func ExampleTimes() {
// Example 15.a, p. 103.
// Venus on 1988 March 20
p := globe.Coord{
Lon: unit.NewAngle(' ', 71, 5, 0),
Lat: unit.NewAngle(' ', 42, 20, 0),
}
Th0 := unit.NewTime(' ', 11, 50, 58.1)
α3 := []unit.RA{
unit.NewRA(2, 42, 43.25),
unit.NewRA(2, 46, 55.51),
unit.NewRA(2, 51, 07.69),
}
δ3 := []unit.Angle{
unit.NewAngle(' ', 18, 02, 51.4),
unit.NewAngle(' ', 18, 26, 27.3),
unit.NewAngle(' ', 18, 49, 38.7),
}
h0 := unit.AngleFromDeg(-.5667)
ΔT := unit.Time(56)
tRise, tTransit, tSet, err := rise.Times(p, ΔT, h0, Th0, α3, δ3)
if err != nil {
fmt.Println(err)
return
}
fmt.Printf("rising: %+.5f %02s\n", tRise/86400, sexa.FmtTime(tRise))
fmt.Printf("transit: %+.5f %02s\n", tTransit/86400, sexa.FmtTime(tTransit))
fmt.Printf("seting: %+.5f %02s\n", tSet/86400, sexa.FmtTime(tSet))
// Output:
// rising: +0.51766 12ʰ25ᵐ26ˢ
// transit: +0.81980 19ʰ40ᵐ30ˢ
// seting: +0.12130 02ʰ54ᵐ40ˢ
}
// First exercise, p. 110.
func TestSep(t *testing.T) {
r1 := unit.NewRA(4, 35, 55.2).Angle()
d1 := unit.NewAngle(' ', 16, 30, 33)
r2 := unit.NewRA(16, 29, 24).Angle()
d2 := unit.NewAngle('-', 26, 25, 55)
d := angle.Sep(r1, d1, r2, d2)
answer := unit.NewAngle(' ', 169, 58, 0)
if math.Abs((d - answer).Rad()) > 1e-4 {
t.Fatal(d, answer)
}
}
func ExampleSep() {
// Example 17.a, p. 110.
r1 := unit.NewRA(14, 15, 39.7).Angle()
d1 := unit.NewAngle(' ', 19, 10, 57)
r2 := unit.NewRA(13, 25, 11.6).Angle()
d2 := unit.NewAngle('-', 11, 9, 41)
d := angle.Sep(r1, d1, r2, d2)
fmt.Println(sexa.FmtAngle(d))
// Output:
// 32°47′35″
}
func TestSepHav(t *testing.T) {
// Example 17.a, p. 110.
r1 := unit.NewRA(14, 15, 39.7).Angle()
d1 := unit.NewAngle(' ', 19, 10, 57)
r2 := unit.NewRA(13, 25, 11.6).Angle()
d2 := unit.NewAngle('-', 11, 9, 41)
d := angle.SepHav(r1, d1, r2, d2)
s := fmt.Sprint(sexa.FmtAngle(d))
if s != "32°47′35″" {
t.Fatal(s)
}
}
func ExampleAngle() {
// Example p. 123.
rδ := unit.NewRA(5, 32, 0.40).Angle()
dδ := unit.NewAngle('-', 0, 17, 56.9)
rε := unit.NewRA(5, 36, 12.81).Angle()
dε := unit.NewAngle('-', 1, 12, 7.0)
rζ := unit.NewRA(5, 40, 45.52).Angle()
dζ := unit.NewAngle('-', 1, 56, 33.3)
n := line.Angle(rδ, dδ, rε, dε, rζ, dζ)
fmt.Printf("%.4f degrees\n", n.Deg())
fmt.Printf("%m\n", sexa.FmtAngle(n))
// Output:
// 172.4830 degrees
// 172°29′
}
func TestPrecessor_Precess(t *testing.T) {
// Exercise, p. 136.
eqFrom := &coord.Equatorial{
RA: unit.NewRA(2, 31, 48.704),
Dec: unit.NewAngle(' ', 89, 15, 50.72),
}
mα := unit.HourAngleFromSec(.19877)
mδ := unit.AngleFromSec(-.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",
sexa.FmtRA(eqTo.RA), sexa.FmtAngle(eqTo.Dec)) {
t.Fatal(i)
}
}
}
func ExampleProperMotion3D() {
// Example 21.d, p. 141.
eqFrom := &coord.Equatorial{
RA: unit.NewRA(6, 45, 8.871),
Dec: unit.NewAngle('-', 16, 42, 57.99),
}
mra := unit.HourAngleFromSec(-0.03847)
mdec := unit.AngleFromSec(-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,
sexa.FmtRA(eqTo.RA), sexa.FmtAngle(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{
unit.NewRA(2, 31, 48.704),
unit.NewAngle(' ', 89, 15, 50.72),
}
eqTo := &coord.Equatorial{}
mα := unit.HourAngleFromSec(0.19877)
mδ := unit.AngleFromSec(-0.0152)
for _, tc := range []struct {
α, δ string
jde float64
}{
{"1ʰ22ᵐ33.90ˢ", "88°46′26.18″", base.BesselianYearToJDE(1900)},
{"3ʰ48ᵐ16.43ˢ", "89°27′15.38″", base.JulianYearToJDE(2050)},
{"5ʰ53ᵐ29.17ˢ", "89°32′22.18″", base.JulianYearToJDE(2100)},
} {
epochTo := base.JDEToJulianYear(tc.jde)
precess.Position(eqFrom, eqTo, 2000.0, epochTo, mα, mδ)
αStr := fmt.Sprintf("%.2s", sexa.FmtRA(eqTo.RA))
δStr := fmt.Sprintf("%.2s", sexa.FmtAngle(eqTo.Dec))
if αStr != tc.α {
t.Fatal("got:", αStr, "want:", tc.α)
}
if δStr != tc.δ {
t.Fatal(δStr)
}
}
}
func ExampleApproxTimes() {
// Example 15.a, p. 103.
// Venus on 1988 March 20
p := globe.Coord{
Lon: unit.NewAngle(' ', 71, 5, 0),
Lat: unit.NewAngle(' ', 42, 20, 0),
}
Th0 := unit.NewTime(' ', 11, 50, 58.1)
α := unit.NewRA(2, 46, 55.51)
δ := unit.NewAngle(' ', 18, 26, 27.3)
h0 := rise.Stdh0Stellar
tRise, tTransit, tSet, err := rise.ApproxTimes(p, h0, Th0, α, δ)
if err != nil {
fmt.Println(err)
return
}
// Units for "m" values given near top of p. 104 are day fraction.
fmt.Printf("rising: %+.5f %02s\n", tRise/86400, sexa.FmtTime(tRise))
fmt.Printf("transit: %+.5f %02s\n", tTransit/86400, sexa.FmtTime(tTransit))
fmt.Printf("seting: %+.5f %02s\n", tSet/86400, sexa.FmtTime(tSet))
// Output:
// rising: +0.51816 12ʰ26ᵐ09ˢ
// transit: +0.81965 19ʰ40ᵐ17ˢ
// seting: +0.12113 02ʰ54ᵐ26ˢ
}
func ExampleAngleError() {
// Example p. 125.
rδ := unit.NewRA(5, 32, 0.40).Angle()
dδ := unit.NewAngle('-', 0, 17, 56.9)
rε := unit.NewRA(5, 36, 12.81).Angle()
dε := unit.NewAngle('-', 1, 12, 7.0)
rζ := unit.NewRA(5, 40, 45.52).Angle()
dζ := unit.NewAngle('-', 1, 56, 33.3)
n, ω := line.AngleError(rδ, dδ, rε, dε, rζ, dζ)
fmt.Printf("%m\n", sexa.FmtAngle(n))
fmt.Println(sexa.FmtAngle(ω))
// Output:
// 7°31′
// -5′24″
}
func ExampleError() {
// Example p. 124.
rδ := unit.NewRA(5, 32, 0.40).Angle()
dδ := unit.NewAngle('-', 0, 17, 56.9)
rε := unit.NewRA(5, 36, 12.81).Angle()
dε := unit.NewAngle('-', 1, 12, 7.0)
rζ := unit.NewRA(5, 40, 45.52).Angle()
dζ := unit.NewAngle('-', 1, 56, 33.3)
ω := line.Error(rζ, dζ, rδ, dδ, rε, dε)
e := sexa.FmtAngle(ω)
fmt.Printf("%.6j\n", e)
fmt.Printf("%.0f″\n", ω.Sec())
fmt.Println(e)
// Output:
// 0°.089876
// 324″
// 5′24″
}
func ExampleSmallest_b() {
// Exercise, p. 128.
r1 := unit.NewRA(9, 5, 41.44).Angle()
r2 := unit.NewRA(9, 9, 29).Angle()
r3 := unit.NewRA(8, 59, 47.14).Angle()
d1 := unit.NewAngle(' ', 18, 30, 30)
d2 := unit.NewAngle(' ', 17, 43, 56.7)
d3 := unit.NewAngle(' ', 17, 49, 36.8)
d, t := circle.Smallest(r1, d1, r2, d2, r3, d3)
fmt.Printf("Δ = %m\n", sexa.FmtAngle(d))
if t {
fmt.Println("type I")
} else {
fmt.Println("type II")
}
// Output:
// Δ = 2°19′
// type I
}
func ExampleSmallest_a() {
// Example 20.a, p. 128.
r1 := unit.NewRA(12, 41, 8.64).Angle()
r2 := unit.NewRA(12, 52, 5.21).Angle()
r3 := unit.NewRA(12, 39, 28.11).Angle()
d1 := unit.NewAngle('-', 5, 37, 54.2)
d2 := unit.NewAngle('-', 4, 22, 26.2)
d3 := unit.NewAngle('-', 1, 50, 3.7)
d, t := circle.Smallest(r1, d1, r2, d2, r3, d3)
fd := sexa.FmtAngle(d)
fmt.Printf("Δ = %.5j = %m\n", fd, fd)
if t {
fmt.Println("type I")
} else {
fmt.Println("type II")
}
// Output:
// Δ = 4°.26363 = 4°16′
// type II
}
func ExampleAberration() {
// Example 23.a, p. 152
α := unit.NewRA(2, 46, 11.331)
δ := unit.NewAngle(' ', 49, 20, 54.54)
jd := julian.CalendarGregorianToJD(2028, 11, 13.19)
Δα2, Δδ2 := apparent.Aberration(α, δ, jd)
fmt.Printf("%.3s %.3s\n",
sexa.FmtAngle(unit.Angle(Δα2)), // (Δα2 is in HourAngle)
sexa.FmtAngle(Δδ2))
// Output:
// 30.045″ 6.697″
}
func TestEqToGal(t *testing.T) {
g := new(coord.Galactic).EqToGal(&coord.Equatorial{
RA: unit.NewRA(17, 48, 59.74),
Dec: unit.NewAngle('-', 14, 43, 8.2),
})
if s := fmt.Sprintf("%.4f", g.Lon.Deg()); s != "12.9593" {
t.Fatal("lon:", s)
}
if s := fmt.Sprintf("%+.4f", g.Lat.Deg()); s != "+6.0463" {
t.Fatal("lat:", s)
}
}
func ExampleAberrationRonVondrak() {
// Example 23.b, p. 156
α := unit.NewRA(2, 44, 12.9747)
δ := unit.NewAngle(' ', 49, 13, 39.896)
jd := julian.CalendarGregorianToJD(2028, 11, 13.19)
Δα, Δδ := apparent.AberrationRonVondrak(α, δ, jd)
fmt.Printf("Δα = %+.9f radian\n", Δα)
fmt.Printf("Δδ = %+.9f radian\n", Δδ)
// Output:
// Δα = +0.000145252 radian
// Δδ = +0.000032723 radian
}
func ExampleNutation() {
// Example 23.a, p. 152
α := unit.NewRA(2, 46, 11.331)
δ := unit.NewAngle(' ', 49, 20, 54.54)
jd := julian.CalendarGregorianToJD(2028, 11, 13.19)
Δα1, Δδ1 := apparent.Nutation(α, δ, jd)
fmt.Printf("%.3s %.3s\n",
sexa.FmtAngle(unit.Angle(Δα1)), // (Δα1 is in HourAngle)
sexa.FmtAngle(Δδ1))
// Output:
// 15.843″ 6.217″
}
func ExampleEcliptic_EqToEcl() {
// Example 13.a, p. 95.
eq := &coord.Equatorial{
unit.NewRA(7, 45, 18.946),
unit.NewAngle(' ', 28, 1, 34.26),
}
obl := coord.NewObliquity(unit.AngleFromDeg(23.4392911))
ecl := new(coord.Ecliptic).EqToEcl(eq, obl)
fmt.Printf("λ = %.5j\n", sexa.FmtAngle(ecl.Lon))
fmt.Printf("β = %+.6j\n", sexa.FmtAngle(ecl.Lat))
// Output:
// λ = 113°.21563
// β = +6°.684170
}
func ExampleApproxAnnualPrecession() {
// Example 21.a, p. 132.
eq := &coord.Equatorial{
unit.NewRA(10, 8, 22.3),
unit.NewAngle(' ', 11, 58, 2),
}
epochFrom := 2000.0
epochTo := 1978.0
Δα, Δδ := precess.ApproxAnnualPrecession(eq, epochFrom, epochTo)
fmt.Printf("%+.3d\n", sexa.FmtHourAngle(Δα))
fmt.Printf("%+.2d\n", sexa.FmtAngle(Δδ))
// Output:
// +3ˢ.207
// -17″.71
}
func ExamplePositionRonVondrak() {
// Example 23.b, p. 156
jd := julian.CalendarGregorianToJD(2028, 11, 13.19)
eq := &coord.Equatorial{
RA: unit.NewRA(2, 44, 11.986),
Dec: unit.NewAngle(' ', 49, 13, 42.48),
}
apparent.PositionRonVondrak(eq, eq, base.JDEToJulianYear(jd),
unit.HourAngleFromSec(.03425),
unit.AngleFromSec(-.0895))
fmt.Printf("α = %0.3d\n", sexa.FmtRA(eq.RA))
fmt.Printf("δ = %0.2d\n", sexa.FmtAngle(eq.Dec))
// Output:
// α = 2ʰ46ᵐ14ˢ.392
// δ = 49°21′07″.45
}
func ExampleApproxPosition() {
// Example 21.a, p. 132.
eq := &coord.Equatorial{
unit.NewRA(10, 8, 22.3),
unit.NewAngle(' ', 11, 58, 2),
}
epochFrom := 2000.0
epochTo := 1978.0
mα := unit.HourAngleFromSec(-0.0169)
mδ := unit.AngleFromSec(0.006)
precess.ApproxPosition(eq, eq, epochFrom, epochTo, mα, mδ)
fmt.Printf("%0.1d\n", sexa.FmtRA(eq.RA))
fmt.Printf("%+0d\n", sexa.FmtAngle(eq.Dec))
// Output:
// 10ʰ07ᵐ12ˢ.1
// +12°04′32″
}
func TestEquatorial_EclToEq(t *testing.T) {
// repeat example above
eq0 := &coord.Equatorial{
unit.NewRA(7, 45, 18.946),
unit.NewAngle(' ', 28, 1, 34.26),
}
obl := coord.NewObliquity(23.4392911 * math.Pi / 180)
ecl := new(coord.Ecliptic).EqToEcl(eq0, obl)
// now reverse transform
eq := new(coord.Equatorial).EclToEq(ecl, obl)
if math.Abs((eq.RA-eq0.RA).Rad()/eq.RA.Rad()) > 1e-15 {
t.Fatal("RA:", eq0.RA, eq.RA)
}
if math.Abs((eq.Dec-eq0.Dec).Rad()/eq.Dec.Rad()) > 1e-15 {
t.Fatal("Dec:", eq0.Dec, eq.Dec)
}
}
func ExamplePosition() {
// Example 21.b, p. 135.
eq := &coord.Equatorial{
unit.NewRA(2, 44, 11.986),
unit.NewAngle(' ', 49, 13, 42.48),
}
epochFrom := 2000.0
jdTo := julian.CalendarGregorianToJD(2028, 11, 13.19)
epochTo := base.JDEToJulianYear(jdTo)
precess.Position(eq, eq, epochFrom, epochTo,
unit.HourAngleFromSec(0.03425),
unit.AngleFromSec(-0.0895))
fmt.Printf("%0.3d\n", sexa.FmtRA(eq.RA))
fmt.Printf("%+0.2d\n", sexa.FmtAngle(eq.Dec))
// Output:
// 2ʰ46ᵐ11ˢ.331
// +49°20′54″.54
}
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 ExampleStellar() {
// Exercise, p. 119.
day1 := 7.
day5 := 27.
r2 := []unit.Angle{
unit.NewRA(15, 3, 51.937).Angle(),
unit.NewRA(15, 9, 57.327).Angle(),
unit.NewRA(15, 15, 37.898).Angle(),
unit.NewRA(15, 20, 50.632).Angle(),
unit.NewRA(15, 25, 32.695).Angle(),
}
d2 := []unit.Angle{
unit.NewAngle('-', 8, 57, 34.51),
unit.NewAngle('-', 9, 9, 03.88),
unit.NewAngle('-', 9, 17, 37.94),
unit.NewAngle('-', 9, 23, 16.25),
unit.NewAngle('-', 9, 26, 01.01),
}
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 := unit.NewRA(15, 17, 0.421) + unit.RAFromSec(pmr*dc)
d1 := unit.NewAngle('-', 9, 22, 58.54) + unit.AngleFromSec(pmd*dc)
fmt.Printf("α′ = %.3d, δ′ = %.2d\n", sexa.FmtRA(r1), sexa.FmtAngle(d1))
day, dd, err := conjunction.Stellar(day1, day5, r1.Angle(), d1, r2, d2)
if err != nil {
fmt.Println(err)
return
}
fmt.Println(sexa.FmtAngle(dd))
dInt, dFrac := math.Modf(day)
fmt.Printf("1996 February %d at %s TD\n", int(dInt),
sexa.FmtTime(unit.TimeFromDay(dFrac)))
// Output:
// -3.87 years
// -0.0387 century
// α′ = 15ʰ17ᵐ0ˢ.446, δ′ = -9°22′58″.47
// 3′38″
// 1996 February 18 at 6ʰ36ᵐ55ˢ TD
}
// 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.
unit.NewHourAngle('-', 0, 0, 0.0169),
unit.NewAngle(' ', 0, 0, 0.006),
2000.0,
// eq coordinates from p. 132.
new(coord.Ecliptic).EqToEcl(&coord.Equatorial{
RA: unit.NewRA(10, 8, 22.3),
Dec: unit.NewAngle(' ', 11, 58, 2),
}, ε))
d := math.Abs((mλ - unit.AngleFromSec(-.2348)).Rad() / mλ.Rad())
if d*169 > 1 { // 169 = significant digits of given lon
t.Fatal("mλ")
}
d = math.Abs((mβ - unit.AngleFromSec(-.0813)).Rad() / mβ.Rad())
if d*6 > 1 { // 6 = significant digit of given lat
t.Fatal("mβ")
}
}
// First exercise, p. 110.
func TestSep(t *testing.T) {
r1 := unit.NewRA(4, 35, 55.2).Angle()
d1 := unit.NewAngle(' ', 16, 30, 33)
r2 := unit.NewRA(16, 29, 24).Angle()
d2 := unit.NewAngle('-', 26, 25, 55)
d := angle.Sep(r1, d1, r2, d2)
answer := unit.NewAngle(' ', 169, 58, 0)
if math.Abs((d - answer).Rad()) > 1e-4 {
t.Fatal(d, answer)
}
}
var (
r1 = []unit.Angle{
unit.NewRA(10, 29, 44.27).Angle(),
unit.NewRA(10, 36, 19.63).Angle(),
unit.NewRA(10, 43, 01.75).Angle(),
}
d1 = []unit.Angle{
unit.NewAngle(' ', 11, 02, 05.9),
unit.NewAngle(' ', 10, 29, 51.7),
unit.NewAngle(' ', 9, 55, 16.7),
}
r2 = []unit.Angle{
unit.NewRA(10, 33, 29.64).Angle(),
unit.NewRA(10, 33, 57.97).Angle(),
unit.NewRA(10, 34, 26.22).Angle(),
}
d2 = []unit.Angle{
unit.NewAngle(' ', 10, 40, 13.2),
func ExamplePlanetary() {
// Example 18.a, p. 117.
// Day of month is sufficient for a time scale.
day1 := 5.
day5 := 9.
// Text asks for Mercury-Venus conjunction, so r1, d1 is Venus ephemeris,
// r2, d2 is Mercury ephemeris.
// Venus
r1 := []unit.Angle{
unit.NewRA(10, 27, 27.175).Angle(),
unit.NewRA(10, 26, 32.410).Angle(),
unit.NewRA(10, 25, 29.042).Angle(),
unit.NewRA(10, 24, 17.191).Angle(),
unit.NewRA(10, 22, 57.024).Angle(),
}
d1 := []unit.Angle{
unit.NewAngle(' ', 4, 04, 41.83),
unit.NewAngle(' ', 3, 55, 54.66),
unit.NewAngle(' ', 3, 48, 03.51),
unit.NewAngle(' ', 3, 41, 10.25),
unit.NewAngle(' ', 3, 35, 16.61),
}
// Mercury
r2 := []unit.Angle{
unit.NewRA(10, 24, 30.125).Angle(),
unit.NewRA(10, 25, 00.342).Angle(),
unit.NewRA(10, 25, 12.515).Angle(),
unit.NewRA(10, 25, 06.235).Angle(),
unit.NewRA(10, 24, 41.185).Angle(),
}
d2 := []unit.Angle{
unit.NewAngle(' ', 6, 26, 32.05),
unit.NewAngle(' ', 6, 10, 57.72),
unit.NewAngle(' ', 5, 57, 33.08),
unit.NewAngle(' ', 5, 46, 27.07),
unit.NewAngle(' ', 5, 37, 48.45),
}
// compute conjunction
day, dd, err := conjunction.Planetary(day1, day5, r1, d1, r2, d2)
if err != nil {
fmt.Println(err)
return
}
// time of conjunction
fmt.Printf("1991 August %.5f\n", day)
// more useful clock format
dInt, dFrac := math.Modf(day)
fmt.Printf("1991 August %d at %s TD\n", int(dInt),
sexa.FmtTime(unit.TimeFromDay(dFrac)))
// deltat func needs jd
jd := julian.CalendarGregorianToJD(1991, 8, day)
// compute UT = TD - ΔT, and separate back into calendar components.
// (we could use our known calendar components, but this illustrates
// the more general technique that would allow for rollovers.)
y, m, d := julian.JDToCalendar(jd - deltat.Interp10A(jd).Day())
// format as before
dInt, dFrac = math.Modf(d)
fmt.Printf("%d %s %d at %s UT\n", y, time.Month(m), int(dInt),
sexa.FmtTime(unit.TimeFromDay(dFrac)))
// Δδ
fmt.Printf("Δδ = %s\n", sexa.FmtAngle(dd))
// Output:
// 1991 August 7.23797
// 1991 August 7 at 5ʰ42ᵐ41ˢ TD
// 1991 August 7 at 5ʰ41ᵐ43ˢ UT
// Δδ = 2°8′22″
}
sH, cH := math.Sincos(H)
sφ, cφ := φ.Sincos()
sδ, cδ := ψ.Sincos()
A = unit.Angle(math.Atan2(sH, cH*sφ-(sδ/cδ)*cφ)) // (13.5) p. 93
h = unit.Angle(math.Asin(sφ*sδ + cφ*cδ*cH)) // (13.6) p. 93
return
}
// Galactic coordinates are referenced to the plane of the Milky Way.
type Galactic struct {
Lat unit.Angle // Latitude (b) in radians
Lon unit.Angle // Longitude (l) in radians
}
var galacticNorth = &Equatorial{
RA: unit.NewRA(12, 49, 0),
Dec: unit.AngleFromDeg(27.4),
}
var galacticLon0 = unit.AngleFromDeg(123)
// EqToGal converts equatorial coordinates to galactic coordinates.
//
// Equatorial coordinates must be referred to the standard equinox of B1950.0.
// For conversion to B1950, see package precess and utility functions in
// package "unit".
func (g *Galactic) EqToGal(eq *Equatorial) *Galactic {
sdα, cdα := (galacticNorth.RA - eq.RA).Sincos()
sgδ, cgδ := galacticNorth.Dec.Sincos()
sδ, cδ := eq.Dec.Sincos()
// (13.7) p. 94