conjunction

Documentation

Overview

Conjunction: Chapter 18: Planetary Conjunctions.

Index

• func Planetary(t1, t5 float64, r1, d1, r2, d2 []unit.Angle) (t float64, Δd unit.Angle, err error)
• func Stellar(t1, t5 float64, r1, d1 unit.Angle, r2, d2 []unit.Angle) (t float64, Δd unit.Angle, err error)

Examples

• Planetary
• Stellar

Functions

func Planetary

func Planetary(t1, t5 float64, r1, d1, r2, d2 []unit.Angle) (t float64, Δd unit.Angle, err error)

Planetary computes a conjunction between two moving objects, such as planets.

Conjunction is found with interpolation against length 5 ephemerides.

T1, t5 are times of first and last rows of ephemerides. The scale is arbitrary.

R1, d1 is the ephemeris of the first object. The columns may be celestial coordinates in right ascension and declination or ecliptic coordinates in longitude and latitude.

R2, d2 is the ephemeris of the second object, in the same frame as the first.

Return value t is time of conjunction in the scale of t1, t5. Δd is the amount that object 2 was "above" object 1 at the time of conjunction.

Example

// 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″

func Stellar

func Stellar(t1, t5 float64, r1, d1 unit.Angle, r2, d2 []unit.Angle) (t float64, Δd unit.Angle, err error)

Stellar computes a conjunction between a moving and non-moving object.

Arguments and return values same as with Planetary, except the non-moving object is r1, d1. The ephemeris of the moving object is r2, d2.

Example

// 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