8752]
]
end

# @return [Array] Periodic terms for the Moon's latitude
def self.periodic_terms_for_moon_latitude
[
[0, 0, 0, 1, 5128122],
[0, 0, 1, 1, 280602],
[0, 0, 1, -1, 277693],
[2, 0, 0, -1, 173237],
[2, 0, -1, 1, 55413],
[2, 0, -1, -1, 46271],
[2, 0, 0, 1, 32573],
[0, 0, 2, 1, 17198],
[2, 0, 1, -1, 9266],
[0, 0, 2, -1, 8822],
[2, -1, 0, -1, 8216],
[2, 0, -2, -1, 4324],
[2, 0, 1, 1, 4200],
[2, 1, 0, -1, -3359],
[2, -1, -1, 1, 2463],
[2, -1, 0, 1, 2211],
[2, -1, -1, -1, 2065],
[0, 1, -1, -1, -1870],
[4, 0, -1, -1, 1828],
[0, 1, 0, 1, -1794],
[0, 0, 0, 3, -1749],
[0, 1, -1, 1, -1565],
[1, 0, 0, 1, -1491],
[0, 1, 1, 1, -1475],
[0, 1, 1, -1, -1410],
[0, 1, 0, -1, -1344],
[1, 0, 0, -1, -1335],
[0, 0, 3, 1, 1107],
[4, 0, 0, -1, 1021],
[4, 0, -1, 1, 833],
[0, 0, 1, -3, 777],
[4, 0, -2, 1, 671],
[2, 0, 0, -3, 607],
[2, 0, 2, -1, 596],
[2, -1, 1, -1, 491],
[2, 0, -2, 1, -451],
[0, 0, 3, -1, 439],
[2, 0, 2, 1, 422],
[2, 0, -3, -1, 421],
[2, 1, -1, 1, -366],
[2, 1, 0, 1, -351],
[4, 0, 0, 1, 331],
[2, -1, 1, 1, 315],
[2, -2, 0, -1, 302],
[0, 0, 1, 3, -283],
[2, 1, 1, -1, -229],
[1, 1, 0, -1, 223],
[1, 1, 0, 1, 223],
[0, 1, -2, -1, -220],
[2, 1, -1, -1, -220],
[1, 0, 1, 1, -185],
[2, -1, -2, -1, 181],
[0, 1, 2, 1, -177],
[4, 0, -2, -1, 176],
[4, -1, -1, -1, 166],
[1, 0, 1, -1, -164],
[4, 0, 1, -1, 132],
[1, 0, -1, -1, -119],
[4, -1, 0, -1, 115],
[2, -2, 0, 1, 107]
]
end
end
end
226 changes: 226 additions & 0 deletions lib/astronoby/bodies/moon.rb
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# frozen_string_literal: true

module Astronoby
class Moon
MEAN_GEOCENTRIC_DISTANCE = 385_000_560

def initialize(time:)
@time = time
end

# Source:
# Title: Astronomical Algorithms
# Author: Jean Meeus
# Edition: 2nd edition
# Chapter: 47 - Position of the Moon

# @return [Coordinates::Ecliptic] Ecliptic coordinates of the Moon
def apparent_ecliptic_coordinates
@ecliptic_coordinates ||= begin
latitude = Astronoby::Angle.from_degrees(
(latitude_terms + additive_latitude_terms) *
EphemerideLunaireParisienne::DEGREES_UNIT
)

longitude = mean_longitude + Astronoby::Angle.from_degrees(
(longitude_terms + additive_longitude_terms) *
EphemerideLunaireParisienne::DEGREES_UNIT
) + nutation

Coordinates::Ecliptic.new(
latitude: latitude,
longitude: longitude
)
end
end

# @return [Integer] Distance between the Earth and the Moon centers in meters
def distance
@distance ||= (MEAN_GEOCENTRIC_DISTANCE + distance_terms).round
end

# @return [Angle] Moon's mean longitude
def mean_longitude
@mean_longitude ||= begin
degrees =
218.3164477 +
481267.88123421 * elapsed_centuries -
0.0015786 * elapsed_centuries**2 +
elapsed_centuries**3 / 538841 -
elapsed_centuries**4 / 65194000
degrees += Constants::DEGREES_PER_CIRCLE while degrees.negative?
Angle.from_degrees(degrees)
end
end

# @return [Angle] Moon's mean elongation
def mean_elongation
@mean_elongation ||= begin
degrees =
297.8501921 +
445267.1114034 * elapsed_centuries -
0.0018819 * elapsed_centuries**2 +
elapsed_centuries**3 / 545868 -
elapsed_centuries**4 / 113065000
degrees += Constants::DEGREES_PER_CIRCLE while degrees.negative?
Angle.from_degrees(degrees)
end
end

# @return [Angle] Moon's mean anomaly
def mean_anomaly
@mean_anomaly ||= begin
degrees =
134.9633964 +
477198.8675055 * elapsed_centuries +
0.0087414 * elapsed_centuries**2 +
elapsed_centuries**3 / 69699 -
elapsed_centuries**4 / 14712000
degrees += Constants::DEGREES_PER_CIRCLE while degrees.negative?
Angle.from_degrees(degrees)
end
end

# @return [Angle] Moon's argument of latitude
def argument_of_latitude
@argument_of_latitude ||= begin
degrees =
93.2720950 +
483202.0175233 * elapsed_centuries -
0.0036539 * elapsed_centuries**2 -
elapsed_centuries**3 / 3526000
degrees += Constants::DEGREES_PER_CIRCLE while degrees.negative?
Angle.from_degrees(degrees)
end
end

private

def terrestrial_time
@terrestrial_time ||= begin
delta = Util::Time.terrestrial_universal_time_delta(@time)
@time + delta
end
end

def julian_date
Epoch.from_time(terrestrial_time)
end

def elapsed_centuries
(julian_date - Epoch::DEFAULT_EPOCH) / Constants::DAYS_PER_JULIAN_CENTURY
end

def sun_mean_anomaly
@sun_mean_anomaly ||= Sun.new(time: @time).mean_anomaly
end

def a1
@a1 ||= begin
degrees = 119.75 + 131.849 * elapsed_centuries
degrees += Constants::DEGREES_PER_CIRCLE while degrees.negative?
Angle.from_degrees(degrees)
end
end

def a2
@a2 ||= begin
degrees = 53.09 + 479264.290 * elapsed_centuries
degrees += Constants::DEGREES_PER_CIRCLE while degrees.negative?
Angle.from_degrees(degrees)
end
end

def a3
@a3 ||= begin
degrees = 313.45 + 481266.484 * elapsed_centuries
degrees += Constants::DEGREES_PER_CIRCLE while degrees.negative?
Angle.from_degrees(degrees)
end
end

def eccentricity_correction
@eccentricity_correction ||=
1 - 0.002516 * elapsed_centuries - 0.0000074 * elapsed_centuries**2
end

def latitude_terms
@latitude_terms ||=
Astronoby::EphemerideLunaireParisienne
.periodic_terms_for_moon_latitude
.inject(0) do |sum, terms|
value = terms[4] * Math.sin(
terms[0] * mean_elongation.radians +
terms[1] * sun_mean_anomaly.radians +
terms[2] * mean_anomaly.radians +
terms[3] * argument_of_latitude.radians
)

value *= eccentricity_correction if terms[1].abs == 1
value *= eccentricity_correction**2 if terms[1].abs == 2

sum + value
end
end

def additive_latitude_terms
@additive_latitude_terms ||=
-2235 * mean_longitude.sin +
382 * a3.sin +
175 * (a1 - argument_of_latitude).sin +
175 * (a1 + argument_of_latitude).sin +
127 * (mean_longitude - mean_anomaly).sin -
115 * (mean_longitude + mean_anomaly).sin
end

def longitude_terms
@longitude_terms ||=
Astronoby::EphemerideLunaireParisienne
.periodic_terms_for_moon_longitude_and_distance
.inject(0) do |sum, terms|
value = terms[4] * Math.sin(
terms[0] * mean_elongation.radians +
terms[1] * sun_mean_anomaly.radians +
terms[2] * mean_anomaly.radians +
terms[3] * argument_of_latitude.radians
)

value *= eccentricity_correction if terms[1].abs == 1
value *= eccentricity_correction**2 if terms[1].abs == 2

sum + value
end
end

def additive_longitude_terms
@additive_longitude_terms ||=
3958 * a1.sin +
1962 * (mean_longitude - argument_of_latitude).sin +
318 * a2.sin
end

def distance_terms
@distance_terms ||=
EphemerideLunaireParisienne
.periodic_terms_for_moon_longitude_and_distance
.inject(0) do |sum, terms|
value = terms[5] * Math.cos(
terms[0] * mean_elongation.radians +
terms[1] * sun_mean_anomaly.radians +
terms[2] * mean_anomaly.radians +
terms[3] * argument_of_latitude.radians
)

value *= eccentricity_correction if terms[1].abs == 1
value *= eccentricity_correction**2 if terms[1].abs == 2

sum + value
end
end

def nutation
@nutation ||=
Astronoby::Nutation.for_ecliptic_longitude(epoch: julian_date)
end
end
end
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