func ExampleEccentricity() {
// Example 25.a, p. 165.
T := base.J2000Century(julian.CalendarGregorianToJD(1992, 10, 13))
fmt.Printf("%.9f\n", solar.Eccentricity(T))
// Output:
// 0.016711668
}
// 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
}
// 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
}
// ESmart computes the "equation of time" for the given JDE.
//
// Result is equation of time as an hour angle.
//
// Result is less accurate that E() but the function has the advantage
// of not requiring the V87Planet object.
func ESmart(jde float64) unit.HourAngle {
ε := nutation.MeanObliquity(jde)
t := ε.Mul(.5).Tan()
y := t * t
T := base.J2000Century(jde)
L0 := l0(T * .1)
e := solar.Eccentricity(T)
M := solar.MeanAnomaly(T)
s2L0, c2L0 := L0.Mul(2).Sincos()
sM := M.Sin()
// (28.3) p. 185, with double angle identity
return unit.HourAngle(y*s2L0 - 2*e*sM + 4*e*y*sM*c2L0 -
y*y*s2L0*c2L0 - 1.25*e*e*M.Mul(2).Sin())
}
// ESmart computes the "equation of time" for the given JDE.
//
// Result is equation of time as an hour angle in radians.
//
// Result is less accurate that E() but the function has the advantage
// of not requiring the V87Planet object.
func ESmart(jde float64) float64 {
ε := nutation.MeanObliquity(jde)
t := math.Tan(ε * .5)
y := t * t
T := base.J2000Century(jde)
L0 := l0(T * .1)
e := solar.Eccentricity(T)
M := solar.MeanAnomaly(T)
s2L0, c2L0 := math.Sincos(2 * L0)
sM := math.Sin(M)
// (28.3) p. 185
return y*s2L0 - 2*e*sM + 4*e*y*sM*c2L0 -
y*y*s2L0*c2L0 - 1.25*e*e*math.Sin(2*M)
}
// 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
}