func ExampleFraction() {
// Example 41.a, p. 284
k := illum.Fraction(.724604, .910947, .983824)
fmt.Printf("%.3f\n", k)
// Output:
// 0.647
}
// Physical computes quantities for physical observations of Mars.
//
// Results:
// DE planetocentric declination of the Earth.
// DS planetocentric declination of the Sun.
// ω Areographic longitude of the central meridian, as seen from Earth.
// P Geocentric position angle of Mars' northern rotation pole.
// Q Position angle of greatest defect of illumination.
// d Apparent diameter of Mars.
// q Greatest defect of illumination.
// k Illuminated fraction of the disk.
func Physical(jde float64, earth, mars *pp.V87Planet) (DE, DS, ω, P, Q, d, q unit.Angle, k float64) {
// Step 1.
T := base.J2000Century(jde)
const p = math.Pi / 180
// (42.1) p. 288
λ0 := 352.9065*p + 1.1733*p*T
β0 := 63.2818*p - .00394*p*T
// Step 2.
l0, b0, R := earth.Position(jde)
l0, b0 = pp.ToFK5(l0, b0, jde)
// Steps 3, 4.
sl0, cl0 := l0.Sincos()
sb0 := b0.Sin()
Δ := .5 // surely better than 0.
τ := base.LightTime(Δ)
var l, b unit.Angle
var r, x, y, z float64
f := func() {
l, b, r = mars.Position(jde - τ)
l, b = pp.ToFK5(l, b, jde)
sb, cb := b.Sincos()
sl, cl := l.Sincos()
// (42.2) p. 289
x = r*cb*cl - R*cl0
y = r*cb*sl - R*sl0
z = r*sb - R*sb0
// (42.3) p. 289
Δ = math.Sqrt(x*x + y*y + z*z)
τ = base.LightTime(Δ)
}
f()
f()
// Step 5.
λ := math.Atan2(y, x)
β := math.Atan(z / math.Hypot(x, y))
// Step 6.
sβ0, cβ0 := math.Sincos(β0)
sβ, cβ := math.Sincos(β)
DE = unit.Angle(math.Asin(-sβ0*sβ - cβ0*cβ*math.Cos(λ0-λ)))
// Step 7.
N := 49.5581*p + .7721*p*T
lʹ := l.Rad() - .00697*p/r
bʹ := b.Rad() - .000225*p*math.Cos(l.Rad()-N)/r
// Step 8.
sbʹ, cbʹ := math.Sincos(bʹ)
DS = unit.Angle(math.Asin(-sβ0*sbʹ - cβ0*cbʹ*math.Cos(λ0-lʹ)))
// Step 9.
W := 11.504*p + 350.89200025*p*(jde-τ-2433282.5)
// Step 10.
ε0 := nutation.MeanObliquity(jde)
sε0, cε0 := ε0.Sincos()
α0, δ0 := coord.EclToEq(unit.Angle(λ0), unit.Angle(β0), sε0, cε0)
// Step 11.
u := y*cε0 - z*sε0
v := y*sε0 + z*cε0
α := math.Atan2(u, x)
δ := math.Atan(v / math.Hypot(x, u))
sδ, cδ := math.Sincos(δ)
sδ0, cδ0 := δ0.Sincos()
sα0α, cα0α := math.Sincos(α0.Rad() - α)
ζ := math.Atan2(sδ0*cδ*cα0α-sδ*cδ0, cδ*sα0α)
// Step 12.
ω = unit.Angle(W - ζ).Mod1()
// Step 13.
Δψ, Δε := nutation.Nutation(jde)
// Step 14.
sl0λ, cl0λ := math.Sincos(l0.Rad() - λ)
λ += .005693 * p * cl0λ / cβ
β += .005693 * p * sl0λ * sβ
// Step 15.
λ0 += Δψ.Rad()
λ += Δψ.Rad()
ε := ε0 + Δε
// Step 16.
sε, cε := ε.Sincos()
α0ʹ, δ0ʹ := coord.EclToEq(unit.Angle(λ0), unit.Angle(β0), sε, cε)
αʹ, δʹ := coord.EclToEq(unit.Angle(λ), unit.Angle(β), sε, cε)
// Step 17.
sδ0ʹ, cδ0ʹ := δ0ʹ.Sincos()
sδʹ, cδʹ := δʹ.Sincos()
sα0ʹαʹ, cα0ʹαʹ := (α0ʹ - αʹ).Sincos()
// (42.4) p. 290
P = unit.Angle(math.Atan2(cδ0ʹ*sα0ʹαʹ, sδ0ʹ*cδʹ-cδ0ʹ*sδʹ*cα0ʹαʹ))
if P < 0 {
P += 2 * math.Pi
}
// Step 18.
s := l0 + math.Pi
ss, cs := s.Sincos()
αs := math.Atan2(cε*ss, cs)
δs := math.Asin(sε * ss)
sδs, cδs := math.Sincos(δs)
sαsα, cαsα := math.Sincos(αs - α)
χ := math.Atan2(cδs*sαsα, sδs*cδ-cδs*sδ*cαsα)
Q = unit.Angle(χ) + math.Pi
// Step 19.
d = unit.AngleFromSec(9.36) / unit.Angle(Δ)
k = illum.Fraction(r, Δ, R)
q = d.Mul(1 - k)
return
}