Ecliptic coordinates for Geometric and Astrometric reference frames (#…

…134)

Ecliptic coordinates already existed in Astronoby, but now we're making them available from `Geometric` and `Astrometric` reference frames.

In Astronoby, ecliptic coordinates are either barycentric (for `Geometric` reference frame) or geocentric (for `Astrometric` reference frame), with reference of the ecliptic plane, using the mean equinox of the standard epoch J2000. Please note that the chosen equninox will be different when we'll introduce the `Apparent` reference frame in the future (true equinox of date).

Please note as well that in the same way the Earth's astrometric equatorial coordinates are null because the astrometric position is geocentric, the Earth's astrometric ecliptic coordinates are also null.

```rb
instant = Astronoby::Instant.from_time(Time.utc(2025, 5, 1))
ephem = Astronoby::Ephem.load("de440s.bsp")

jupiter = Astronoby::Jupiter.new(instant: instant, ephem: ephem)

jupiter.geometric.ecliptic.latitude.str(:dms)
# => "-0° 16′ 22.9896″"

jupiter.geometric.ecliptic.longitude.str(:dms)
# => "+88° 24′ 41.3024″"

jupiter.astrometric.ecliptic.latitude.str(:dms)
# => "-0° 14′ 27.7664″"

jupiter.astrometric.ecliptic.longitude.str(:dms)
# => "+81° 1′ 11.959″"
```

lib/astronoby/coordinates/ecliptic.rb

@@ -10,6 +10,10 @@ def initialize(latitude:, longitude:)
         @longitude = longitude
       end
 
+      def self.zero
+        new(latitude: Angle.zero, longitude: Angle.zero)
+      end
+
       # Source:
       #  Title: Celestial Calculations
       #  Author: J. L. Lawrence

lib/astronoby/reference_frame.rb

@@ -28,6 +28,12 @@ def equatorial
       Coordinates::Equatorial.from_position_vector(@position)
     end
 
+    def ecliptic
+      return Coordinates::Ecliptic.zero if distance.zero?
+
+      equatorial.to_ecliptic(epoch: Epoch::J2000)
+    end
+
     def distance
       return Distance.zero if @position.zero?
 

spec/astronoby/bodies/earth_spec.rb

@@ -58,6 +58,21 @@
         .to eq("+7° 34′ 11.406″")
       # IMCCE:    +7° 34′ 11.407″
       # Skyfield: +7° 34′ 11.4″
+
+      expect(geometric.ecliptic.latitude.str(:dms))
+        .to eq("+0° 0′ 32.9716″")
+      # IMCCE:    +0° 0′ 32.971″
+      # Skyfield: +0° 0′ 33.2″
+
+      expect(geometric.ecliptic.longitude.str(:dms))
+        .to eq("+160° 40′ 55.7988″")
+      # IMCCE:    +160° 40′ 55.794″
+      # Skyfield: +160° 40′ 56.4″
+
+      expect(geometric.distance.au)
+        .to eq(0.9941296922100833)
+      # IMCCE:    0.994129567869
+      # Skyfield: 0.9941296929553649
     end
 
     it "computes the correct velocity" do
@@ -105,6 +120,8 @@
       expect(astrometric.equatorial.right_ascension)
         .to eq(Astronoby::Angle.zero)
       expect(astrometric.equatorial.declination).to eq(Astronoby::Angle.zero)
+      expect(astrometric.ecliptic.latitude).to eq(Astronoby::Angle.zero)
+      expect(astrometric.ecliptic.longitude).to eq(Astronoby::Angle.zero)
       expect(astrometric.distance).to eq(Astronoby::Distance.zero)
     end
 

spec/astronoby/bodies/jupiter_spec.rb

@@ -58,6 +58,21 @@
         .to eq("+23° 9′ 24.1204″")
       # IMCCE:    +23° 9′ 24.118″
       # Skyfield: +23° 9′ 24.1″
+
+      expect(geometric.ecliptic.latitude.str(:dms))
+        .to eq("-0° 16′ 22.9896″")
+      # IMCCE:    -0° 16′ 22.992″
+      # Skyfield: -0° 16′ 11.1″
+
+      expect(geometric.ecliptic.longitude.str(:dms))
+        .to eq("+88° 24′ 41.3024″")
+      # IMCCE:    +88° 24′ 41.297″
+      # Skyfield: +88° 24′ 55.4″
+
+      expect(geometric.distance.au)
+        .to eq(5.118010310588575)
+      # IMCCE:    5.11801034937
+      # Skyfield: 5.118010311352852
     end
 
     it "computes the correct velocity" do
@@ -112,6 +127,16 @@
       # IMCCE:    +22° 53′ 40.753″
       # Skyfield: +22° 53′ 40.8″
 
+      expect(astrometric.ecliptic.latitude.str(:dms))
+        .to eq("-0° 14′ 27.7664″")
+      # IMCCE:    -0° 14′ 27.769″
+      # Skyfield: -0° 14′ 15.9″
+
+      expect(astrometric.ecliptic.longitude.str(:dms))
+        .to eq("+81° 1′ 11.959″")
+      # IMCCE:    +81° 1′ 11.962″
+      # Skyfield: +81° 22′ 26.1″
+
       expect(astrometric.distance.au)
         .to eq(5.847692982822113)
       # IMCCE:    5.847693029715

spec/astronoby/bodies/mars_spec.rb

@@ -58,6 +58,21 @@
         .to eq("+13° 22′ 23.046″")
       # IMCCE:    +13° 22′ 23.048″
       # Skyfield: +13° 22′ 23.0″
+
+      expect(geometric.ecliptic.latitude.str(:dms))
+        .to eq("+1° 49′ 29.7913″")
+      # IMCCE:    +1° 49′ 29.791″
+      # Skyfield: +1° 49′ 34.9″
+
+      expect(geometric.ecliptic.longitude.str(:dms))
+        .to eq("+149° 27′ 6.5779″")
+      # IMCCE:    +149° 27′ 6.571″
+      # Skyfield: +149° 27′ 17.0″
+
+      expect(geometric.distance.au)
+        .to eq(1.6665243265178227)
+      # IMCCE:    1.666524219608
+      # Skyfield: 1.66652432695766
     end
 
     it "computes the correct velocity" do
@@ -112,6 +127,16 @@
       # IMCCE:    +24° 3′ 35.868″
       # Skyfield: +24° 3′ 35.9″
 
+      expect(astrometric.ecliptic.latitude.str(:dms))
+        .to eq("+2° 39′ 41.3343″")
+      # IMCCE:    +2° 39′ 41.334″
+      # Skyfield: +2° 39′ 51.8″
+
+      expect(astrometric.ecliptic.longitude.str(:dms))
+        .to eq("+113° 14′ 47.4513″")
+      # IMCCE:    +113° 14′ 47.455″
+      # Skyfield: +113° 35′ 57.8″
+
       expect(astrometric.distance.au)
         .to eq(1.138989231808293)
       # IMCCE:    1.138989267589

spec/astronoby/bodies/mercury_spec.rb

@@ -58,6 +58,21 @@
         .to eq("-6° 7′ 53.664″")
       # IMCCE:    -6° 7′ 53.680″
       # Skyfield: -6° 7′ 53.7″
+
+      expect(geometric.ecliptic.latitude.str(:dms))
+        .to eq("+3° 0′ 54.0574″")
+      # IMCCE:    +3° 0′ 54.055″
+      # Skyfield: +3° 0′ 48.5″
+
+      expect(geometric.ecliptic.longitude.str(:dms))
+        .to eq("+202° 58′ 41.4354″")
+      # IMCCE:    +202° 58′ 41.473″
+      # Skyfield: +202° 58′ 39.5″
+
+      expect(geometric.distance.au)
+        .to eq(0.4274945347661314)
+      # IMCCE:    0.427494398892
+      # Skyfield: 0.4274945451749377
     end
 
     it "computes the correct velocity" do
@@ -112,6 +127,16 @@
       # IMCCE:    -21° 54′ 45.557″
       # Skyfield: -21° 54′ 45.6″
 
+      expect(astrometric.ecliptic.latitude.str(:dms))
+        .to eq("+1° 7′ 0.4406″")
+      # IMCCE:    +1° 7′ 0.440″
+      # Skyfield: +1° 6′ 48.8″
+
+      expect(astrometric.ecliptic.longitude.str(:dms))
+        .to eq("+259° 31′ 33.854″")
+      # IMCCE:    +259° 31′ 33.864″
+      # Skyfield: +259° 52′ 31.4″
+
       expect(astrometric.distance.au)
         .to eq(1.1479011885933859)
       # IMCCE:    1.147901225109

spec/astronoby/bodies/neptune_spec.rb

@@ -58,6 +58,21 @@
         .to eq("-1° 11′ 21.2403″")
       # IMCCE:    -1° 11′ 21.197″
       # Skyfield: -1° 11′ 21.2″
+
+      expect(geometric.ecliptic.latitude.str(:dms))
+        .to eq("-1° 19′ 17.0443″")
+      # IMCCE:    -1° 19′ 17.013″
+      # Skyfield: -1° 19′ 16.0″
+
+      expect(geometric.ecliptic.longitude.str(:dms))
+        .to eq("+0° 3′ 29.1763″")
+      # IMCCE:    +0° 3′ 29.214″
+      # Skyfield: +0° 24′ 59.8″
+
+      expect(geometric.distance.au)
+        .to eq(29.884550201759172)
+      # IMCCE:    29.884551127591
+      # Skyfield: 29.88455020171849
     end
 
     it "computes the correct velocity" do
@@ -112,6 +127,16 @@
       # IMCCE:    -0° 35′ 37.211″
       # Skyfield: -0° 35′ 37.3″
 
+      expect(astrometric.ecliptic.latitude.str(:dms))
+        .to eq("-1° 20′ 58.8551″")
+      # IMCCE:    -1° 20′ 58.823″
+      # Skyfield: -1° 20′ 57.5″
+
+      expect(astrometric.ecliptic.longitude.str(:dms))
+        .to eq("+1° 37′ 15.5232″")
+      # IMCCE:    +1° 37′ 15.560″
+      # Skyfield: +1° 58′ 46.1″
+
       expect(astrometric.distance.au)
         .to eq(29.266429831403105)
       # IMCCE:    29.26643067546

spec/astronoby/bodies/saturn_spec.rb

@@ -58,6 +58,21 @@
         .to eq("-4° 13′ 34.4575″")
       # IMCCE:    -4° 13′ 34.458″
       # Skyfield: -4° 13′ 34.5″
+
+      expect(geometric.ecliptic.latitude.str(:dms))
+        .to eq("-2° 10′ 18.0315″")
+      # IMCCE:    -2° 10′ 18.032″
+      # Skyfield: -2° 10′ 18.1″
+
+      expect(geometric.ecliptic.longitude.str(:dms))
+        .to eq("+354° 22′ 47.1815″")
+      # IMCCE:    +354° 22′ 47.182″
+      # Skyfield: +354° 44′ 7.3″
+
+      expect(geometric.distance.au)
+        .to eq(9.580357829890923)
+      # IMCCE:    9.580357970998
+      # Skyfield: 9.580357829243903
     end
 
     it "computes the correct velocity" do
@@ -112,6 +127,16 @@
       # IMCCE:    -1° 52′ 50.722″
       # Skyfield: -1° 52′ 50.7″
 
+      expect(astrometric.ecliptic.latitude.str(:dms))
+        .to eq("-2° 6′ 26.3397″")
+      # IMCCE:    -2° 6′ 26.340″
+      # Skyfield: -2° 6′ 25.3″
+
+      expect(astrometric.ecliptic.longitude.str(:dms))
+        .to eq("+0° 7′ 56.1071″")
+      # IMCCE:    +0° 7′ 56.108″
+      # Skyfield: +0° 29′ 16.2″
+
       expect(astrometric.distance.au)
         .to eq(9.878564650795877)
       # IMCCE:    9.878564573683

spec/astronoby/bodies/uranus_spec.rb

@@ -58,6 +58,21 @@
         .to eq("+19° 22′ 35.4493″")
       # IMCCE:    +19° 22′ 35.421″
       # Skyfield: +19° 22′ 35.4″
+
+      expect(geometric.ecliptic.latitude.str(:dms))
+        .to eq("-0° 13′ 11.9158″")
+      # IMCCE:    -0° 13′ 11.922″
+      # Skyfield: -0° 13′ 1.3″
+
+      expect(geometric.ecliptic.longitude.str(:dms))
+        .to eq("+57° 27′ 4.2182″")
+      # IMCCE:    +57° 27′ 4.118″
+      # Skyfield: +57° 48′ 29.4″
+
+      expect(geometric.distance.au)
+        .to eq(19.515391974096183)
+      # IMCCE:    19.51539553769
+      # Skyfield: 19.51539197373322
     end
 
     it "computes the correct velocity" do
@@ -112,6 +127,16 @@
       # IMCCE:    +19° 48′ 18.795″
       # Skyfield: +19° 48′ 18.8″
 
+      expect(astrometric.ecliptic.latitude.str(:dms))
+        .to eq("-0° 12′ 43.8064″")
+      # IMCCE:    -0° 12′ 43.812″
+      # Skyfield: -0° 12′ 33.0″
+
+      expect(astrometric.ecliptic.longitude.str(:dms))
+        .to eq("+59° 21′ 17.3489″")
+      # IMCCE:    +59° 21′ 17.253″
+      # Skyfield: +59° 42′ 42.6″
+
       expect(astrometric.distance.au)
         .to eq(20.293374076651755)
       # IMCCE:    20.293377161363

spec/astronoby/bodies/venus_spec.rb

@@ -58,6 +58,21 @@
         .to eq("+24° 21′ 26.4794″")
       # IMCCE:    +24° 21′ 26.481″
       # Skyfield: +24° 21′ 26.5″
+
+      expect(geometric.ecliptic.latitude.str(:dms))
+        .to eq("+1° 25′ 43.096″")
+      # IMCCE:    +1° 25′ 43.095″
+      # Skyfield: +1° 25′ 54.4″
+
+      expect(geometric.ecliptic.longitude.str(:dms))
+        .to eq("+101° 35′ 6.7601″")
+      # IMCCE:    +101° 35′ 6.733″
+      # Skyfield: +101° 56′ 10.0″
+
+      expect(geometric.distance.au)
+        .to eq(0.7152904564103618)
+      # IMCCE:    0.715290459923
+      # Skyfield: 0.7152904566396294
     end
 
     it "computes the correct velocity" do
@@ -112,6 +127,16 @@
       # IMCCE:    +0° 37′ 33.706″
       # Skyfield: +0° 37′ 33.7″
 
+      expect(astrometric.ecliptic.latitude.str(:dms))
+        .to eq("+1° 56′ 23.8202″")
+      # IMCCE:    +1° 56′ 23.821″
+      # Skyfield: +1° 56′ 24.3″
+
+      expect(astrometric.ecliptic.longitude.str(:dms))
+        .to eq("+357° 5′ 49.9018″")
+      # IMCCE:    +357° 5′ 49.909″
+      # Skyfield: +357° 26′ 52.6″
+
       expect(astrometric.distance.au)
         .to eq(0.5226080600832164)
       # IMCCE:    0.522608040526

spec/astronoby/coordinates/ecliptic_spec.rb

@@ -1,6 +1,15 @@
 # frozen_string_literal: true
 
 RSpec.describe Astronoby::Coordinates::Ecliptic do
+  describe "::zero" do
+    it "returns a new instance with zero angles" do
+      coordinates = described_class.zero
+
+      expect(coordinates.latitude).to eq(Astronoby::Angle.zero)
+      expect(coordinates.longitude).to eq(Astronoby::Angle.zero)
+    end
+  end
+
   describe "#to_true_equatorial" do
     # Source:
     #  Title: Celestial Calculations