// EclipticPosition precesses ecliptic coordinates from one epoch to another,
// including proper motions.
//
// While eclFrom is given as ecliptic coordinates, proper motions mα, mδ are
// still expected to be equatorial. If proper motions are not to be considered
// or are not applicable, pass 0, 0.
//
// Both eclFrom and eclTo must be non-nil, although they may point to the same
// struct. EclTo is returned for convenience.
func EclipticPosition(eclFrom, eclTo *coord.Ecliptic, epochFrom, epochTo float64, mα base.HourAngle, mδ base.Angle) *coord.Ecliptic {
p := NewEclipticPrecessor(epochFrom, epochTo)
*eclTo = *eclFrom
if mα != 0 || mδ != 0 {
mλ, mβ := eqProperMotionToEcl(mα.Rad(), mδ.Rad(), epochFrom, eclFrom)
t := epochTo - epochFrom
eclTo.Lon += mλ * t
eclTo.Lat += mβ * t
}
return p.Precess(eclTo, eclTo)
}
// EclipticPosition precesses ecliptic coordinates from one epoch to another,
// including proper motions.
//
// While eclFrom is given as ecliptic coordinates, proper motions mα, mδ are
// still expected to be equatorial. If proper motions are not to be considered
// or are not applicable, pass 0, 0.
//
// Both eclFrom and eclTo must be non-nil, although they may point to the same
// struct. EclTo is returned for convenience.
func EclipticPosition(eclFrom, eclTo *coord.Ecliptic, epochFrom, epochTo float64, mα unit.HourAngle, mδ unit.Angle) *coord.Ecliptic {
p := NewEclipticPrecessor(epochFrom, epochTo)
*eclTo = *eclFrom
if mα != 0 || mδ != 0 {
mλ, mβ := eqProperMotionToEcl(mα, mδ, epochFrom, eclFrom)
t := epochTo - epochFrom
eclTo.Lon += mλ.Mul(t)
eclTo.Lat += mβ.Mul(t)
}
return p.Precess(eclTo, eclTo)
}
// EclipticPrecess precesses coordinates eclFrom, leaving result in eclTo.
//
// The same struct may be used for eclFrom and eclTo.
// EclTo is returned for convenience.
func (p *EclipticPrecessor) Precess(eclFrom, eclTo *coord.Ecliptic) *coord.Ecliptic {
// (21.7) p. 137
sβ, cβ := math.Sincos(eclFrom.Lat)
sd, cd := math.Sincos(p.π - eclFrom.Lon)
A := p.cη*cβ*sd - p.sη*sβ
B := cβ * cd
C := p.cη*sβ + p.sη*cβ*sd
eclTo.Lon = p.p + p.π - math.Atan2(A, B)
if C < base.CosSmallAngle {
eclTo.Lat = math.Asin(C)
} else {
eclTo.Lat = math.Acos(math.Hypot(A, B)) // near pole
}
return eclTo
}