// Position returns observed equatorial coordinates of a body with Keplerian elements.
//
// Argument e must be a valid V87Planet object for Earth.
//
// Results are right ascension and declination α and δ, and elongation ψ,
// all in radians.
func (k *Elements) Position(jde float64, e *pp.V87Planet) (α, δ, ψ float64) {
// (33.6) p. 227
n := base.K / k.Axis / math.Sqrt(k.Axis)
const sε = base.SOblJ2000
const cε = base.COblJ2000
sΩ, cΩ := math.Sincos(k.Node)
si, ci := math.Sincos(k.Inc)
// (33.7) p. 228
F := cΩ
G := sΩ * cε
H := sΩ * sε
P := -sΩ * ci
Q := cΩ*ci*cε - si*sε
R := cΩ*ci*sε + si*cε
// (33.8) p. 229
A := math.Atan2(F, P)
B := math.Atan2(G, Q)
C := math.Atan2(H, R)
a := math.Hypot(F, P)
b := math.Hypot(G, Q)
c := math.Hypot(H, R)
f := func(jde float64) (x, y, z float64) {
M := n * (jde - k.TimeP)
E, err := kepler.Kepler2b(k.Ecc, M, 15)
if err != nil {
E = kepler.Kepler3(k.Ecc, M)
}
ν := kepler.True(E, k.Ecc)
r := kepler.Radius(E, k.Ecc, k.Axis)
// (33.9) p. 229
x = r * a * math.Sin(A+k.ArgP+ν)
y = r * b * math.Sin(B+k.ArgP+ν)
z = r * c * math.Sin(C+k.ArgP+ν)
return
}
return AstrometricJ2000(f, jde, e)
}
func ExampleKepler3() {
// Example data from p. 205
fmt.Printf("%.12f\n", kepler.Kepler3(.99, .2))
// Output:
// 1.066997365282
}