// ReduceElements reduces orbital elements of a solar system body from one
// equinox to another.
//
// This function is described in chapter 24, but is located in this
// package so it can be a method of EclipticPrecessor.
func (p *EclipticPrecessor) ReduceElements(eFrom, eTo *elementequinox.Elements) *elementequinox.Elements {
ψ := p.π + p.p
si, ci := math.Sincos(eFrom.Inc)
snp, cnp := math.Sincos(eFrom.Node - p.π)
// (24.1) p. 159
eTo.Inc = math.Acos(ci*p.cη + si*p.sη*cnp)
// (24.2) p. 159
eTo.Node = math.Atan2(si*snp, p.cη*si*cnp-p.sη*ci) + ψ
// (24.3) p. 159
eTo.Peri = math.Atan2(-p.sη*snp, si*p.cη-ci*p.sη*cnp) + eFrom.Peri
return eTo
}
// ReduceElements reduces orbital elements of a solar system body from one
// equinox to another.
//
// This function is described in chapter 24, but is located in this
// package so it can be a method of EclipticPrecessor.
func (p *EclipticPrecessor) ReduceElements(eFrom, eTo *elementequinox.Elements) *elementequinox.Elements {
ψ := p.π + p.p
si, ci := eFrom.Inc.Sincos()
snp, cnp := (eFrom.Node - p.π).Sincos()
// (24.1) p. 159
eTo.Inc = unit.Angle(math.Acos(ci*p.cη + si*p.sη*cnp))
// (24.2) p. 159
eTo.Node = ψ +
unit.Angle(math.Atan2(si*snp, p.cη*si*cnp-p.sη*ci))
// (24.3) p. 160
eTo.Peri = eFrom.Peri +
unit.Angle(math.Atan2(-p.sη*snp, si*p.cη-ci*p.sη*cnp))
return eTo
}