// EclipticAberration returns corrections due to aberration for ecliptic
// coordinates of an object.
func EclipticAberration(λ, β, jd float64) (Δλ, Δβ float64) {
T := base.J2000Century(jd)
s, _ := solar.True(T)
e := solar.Eccentricity(T)
π := perihelion(T)
sβ, cβ := math.Sincos(β)
ssλ, csλ := math.Sincos(s - λ)
sπλ, cπλ := math.Sincos(π - λ)
// (23.2) p. 151
Δλ = κ * (e*cπλ - csλ) / cβ
Δβ = -κ * sβ * (ssλ - e*sπλ)
return
}
func ExampleTrue() {
// Example 25.a, p. 165.
jd := julian.CalendarGregorianToJD(1992, 10, 13)
fmt.Printf("JDE: %.1f\n", jd)
T := base.J2000Century(jd)
fmt.Printf("T: %.9f\n", T)
s, _ := solar.True(T)
fmt.Printf("☉: %.5f\n", (s * 180 / math.Pi))
// Output:
// JDE: 2448908.5
// T: -0.072183436
// ☉: 199.90987
}
// EclipticAberration returns corrections due to aberration for ecliptic
// coordinates of an object.
func EclipticAberration(λ, β unit.Angle, jd float64) (Δλ, Δβ unit.Angle) {
T := base.J2000Century(jd)
s, _ := solar.True(T)
e := solar.Eccentricity(T)
π := perihelion(T)
sβ, cβ := β.Sincos()
ssλ, csλ := (s - λ).Sincos()
sπλ, cπλ := (π - λ).Sincos()
// (23.2) p. 151
Δλ = κ.Mul((e*cπλ - csλ) / cβ)
Δβ = -κ.Mul(sβ * (ssλ - e*sπλ))
return
}
// Aberration returns corrections due to aberration for equatorial
// coordinates of an object.
func Aberration(α, δ, jd float64) (Δα2, Δδ2 float64) {
ε := nutation.MeanObliquity(jd)
T := base.J2000Century(jd)
s, _ := solar.True(T)
e := solar.Eccentricity(T)
π := perihelion(T)
sα, cα := math.Sincos(α)
sδ, cδ := math.Sincos(δ)
ss, cs := math.Sincos(s)
sπ, cπ := math.Sincos(π)
cε := math.Cos(ε)
tε := math.Tan(ε)
q1 := cα * cε
// (23.3) p. 152
Δα2 = κ * (e*(q1*cπ+sα*sπ) - (q1*cs + sα*ss)) / cδ
q2 := cε * (tε*cδ - sα*sδ)
q3 := cα * sδ
Δδ2 = κ * (e*(cπ*q2+sπ*q3) - (cs*q2 + ss*q3))
return
}
// Aberration returns corrections due to aberration for equatorial
// coordinates of an object.
func Aberration(α unit.RA, δ unit.Angle, jd float64) (Δα2 unit.HourAngle, Δδ2 unit.Angle) {
ε := nutation.MeanObliquity(jd)
T := base.J2000Century(jd)
s, _ := solar.True(T)
e := solar.Eccentricity(T)
π := perihelion(T)
sα, cα := α.Sincos()
sδ, cδ := δ.Sincos()
ss, cs := s.Sincos()
sπ, cπ := π.Sincos()
cε := ε.Cos()
tε := ε.Tan()
q1 := cα * cε
// (23.3) p. 152
Δα2 = unit.HourAngle(κ.Rad() * (e*(q1*cπ+sα*sπ) - (q1*cs + sα*ss)) / cδ)
q2 := cε * (tε*cδ - sα*sδ)
q3 := cα * sδ
Δδ2 = κ.Mul(e*(cπ*q2+sπ*q3) - (cs*q2 + ss*q3))
return
}