// Times computes UT rise, transit and set times for a celestial object on
// a day of interest.
//
// The function argurments do not actually include the day, but do include
// a number of values computed from the day.
//
// p is geographic coordinates of observer.
// ΔT is delta T.
// h0 is "standard altitude" of the body.
// Th0 is apparent sidereal time at 0h UT at Greenwich.
// α3, δ3 are slices of three right ascensions and declinations.
//
// h0 unit is radians.
//
// Th0 must be the time on the day of interest, in seconds.
// See sidereal.Apparent0UT.
//
// α3, δ3 must be values at 0h dynamical time for the day before, the day of,
// and the day after the day of interest. Units are radians.
//
// Result units are seconds of day and are in the range [0,86400).
func Times(p globe.Coord, ΔT unit.Time, h0 unit.Angle, Th0 unit.Time, α3 []unit.RA, δ3 []unit.Angle) (tRise, tTransit, tSet unit.Time, err error) {
tRise, tTransit, tSet, err = ApproxTimes(p, h0, Th0, α3[1], δ3[1])
if err != nil {
return
}
αf := make([]float64, 3)
for i, α := range α3 {
αf[i] = α.Rad()
}
δf := make([]float64, 3)
for i, δ := range δ3 {
δf[i] = δ.Rad()
}
var d3α, d3δ *interp.Len3
d3α, err = interp.NewLen3(-86400, 86400, αf)
if err != nil {
return
}
d3δ, err = interp.NewLen3(-86400, 86400, δf)
if err != nil {
return
}
// adjust tTransit
{
th0 := (Th0 + tTransit.Mul(360.985647/360)).Mod1()
α := d3α.InterpolateX((tTransit + ΔT).Sec())
// local hour angle as Time
H := th0 - unit.TimeFromRad(p.Lon.Rad()+α)
tTransit -= H
}
// adjust tRise, tSet
sLat, cLat := p.Lat.Sincos()
adjustRS := func(m unit.Time) (unit.Time, error) {
th0 := (Th0 + m.Mul(360.985647/360)).Mod1()
ut := (m + ΔT).Sec()
α := d3α.InterpolateX(ut)
δ := d3δ.InterpolateX(ut)
Hrad := th0.Rad() - p.Lon.Rad() - α
sδ, cδ := math.Sincos(δ)
sH, cH := math.Sincos(Hrad)
h := math.Asin(sLat*sδ + cLat*cδ*cH)
md := (unit.TimeFromRad(h) - h0.Time()).Div(cδ * cLat * sH)
return m + md, nil
}
tRise, err = adjustRS(tRise)
if err != nil {
return
}
tSet, err = adjustRS(tSet)
return
}
// ApproxTimes computes approximate UT rise, transit and set times for
// a celestial object on a day of interest.
//
// The function argurments do not actually include the day, but do include
// values computed from the day.
//
// p is geographic coordinates of observer.
// h0 is "standard altitude" of the body.
// Th0 is apparent sidereal time at 0h UT at Greenwich.
// α, δ are right ascension and declination of the body.
//
// Th0 must be the time on the day of interest.
// See sidereal.Apparent0UT.
//
// α, δ must be values at 0h dynamical time for the day of interest.
func ApproxTimes(p globe.Coord, h0 unit.Angle, Th0 unit.Time, α unit.RA, δ unit.Angle) (tRise, tTransit, tSet unit.Time, err error) {
// approximate local hour angle
sLat, cLat := p.Lat.Sincos()
sδ1, cδ1 := δ.Sincos()
cH0 := (h0.Sin() - sLat*sδ1) / (cLat * cδ1) // (15.1) p. 102
if cH0 < -1 || cH0 > 1 {
err = ErrorCircumpolar
return
}
H0 := unit.TimeFromRad(math.Acos(cH0))
// approximate transit, rise, set times.
// (15.2) p. 102.
mt := unit.TimeFromRad(α.Rad()+p.Lon.Rad()) - Th0
tTransit = mt.Mod1()
tRise = (mt - H0).Mod1()
tSet = (mt + H0).Mod1()
return
}