func ExampleProperMotion3D() {
// Example 21.d, p. 141.
eqFrom := &coord.Equatorial{
RA: base.NewRA(6, 45, 8.871).Rad(),
Dec: base.NewAngle(true, 16, 42, 57.99).Rad(),
}
mra := base.NewHourAngle(false, 0, 0, -0.03847)
mdec := base.NewAngle(false, 0, 0, -1.2053)
r := 2.64 // given in correct unit
mr := -7.6 / 977792 // magic conversion factor
eqTo := &coord.Equatorial{}
fmt.Printf("Δr = %.9f, Δα = %.10f, Δδ = %.10f\n", mr, mra, mdec)
for _, epoch := range []float64{1000, 0, -1000, -2000, -10000} {
precess.ProperMotion3D(eqFrom, eqTo, 2000, epoch, r, mr, mra, mdec)
fmt.Printf("%8.1f %0.2d %-0.1d\n", epoch,
base.NewFmtRA(eqTo.RA), base.NewFmtAngle(eqTo.Dec))
}
// Output:
// Δr = -0.000007773, Δα = -0.0000027976, Δδ = -0.0000058435
// 1000.0 6ʰ45ᵐ47ˢ.16 -16°22′56″.0
// 0.0 6ʰ46ᵐ25ˢ.09 -16°03′00″.8
// -1000.0 6ʰ47ᵐ02ˢ.67 -15°43′12″.3
// -2000.0 6ʰ47ᵐ39ˢ.91 -15°23′30″.6
// -10000.0 6ʰ52ᵐ25ˢ.72 -12°50′06″.7
}
// Exercise, p. 136.
func TestPosition(t *testing.T) {
eqFrom := &coord.Equatorial{
base.NewRA(2, 31, 48.704).Rad(),
base.NewAngle(false, 89, 15, 50.72).Rad(),
}
eqTo := &coord.Equatorial{}
mα := base.NewHourAngle(false, 0, 0, 0.19877)
mδ := base.NewAngle(true, 0, 0, 0.0152)
for _, tc := range []struct {
α, δ string
jde float64
}{
{"1 22 33.90", "88 46 26.18", base.BesselianYearToJDE(1900)},
{"3 48 16.43", "89 27 15.38", base.JulianYearToJDE(2050)},
{"5 53 29.17", "89 32 22.18", base.JulianYearToJDE(2100)},
} {
epochTo := base.JDEToJulianYear(tc.jde)
precess.Position(eqFrom, eqTo, 2000.0, epochTo, mα, mδ)
αStr := fmt.Sprintf("%.2x", base.NewFmtRA(eqTo.RA))
δStr := fmt.Sprintf("%.2x", base.NewFmtAngle(eqTo.Dec))
if αStr != tc.α {
t.Fatal("got:", αStr, "want:", tc.α)
}
if δStr != tc.δ {
t.Fatal(δStr)
}
}
}
func TestPrecessor_Precess(t *testing.T) {
// Exercise, p. 136.
eqFrom := &coord.Equatorial{
RA: base.NewRA(2, 31, 48.704).Rad(),
Dec: base.NewAngle(false, 89, 15, 50.72).Rad(),
}
mα := base.NewHourAngle(false, 0, 0, .19877)
mδ := base.NewAngle(false, 0, 0, -.0152)
epochs := []float64{
base.JDEToJulianYear(base.B1900),
2050,
2100,
}
answer := []string{
"α = 1ʰ22ᵐ33ˢ.90 δ = +88°46′26″.18",
"α = 3ʰ48ᵐ16ˢ.43 δ = +89°27′15″.38",
"α = 5ʰ53ᵐ29ˢ.17 δ = +89°32′22″.18",
}
eqTo := &coord.Equatorial{}
for i, epochTo := range epochs {
precess.Position(eqFrom, eqTo, 2000, epochTo, mα, mδ)
if answer[i] != fmt.Sprintf("α = %0.2d δ = %+0.2d",
base.NewFmtRA(eqTo.RA), base.NewFmtAngle(eqTo.Dec)) {
t.Fatal(i)
}
}
}
// ApproxAnnualPrecession returns approximate annual precision in right
// ascension and declination.
//
// The two epochs should be within a few hundred years.
// The declinations should not be too close to the poles.
func ApproxAnnualPrecession(eq *coord.Equatorial, epochFrom, epochTo float64) (Δα base.HourAngle, Δδ base.Angle) {
m, na, nd := mn(epochFrom, epochTo)
sa, ca := math.Sincos(eq.RA)
// (21.1) p. 132
Δαs := m + na*sa*math.Tan(eq.Dec) // seconds of RA
Δδs := nd * ca // seconds of Dec
return base.NewHourAngle(false, 0, 0, Δαs), base.NewAngle(false, 0, 0, Δδs)
}
func ExampleTopocentric2() {
// Example 40.a, p. 280
Δα, Δδ := parallax.Topocentric2(339.530208*math.Pi/180,
-15.771083*math.Pi/180,
.37276, .546861, .836339,
base.NewHourAngle(false, 7, 47, 27).Rad(),
julian.CalendarGregorianToJD(2003, 8, 28+(3+17./60)/24))
fmt.Printf("Δα = %.2f sec of RA\n", Δα*180/math.Pi*60*60/15)
fmt.Printf("Δδ = %.1f sec\n", Δδ*180/math.Pi*60*60)
// Output:
// Δα = 1.29 sec of RA
// Δδ = -14.1 sec
}
func ExampleTopocentric() {
// Example 40.a, p. 280
α, δ := parallax.Topocentric(339.530208*math.Pi/180,
-15.771083*math.Pi/180,
.37276, .546861, .836339,
base.NewHourAngle(false, 7, 47, 27).Rad(),
julian.CalendarGregorianToJD(2003, 8, 28+(3+17./60)/24))
fmt.Printf("α' = %.2d\n", base.NewFmtRA(α))
fmt.Printf("δ' = %.1d\n", base.NewFmtAngle(δ))
// Output:
// α' = 22ʰ38ᵐ8ˢ.54
// δ' = -15°46′30″.0
}
func ExamplePositionRonVondrak() {
// Example 23.b, p. 156
jd := julian.CalendarGregorianToJD(2028, 11, 13.19)
eq := &coord.Equatorial{
RA: base.NewRA(2, 44, 11.986).Rad(),
Dec: base.NewAngle(false, 49, 13, 42.48).Rad(),
}
apparent.PositionRonVondrak(eq, eq, base.JDEToJulianYear(jd),
base.NewHourAngle(false, 0, 0, 0.03425),
base.NewAngle(true, 0, 0, 0.0895))
fmt.Printf("α = %0.3d\n", base.NewFmtRA(eq.RA))
fmt.Printf("δ = %0.2d\n", base.NewFmtAngle(eq.Dec))
// Output:
// α = 2ʰ46ᵐ14ˢ.392
// δ = 49°21′07″.45
}
func ExampleApproxPosition() {
// Example 21.a, p. 132.
eq := &coord.Equatorial{
base.NewRA(10, 8, 22.3).Rad(),
base.NewAngle(false, 11, 58, 2).Rad(),
}
epochFrom := 2000.0
epochTo := 1978.0
mα := base.NewHourAngle(true, 0, 0, 0.0169)
mδ := base.NewAngle(false, 0, 0, 0.006)
precess.ApproxPosition(eq, eq, epochFrom, epochTo, mα, mδ)
fmt.Printf("%0.1d\n", base.NewFmtRA(eq.RA))
fmt.Printf("%+0d\n", base.NewFmtAngle(eq.Dec))
// Output:
// 10ʰ07ᵐ12ˢ.1
// +12°04′32″
}
func ExamplePosition() {
// Example 21.b, p. 135.
eq := &coord.Equatorial{
base.NewRA(2, 44, 11.986).Rad(),
base.NewAngle(false, 49, 13, 42.48).Rad(),
}
epochFrom := 2000.0
jdTo := julian.CalendarGregorianToJD(2028, 11, 13.19)
epochTo := base.JDEToJulianYear(jdTo)
precess.Position(eq, eq, epochFrom, epochTo,
base.NewHourAngle(false, 0, 0, 0.03425),
base.NewAngle(true, 0, 0, 0.0895))
fmt.Printf("%0.3d\n", base.NewFmtRA(eq.RA))
fmt.Printf("%+0.2d\n", base.NewFmtAngle(eq.Dec))
// Output:
// 2ʰ46ᵐ11ˢ.331
// +49°20′54″.54
}
// Test with proper motion of Regulus, with equatorial motions given
// in Example 21.a, p. 132, and ecliptic motions given in table 21.A,
// p. 138.
func TestEqProperMotionToEcl(t *testing.T) {
ε := coord.NewObliquity(nutation.MeanObliquity(base.J2000))
mλ, mβ := eqProperMotionToEcl(
// eq motions from p. 132.
base.NewHourAngle(true, 0, 0, 0.0169).Rad(),
base.NewAngle(false, 0, 0, 0.006).Rad(),
2000.0,
// eq coordinates from p. 132.
new(coord.Ecliptic).EqToEcl(&coord.Equatorial{
RA: base.NewRA(10, 8, 22.3).Rad(),
Dec: base.NewAngle(false, 11, 58, 2).Rad(),
}, ε))
d := math.Abs((mλ - base.NewAngle(true, 0, 0, .2348).Rad()) / mλ)
if d*169 > 1 { // 169 = significant digits of given lon
t.Fatal("mλ")
}
d = math.Abs((mβ - base.NewAngle(true, 0, 0, 0.0813).Rad()) / mβ)
if d*6 > 1 { // 6 = significant digit of given lat
t.Fatal("mβ")
}
}
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)
}
}