// Position returns ecliptic position of planets at equinox and ecliptic of date.
//
// Argument jde is the date for which positions are desired.
//
// Results are positions consistent with those from Meeus's Apendix III,
// that is, at equinox and ecliptic of date.
//
// L is heliocentric longitude in radians.
// B is heliocentric latitude in radians.
// R is heliocentric range in AU.
func (vt *V87Planet) Position(jde float64) (L, B, R float64) {
L, B, R = vt.Position2000(jde)
eclFrom := &coord.Ecliptic{
Lat: B,
Lon: L,
}
eclTo := &coord.Ecliptic{}
epochFrom := 2000.0
epochTo := base.JDEToJulianYear(jde)
precess.EclipticPosition(eclFrom, eclTo, epochFrom, epochTo, 0, 0)
return eclTo.Lon, eclTo.Lat, R
}
func ExampleEclipticPosition() {
// Example 21.c, p. 137.
eclFrom := &coord.Ecliptic{
Lat: 1.76549 * math.Pi / 180,
Lon: 149.48194 * math.Pi / 180,
}
eclTo := &coord.Ecliptic{}
epochFrom := 2000.0
epochTo := base.JDEToJulianYear(julian.CalendarJulianToJD(-214, 6, 30))
precess.EclipticPosition(eclFrom, eclTo, epochFrom, epochTo, 0, 0)
fmt.Printf("%.3f\n", eclTo.Lon*180/math.Pi)
fmt.Printf("%+.3f\n", eclTo.Lat*180/math.Pi)
// Output:
// 118.704
// +1.615
}
func ExampleEclipticPosition() {
// Example 21.c, p. 137.
eclFrom := &coord.Ecliptic{
Lat: unit.AngleFromDeg(1.76549),
Lon: unit.AngleFromDeg(149.48194),
}
eclTo := &coord.Ecliptic{}
epochFrom := 2000.0
epochTo := base.JDEToJulianYear(julian.CalendarJulianToJD(-214, 6, 30))
precess.EclipticPosition(eclFrom, eclTo, epochFrom, epochTo, 0, 0)
fmt.Printf("%.3f\n", eclTo.Lon.Deg())
fmt.Printf("%+.3f\n", eclTo.Lat.Deg())
// Output:
// 118.704
// +1.615
}
// Positions returns positions of the eight major moons of Saturn.
//
// Results returned in argument pos, which must not be nil.
//
// Result units are Saturn radii.
func Positions(jde float64, earth, saturn *pp.V87Planet, pos *[8]XY) {
s, β, R := solar.TrueVSOP87(earth, jde)
ss, cs := s.Sincos()
sβ := β.Sin()
Δ := 9.
var x, y, z float64
var JDE float64
f := func() {
τ := base.LightTime(Δ)
JDE = jde - τ
l, b, r := saturn.Position(JDE)
l, b = pp.ToFK5(l, b, JDE)
sl, cl := l.Sincos()
sb, cb := b.Sincos()
x = r*cb*cl + R*cs
y = r*cb*sl + R*ss
z = r*sb + R*sβ
Δ = math.Sqrt(x*x + y*y + z*z)
}
f()
f()
λ0 := unit.Angle(math.Atan2(y, x))
β0 := unit.Angle(math.Atan(z / math.Hypot(x, y)))
ecl := &coord.Ecliptic{λ0, β0}
precess.EclipticPosition(ecl, ecl,
base.JDEToJulianYear(jde), base.JDEToJulianYear(base.B1950), 0, 0)
λ0, β0 = ecl.Lon, ecl.Lat
q := newQs(JDE)
s4 := [9]r4{{}, // 0 unused
q.mimas(),
q.enceladus(),
q.tethys(),
q.dione(),
q.rhea(),
q.titan(),
q.hyperion(),
q.iapetus(),
}
var X, Y, Z [9]float64
for j := 1; j <= 8; j++ {
u := s4[j].λ - s4[j].Ω
w := s4[j].Ω - 168.8112*d
su, cu := math.Sincos(u)
sw, cw := math.Sincos(w)
sγ, cγ := math.Sincos(s4[j].γ)
r := s4[j].r
X[j] = r * (cu*cw - su*cγ*sw)
Y[j] = r * (su*cw*cγ + cu*sw)
Z[j] = r * su * sγ
}
Z[0] = 1
sλ0, cλ0 := λ0.Sincos()
sβ0, cβ0 := β0.Sincos()
var A, B, C [9]float64
for j := range X {
a := X[j]
b := q.c1*Y[j] - q.s1*Z[j]
c := q.s1*Y[j] + q.c1*Z[j]
a, b =
q.c2*a-q.s2*b,
q.s2*a+q.c2*b
A[j], b =
a*sλ0-b*cλ0,
a*cλ0+b*sλ0
B[j], C[j] =
b*cβ0+c*sβ0,
c*cβ0-b*sβ0
}
D := math.Atan2(A[0], C[0])
sD, cD := math.Sincos(D)
for j := 1; j <= 8; j++ {
X[j] = A[j]*cD - C[j]*sD
Y[j] = A[j]*sD + C[j]*cD
Z[j] = B[j]
d := X[j] / s4[j].r
X[j] += math.Abs(Z[j]) / k[j] * math.Sqrt(1-d*d)
W := Δ / (Δ + Z[j]/2475)
pos[j-1].X = X[j] * W
pos[j-1].Y = Y[j] * W
}
return
}
