// 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)
}
}
}
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
}
func ExampleElements_Position() {
// Example 33.b, p. 232.
earth, err := pp.LoadPlanet(pp.Earth, "")
if err != nil {
fmt.Println(err)
return
}
k := &elliptic.Elements{
TimeP: julian.CalendarGregorianToJD(1990, 10, 28.54502),
Axis: 2.2091404,
Ecc: .8502196,
Inc: 11.94524 * math.Pi / 180,
Node: 334.75006 * math.Pi / 180,
ArgP: 186.23352 * math.Pi / 180,
}
j := julian.CalendarGregorianToJD(1990, 10, 6)
α, δ, ψ := k.Position(j, earth)
fmt.Printf("α = %.1d\n", base.NewFmtRA(α))
fmt.Printf("δ = %.0d\n", base.NewFmtAngle(δ))
fmt.Printf("ψ = %.2f\n", ψ*180/math.Pi)
// Output:
// α = 10ʰ34ᵐ14ˢ.2
// δ = 19°9′31″
// ψ = 40.51
}
func ExampleApparentEquatorial() {
// Example 25.a, p. 165.
jde := julian.CalendarGregorianToJD(1992, 10, 13)
α, δ := solar.ApparentEquatorial(jde)
fmt.Printf("α: %.1d\n", base.NewFmtRA(α))
fmt.Printf("δ: %d\n", base.NewFmtAngle(δ))
// Output:
// α: 13ʰ13ᵐ31ˢ.4
// δ: -7°47′6″
}
func ExampleStellar() {
// Exercise, p. 119.
day1 := 7.
day5 := 27.
r2 := []float64{
base.NewRA(15, 3, 51.937).Rad(),
base.NewRA(15, 9, 57.327).Rad(),
base.NewRA(15, 15, 37.898).Rad(),
base.NewRA(15, 20, 50.632).Rad(),
base.NewRA(15, 25, 32.695).Rad(),
}
d2 := []float64{
base.NewAngle(true, 8, 57, 34.51).Rad(),
base.NewAngle(true, 9, 9, 03.88).Rad(),
base.NewAngle(true, 9, 17, 37.94).Rad(),
base.NewAngle(true, 9, 23, 16.25).Rad(),
base.NewAngle(true, 9, 26, 01.01).Rad(),
}
jd := julian.CalendarGregorianToJD(1996, 2, 17)
dt := jd - base.J2000
dy := dt / base.JulianYear
dc := dy / 100
fmt.Printf("%.2f years\n", dy)
fmt.Printf("%.4f century\n", dc)
pmr := -.649 // sec/cen
pmd := -1.91 // sec/cen
r1 := base.NewRA(15, 17, 0.421+pmr*dc).Rad()
// Careful with quick and dirty way of applying correction to seconds
// component before converting to radians. The dec here is negative
// so correction must be subtracted. Alternative, less error-prone,
// way would be to convert both to radians, then add.
d1 := base.NewAngle(true, 9, 22, 58.54-pmd*dc).Rad()
fmt.Printf("α′ = %.3d, δ′ = %.2d\n",
base.NewFmtRA(r1), base.NewFmtAngle(d1))
day, dd, err := conjunction.Stellar(day1, day5, r1, d1, r2, d2)
if err != nil {
fmt.Println(err)
return
}
fmt.Println(base.NewFmtAngle(dd))
dInt, dFrac := math.Modf(day)
fmt.Printf("1996 February %d at %s TD\n", int(dInt),
base.NewFmtTime(dFrac*24*3600))
// Output:
// -3.87 years
// -0.0387 century
// α′ = 15ʰ17ᵐ0ˢ.446, δ′ = -9°22′58″.47
// 3′38″
// 1996 February 18 at 6ʰ36ᵐ55ˢ TD
}
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 ExampleAstrometric() {
// Example 37.a, p. 266
e, err := pp.LoadPlanet(pp.Earth, "")
if err != nil {
fmt.Println(err)
return
}
α, δ := pluto.Astrometric(2448908.5, e)
fmt.Printf("α: %.1d\n", base.NewFmtRA(α))
fmt.Printf("δ: %.0d\n", base.NewFmtAngle(δ))
// Output:
// α: 15ʰ31ᵐ43ˢ.8
// δ: -4°27′29″
}
func ExampleLen4Half() {
// Example 3.f, p. 32.
half, err := interp.Len4Half([]float64{
base.NewRA(10, 18, 48.732).Rad(),
base.NewRA(10, 23, 22.835).Rad(),
base.NewRA(10, 27, 57.247).Rad(),
base.NewRA(10, 32, 31.983).Rad(),
})
if err != nil {
fmt.Println(err)
return
}
fmt.Printf("%.3d", base.NewFmtRA(half))
// Output:
// 10ʰ25ᵐ40ˢ.001
}
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 ExampleApparentEquatorialVSOP87() {
// Example 25.b, p. 169, but as this code uses the full VSOP87 theory,
// results match those at bottom of p. 165.
e, err := pp.LoadPlanet(pp.Earth, "")
if err != nil {
fmt.Println(err)
return
}
jde := julian.CalendarGregorianToJD(1992, 10, 13)
α, δ, _ := solar.ApparentEquatorialVSOP87(e, jde)
fmt.Printf("α: %.3d\n", base.NewFmtRA(α))
fmt.Printf("δ: %+.2d\n", base.NewFmtAngle(δ))
// Output:
// α: 13ʰ13ᵐ30ˢ.749
// δ: -7°47′1″.74
}
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
}
func ExamplePosition() {
// Example 33.a, p. 225. VSOP87 result p. 227.
earth, err := pp.LoadPlanet(pp.Earth, "")
if err != nil {
fmt.Println(err)
return
}
venus, err := pp.LoadPlanet(pp.Venus, "")
if err != nil {
fmt.Println(err)
return
}
α, δ := elliptic.Position(venus, earth, 2448976.5)
fmt.Printf("α = %.3d\n", base.NewFmtRA(α))
fmt.Printf("δ = %.2d\n", base.NewFmtAngle(δ))
// Output:
// α = 21ʰ4ᵐ41ˢ.454
// δ = -18°53′16″.84
}
