feat: add ConvertEquatorialToHorizontalCoordinate(datetime time.Time) to coordinates module in @observerly/sidera.

pkg/coordinates/coordinates.go

@@ -57,3 +57,44 @@ func ConvertEclipticToEquatorialCoordinate(
 }
 
 /*****************************************************************************************************************/
+
+/*
+converts equatorial to horizontal coordinates
+
+The equatorial coordinate system is a celestial coordinate system widely used to specify the positions of
+celestial objects. It may be implemented in spherical or rectangular coordinates, both defined by an
+origin at the center of Earth, a fundamental plane consisting of the projection of Earth's equator onto
+the celestial sphere (forming the celestial equator), a primary direction towards the vernal equinox,
+
+The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon
+as the fundamental plane. The horizontal coordinate system is widely used in astronomy to specify the
+positions of celestial objects in the sky.
+*/
+func ConvertEquatorialToHorizontalCoordinate(
+	datetime time.Time,
+	observer common.GeographicCoordinate,
+	target common.EquatorialCoordinate,
+) (horizontal common.HorizontalCoordinate) {
+	δ := common.Radians(target.Declination)
+
+	φ := common.Radians(observer.Latitude)
+
+	ha := common.Radians(astrometry.GetHourAngle(datetime, observer, target))
+
+	// calculate the altitude in radians.
+	alt := math.Asin(math.Sin(δ)*math.Sin(φ) + math.Cos(δ)*math.Cos(φ)*math.Cos(ha))
+
+	// calculate the azimuth in radians.
+	az := common.Degrees(math.Acos((math.Sin(δ) - math.Sin(alt)*math.Sin(φ)) / (math.Cos(alt) * math.Cos(φ))))
+
+	if math.Sin(ha) > 0 {
+		az = 360 - az
+	}
+
+	return common.HorizontalCoordinate{
+		Azimuth:  math.Mod(az, 360),
+		Altitude: common.Degrees(alt),
+	}
+}
+
+/*****************************************************************************************************************/

pkg/coordinates/coordinates_test.go

@@ -23,6 +23,21 @@ var datetime time.Time = time.Date(2021, 5, 14, 0, 0, 0, 0, time.UTC)
 
 /*****************************************************************************************************************/
 
+var observer common.GeographicCoordinate = common.GeographicCoordinate{
+	Latitude:  19.8207,
+	Longitude: -155.468094,
+	Elevation: 4205,
+}
+
+/*****************************************************************************************************************/
+
+var betelgeuse common.EquatorialCoordinate = common.EquatorialCoordinate{
+	RightAscension: 88.7929583,
+	Declination:    7.4070639,
+}
+
+/*****************************************************************************************************************/
+
 func TestConvertEclipticToEquatorialCoordinate(t *testing.T) {
 	venus := common.EclipticCoordinate{
 		Longitude: 245.79403406596947,
@@ -36,3 +51,12 @@ func TestConvertEclipticToEquatorialCoordinate(t *testing.T) {
 }
 
 /*****************************************************************************************************************/
+
+func TestConvertEquatorialToHorizontalCoordinate(t *testing.T) {
+	hz := ConvertEquatorialToHorizontalCoordinate(datetime, observer, betelgeuse)
+
+	assert.Equal(t, hz.Altitude, 72.7850383767226)
+	assert.Equal(t, hz.Azimuth, 134.4479059877678)
+}
+
+/*****************************************************************************************************************/