// Topocentric2 returns topocentric corrections including parallax.
//
// This function implements the "non-rigorous" method descripted in the text.
//
// Note that results are corrections, not corrected coordinates.
func Topocentric2(α unit.RA, δ unit.Angle, Δ, ρsφʹ, ρcφʹ float64, L unit.Angle, jde float64) (Δα unit.HourAngle, Δδ unit.Angle) {
π := Horizontal(Δ)
θ0 := sidereal.Apparent(jde)
H := (θ0.Angle() - L - unit.Angle(α)).Mod1()
sH, cH := H.Sincos()
sδ, cδ := δ.Sincos()
Δα = unit.HourAngle(-π.Mul(ρcφʹ * sH / cδ)) // (40.4) p. 280
Δδ = -π.Mul(ρsφʹ*cδ - ρcφʹ*cH*sδ) // (40.5) p. 280
return
}
// Topocentric2 returns topocentric corrections including parallax.
//
// This function implements the "non-rigorous" method descripted in the text.
//
// Note that results are corrections, not corrected coordinates.
func Topocentric2(α, δ, Δ, ρsφʹ, ρcφʹ, L, jde float64) (Δα, Δδ float64) {
π := Horizontal(Δ)
θ0 := base.Time(sidereal.Apparent(jde)).Rad()
H := base.PMod(θ0-L-α, 2*math.Pi)
sH, cH := math.Sincos(H)
sδ, cδ := math.Sincos(δ)
Δα = -π * ρcφʹ * sH / cδ // (40.4) p. 280
Δδ = -π * (ρsφʹ*cδ - ρcφʹ*cH*sδ) // (40.5) p. 280
return
}
func ExampleMean_a() {
// Example 12.a, p. 88.
jd := 2446895.5
s := sidereal.Mean(jd)
sa := sidereal.Apparent(jd)
fmt.Printf("%.4d\n", sexa.NewFmtTime(s))
fmt.Printf("%.4d\n", sexa.NewFmtTime(sa))
// Output:
// 13ʰ10ᵐ46ˢ.3668
// 13ʰ10ᵐ46ˢ.1351
}
// Topocentric returns topocentric positions including parallax.
//
// Arguments α, δ are geocentric right ascension and declination in radians.
// Δ is distance to the observed object in AU. ρsφʹ, ρcφʹ are parallax
// constants (see package globe.) L is geographic longitude of the observer,
// jde is time of observation.
//
// Results are observed topocentric ra and dec in radians.
func Topocentric(α, δ, Δ, ρsφʹ, ρcφʹ, L, jde float64) (αʹ, δʹ float64) {
π := Horizontal(Δ)
θ0 := base.Time(sidereal.Apparent(jde)).Rad()
H := base.PMod(θ0-L-α, 2*math.Pi)
sπ := math.Sin(π)
sH, cH := math.Sincos(H)
sδ, cδ := math.Sincos(δ)
Δα := math.Atan2(-ρcφʹ*sπ*sH, cδ-ρcφʹ*sπ*cH) // (40.2) p. 279
αʹ = α + Δα
δʹ = math.Atan2((sδ-ρsφʹ*sπ)*math.Cos(Δα), cδ-ρcφʹ*sπ*cH) // (40.3) p. 279
return
}
// Topocentric returns topocentric positions including parallax.
//
// Arguments α, δ are geocentric right ascension and declination in radians.
// Δ is distance to the observed object in AU. ρsφʹ, ρcφʹ are parallax
// constants (see package globe.) L is geographic longitude of the observer,
// jde is time of observation.
//
// Results are observed topocentric ra and dec in radians.
func Topocentric(α unit.RA, δ unit.Angle, Δ, ρsφʹ, ρcφʹ float64, L unit.Angle, jde float64) (αʹ unit.RA, δʹ unit.Angle) {
π := Horizontal(Δ)
θ0 := sidereal.Apparent(jde)
H := (θ0.Angle() - L - unit.Angle(α)).Mod1()
sπ := π.Sin()
sH, cH := H.Sincos()
sδ, cδ := δ.Sincos()
// (40.2) p. 279
Δα := unit.HourAngle(math.Atan2(-ρcφʹ*sπ*sH, cδ-ρcφʹ*sπ*cH))
αʹ = α.Add(Δα)
// (40.3) p. 279
δʹ = unit.Angle(math.Atan2((sδ-ρsφʹ*sπ)*Δα.Cos(), cδ-ρcφʹ*sπ*cH))
return
}
// Topocentric3 returns topocentric hour angle and declination including parallax.
//
// This function implements the "alternative" method described in the text.
// The method should be similarly rigorous to that of Topocentric() and results
// should be virtually consistent.
func Topocentric3(α unit.RA, δ unit.Angle, Δ, ρsφʹ, ρcφʹ float64, L unit.Angle, jde float64) (Hʹ unit.HourAngle, δʹ unit.Angle) {
π := Horizontal(Δ)
θ0 := sidereal.Apparent(jde)
H := (θ0.Angle() - L - unit.Angle(α)).Mod1()
sπ := π.Sin()
sH, cH := H.Sincos()
sδ, cδ := δ.Sincos()
A := cδ * sH
B := cδ*cH - ρcφʹ*sπ
C := sδ - ρsφʹ*sπ
q := math.Sqrt(A*A + B*B + C*C)
Hʹ = unit.HourAngle(math.Atan2(A, B))
δʹ = unit.Angle(math.Asin(C / q))
return
}
// Topocentric3 returns topocentric hour angle and declination including parallax.
//
// This function implements the "alternative" method described in the text.
// The method should be similarly rigorous to that of Topocentric() and results
// should be virtually consistent.
func Topocentric3(α, δ, Δ, ρsφʹ, ρcφʹ, L, jde float64) (Hʹ, δʹ float64) {
π := Horizontal(Δ)
θ0 := base.Time(sidereal.Apparent(jde)).Rad()
H := base.PMod(θ0-L-α, 2*math.Pi)
sπ := math.Sin(π)
sH, cH := math.Sincos(H)
sδ, cδ := math.Sincos(δ)
A := cδ * sH
B := cδ*cH - ρcφʹ*sπ
C := sδ - ρsφʹ*sπ
q := math.Sqrt(A*A + B*B + C*C)
Hʹ = math.Atan2(A, B)
δʹ = math.Asin(C / q)
return
}
func ExampleHorizontal_EqToHz() {
// Example 13.b, p. 95.
eq := &coord.Equatorial{
RA: unit.NewRA(23, 9, 16.641),
Dec: unit.NewAngle('-', 6, 43, 11.61),
}
g := &globe.Coord{
Lat: unit.NewAngle(' ', 38, 55, 17),
Lon: unit.NewAngle(' ', 77, 3, 56),
}
jd := julian.TimeToJD(time.Date(1987, 4, 10, 19, 21, 0, 0, time.UTC))
st := sidereal.Apparent(jd)
hz := new(coord.Horizontal).EqToHz(eq, g, st)
fmt.Printf("A = %+.3j\n", sexa.FmtAngle(hz.Az))
fmt.Printf("h = %+.3j\n", sexa.FmtAngle(hz.Alt))
// Output:
// A = +68°.034
// h = +15°.125
}
func ExampleHorizontal_EqToHz() {
// Example 13.b, p. 95.
eq := &coord.Equatorial{
RA: sexa.NewRA(23, 9, 16.641).Rad(),
Dec: sexa.NewAngle(true, 6, 43, 11.61).Rad(),
}
g := &globe.Coord{
Lat: sexa.NewAngle(false, 38, 55, 17).Rad(),
Lon: sexa.NewAngle(false, 77, 3, 56).Rad(),
}
jd := julian.TimeToJD(time.Date(1987, 4, 10, 19, 21, 0, 0, time.UTC))
st := sidereal.Apparent(jd)
hz := new(coord.Horizontal).EqToHz(eq, g, st)
AStr := fmt.Sprintf("%+.3j", sexa.NewFmtAngle(hz.Az))
hStr := fmt.Sprintf("%+.3j", sexa.NewFmtAngle(hz.Alt))
fmt.Println("A =", AStr)
fmt.Println("h =", hStr)
// Output:
// A = +68°.034
// h = +15°.125
}
func ExampleTopocentric3() {
// same test case as example 40.a, p. 280
α := unit.RAFromDeg(339.530208)
δ := unit.AngleFromDeg(-15.771083)
Δ := .37276
ρsφʹ := .546861
ρcφʹ := .836339
L := unit.Angle(unit.NewHourAngle(' ', 7, 47, 27))
jde := julian.CalendarGregorianToJD(2003, 8, 28+
unit.NewTime(' ', 3, 17, 0).Day())
Hʹ, δʹ := parallax.Topocentric3(α, δ, Δ, ρsφʹ, ρcφʹ, L, jde)
fmt.Printf("Hʹ = %.2d\n", sexa.FmtHourAngle(Hʹ))
θ0 := sidereal.Apparent(jde)
αʹ := unit.RAFromRad(θ0.Rad() - L.Rad() - Hʹ.Rad())
// same result as example 40.a, p. 280
fmt.Printf("αʹ = %.2d\n", sexa.FmtRA(αʹ))
fmt.Printf("δʹ = %.1d\n", sexa.FmtAngle(δʹ))
// Output:
// Hʹ = -4ʰ44ᵐ50ˢ.28
// αʹ = 22ʰ38ᵐ8ˢ.54
// δʹ = -15°46′30″.0
}
func TestTopocentric3(t *testing.T) {
// same test case as example 40.a, p. 280
α := 339.530208 * math.Pi / 180
δ := -15.771083 * math.Pi / 180
Δ := .37276
ρsφʹ := .546861
ρcφʹ := .836339
L := base.NewHourAngle(false, 7, 47, 27).Rad()
jde := julian.CalendarGregorianToJD(2003, 8, 28+(3+17./60)/24)
// reference result
αʹ, δʹ1 := parallax.Topocentric(α, δ, Δ, ρsφʹ, ρcφʹ, L, jde)
// result to test
Hʹ, δʹ3 := parallax.Topocentric3(α, δ, Δ, ρsφʹ, ρcφʹ, L, jde)
// test
θ0 := base.Time(sidereal.Apparent(jde)).Rad()
if math.Abs(base.PMod(Hʹ-(θ0-L-αʹ)+1, 2*math.Pi)-1) > 1e-15 {
t.Fatal(Hʹ, θ0-L-αʹ)
}
if math.Abs(δʹ3-δʹ1) > 1e-15 {
t.Fatal(δʹ3, δʹ1)
}
}