// EqToHz computes Horizontal coordinates from equatorial coordinates.
//
// α: right ascension coordinate to transform
// δ: declination coordinate to transform
// φ: latitude of observer on Earth
// ψ: longitude of observer on Earth
// st: sidereal time at Greenwich at time of observation.
//
// Sidereal time must be consistent with the equatorial coordinates.
// If coordinates are apparent, sidereal time must be apparent as well.
//
// Results:
//
// A: azimuth of observed point, measured westward from the South.
// h: elevation, or height of observed point above horizon.
func EqToHz(α unit.RA, δ, φ, ψ unit.Angle, st unit.Time) (A, h unit.Angle) {
H := st.Rad() - ψ.Rad() - α.Rad()
sH, cH := math.Sincos(H)
sφ, cφ := φ.Sincos()
sδ, cδ := ψ.Sincos()
A = unit.Angle(math.Atan2(sH, cH*sφ-(sδ/cδ)*cφ)) // (13.5) p. 93
h = unit.Angle(math.Asin(sφ*sδ + cφ*cδ*cH)) // (13.6) p. 93
return
}
// HzToEq transforms horizontal coordinates to equatorial coordinates.
//
// A: azimuth
// h: elevation
// φ: latitude of observer on Earth
// ψ: longitude of observer on Earth
// st: sidereal time at Greenwich at time of observation.
//
// Sidereal time must be consistent with the equatorial coordinates
// in the sense that tf coordinates are apparent, sidereal time must be
// apparent as well.
//
// Results:
//
// α: right ascension
// δ: declination
func HzToEq(A, h, φ, ψ unit.Angle, st unit.Time) (α unit.RA, δ unit.Angle) {
sA, cA := A.Sincos()
sh, ch := h.Sincos()
sφ, cφ := φ.Sincos()
H := math.Atan2(sA, cA*sφ+sh/ch*cφ)
α = unit.RAFromRad(st.Rad() - ψ.Rad() - H)
δ = unit.Angle(math.Asin(sφ*sh - cφ*ch*cA))
return
}
// EqToHz computes Horizontal coordinates from equatorial coordinates.
//
// Argument g is the location of the observer on the Earth. Argument st
// is the sidereal time at Greenwich.
//
// Sidereal time must be consistent with the equatorial coordinates.
// If coordinates are apparent, sidereal time must be apparent as well.
func (hz *Horizontal) EqToHz(eq *Equatorial, g *globe.Coord, st unit.Time) *Horizontal {
H := st.Rad() - g.Lon.Rad() - eq.RA.Rad()
sH, cH := math.Sincos(H)
sφ, cφ := g.Lat.Sincos()
sδ, cδ := eq.Dec.Sincos()
hz.Az = unit.Angle(math.Atan2(sH, cH*sφ-(sδ/cδ)*cφ)) // (13.5) p. 93
hz.Alt = unit.Angle(math.Asin(sφ*sδ + cφ*cδ*cH)) // (13.6) p. 93
return hz
}
// HzToEq transforms horizontal coordinates to equatorial coordinates.
//
// Sidereal time st must be consistent with the equatorial coordinates
// in the sense that if coordinates are apparent, sidereal time must be
// apparent as well.
func (eq *Equatorial) HzToEq(hz *Horizontal, g globe.Coord, st unit.Time) *Equatorial {
sA, cA := hz.Az.Sincos()
sh, ch := hz.Alt.Sincos()
sφ, cφ := g.Lat.Sincos()
H := math.Atan2(sA, cA*sφ+sh/ch*cφ)
eq.RA = unit.RAFromRad(st.Rad() - g.Lon.Rad() - H)
eq.Dec = unit.Angle(math.Asin(sφ*sh - cφ*ch*cA))
return eq
}