// PositionRonVondrak computes the apparent position of an object using
// the Ron-Vondrák expression for aberration.
//
// Position is computed for equatorial coordinates in eqFrom, considering
// proper motion, aberration, precession, and nutation. Result is in
// eqTo. EqFrom and eqTo must be non-nil, but may point to the same struct.
//
// Note the Ron-Vondrák expression is only valid for the epoch J2000.
// EqFrom must be coordinates at epoch J2000.
func PositionRonVondrak(eqFrom, eqTo *coord.Equatorial, epochTo float64, mα sexa.HourAngle, mδ sexa.Angle) *coord.Equatorial {
t := epochTo - 2000
eqTo.RA = eqFrom.RA + mα.Rad()*t
eqTo.Dec = eqFrom.Dec + mδ.Rad()*t
jd := base.JulianYearToJDE(epochTo)
Δα, Δδ := AberrationRonVondrak(eqTo.RA, eqTo.Dec, jd)
eqTo.RA += Δα
eqTo.Dec += Δδ
precess.Position(eqTo, eqTo, 2000, epochTo, 0, 0)
Δα1, Δδ1 := Nutation(eqTo.RA, eqTo.Dec, jd)
eqTo.RA += Δα1
eqTo.Dec += Δδ1
return eqTo
}
// PositionRonVondrak computes the apparent position of an object using
// the Ron-Vondrák expression for aberration.
//
// Position is computed for equatorial coordinates in eqFrom, considering
// proper motion, aberration, precession, and nutation. Result is in
// eqTo. EqFrom and eqTo must be non-nil, but may point to the same struct.
//
// Note the Ron-Vondrák expression is only valid for the epoch J2000.
// EqFrom must be coordinates at epoch J2000.
func PositionRonVondrak(eqFrom, eqTo *coord.Equatorial, epochTo float64, mα unit.HourAngle, mδ unit.Angle) *coord.Equatorial {
t := epochTo - 2000
eqTo.RA = eqFrom.RA.Add(mα.Mul(t))
eqTo.Dec = eqFrom.Dec + mδ.Mul(t)
jd := base.JulianYearToJDE(epochTo)
Δα, Δδ := AberrationRonVondrak(eqTo.RA, eqTo.Dec, jd)
eqTo.RA = eqTo.RA.Add(Δα)
eqTo.Dec += Δδ
precess.Position(eqTo, eqTo, 2000, epochTo, 0, 0)
Δα1, Δδ1 := Nutation(eqTo.RA, eqTo.Dec, jd)
eqTo.RA = eqTo.RA.Add(Δα1)
eqTo.Dec += Δδ1
return eqTo
}
// Precess precesses coordinates eqFrom, leaving result in eqTo.
//
// The same struct may be used for eqFrom and eqTo.
// EqTo is returned for convenience.
func (p *Precessor) Precess(eqFrom, eqTo *coord.Equatorial) *coord.Equatorial {
// (21.4) p. 134
sδ, cδ := math.Sincos(eqFrom.Dec)
sαζ, cαζ := math.Sincos(eqFrom.RA + p.ζ)
A := cδ * sαζ
B := p.cθ*cδ*cαζ - p.sθ*sδ
C := p.sθ*cδ*cαζ + p.cθ*sδ
eqTo.RA = math.Atan2(A, B) + p.z
if C < base.CosSmallAngle {
eqTo.Dec = math.Asin(C)
} else {
eqTo.Dec = math.Acos(math.Hypot(A, B)) // near pole
}
return eqTo
}
// ApproxPosition uses ApproxAnnualPrecession to compute a simple and quick
// precession while still considering proper motion.
//
// Both eqFrom and eqTo must be non-nil, although they may point to the same
// struct. EqTo is returned for convenience.
func ApproxPosition(eqFrom, eqTo *coord.Equatorial, epochFrom, epochTo float64, mα base.HourAngle, mδ base.Angle) *coord.Equatorial {
Δα, Δδ := ApproxAnnualPrecession(eqFrom, epochFrom, epochTo)
dy := epochTo - epochFrom
eqTo.RA = eqFrom.RA + (Δα+mα).Rad()*dy
eqTo.Dec = eqFrom.Dec + (Δδ+mδ).Rad()*dy
return eqTo
}
// Position precesses equatorial coordinates from one epoch to another,
// including proper motions.
//
// If proper motions are not to be considered or are not applicable, pass 0, 0
// for mα, mδ
//
// Both eqFrom and eqTo must be non-nil, although they may point to the same
// struct. EqTo is returned for convenience.
func Position(eqFrom, eqTo *coord.Equatorial, epochFrom, epochTo float64, mα base.HourAngle, mδ base.Angle) *coord.Equatorial {
p := NewPrecessor(epochFrom, epochTo)
t := epochTo - epochFrom
eqTo.RA = eqFrom.RA + mα.Rad()*t
eqTo.Dec = eqFrom.Dec + mδ.Rad()*t
return p.Precess(eqTo, eqTo)
}
// ApproxPosition uses ApproxAnnualPrecession to compute a simple and quick
// precession while still considering proper motion.
//
// Both eqFrom and eqTo must be non-nil, although they may point to the same
// struct. EqTo is returned for convenience.
func ApproxPosition(eqFrom, eqTo *coord.Equatorial, epochFrom, epochTo float64, mα unit.HourAngle, mδ unit.Angle) *coord.Equatorial {
Δα, Δδ := ApproxAnnualPrecession(eqFrom, epochFrom, epochTo)
dy := epochTo - epochFrom
eqTo.RA = eqFrom.RA.Add((Δα + mα).Mul(dy))
eqTo.Dec = eqFrom.Dec + (Δδ + mδ).Mul(dy)
return eqTo
}
// Position precesses equatorial coordinates from one epoch to another,
// including proper motions.
//
// If proper motions are not to be considered or are not applicable, pass 0, 0
// for mα, mδ
//
// Both eqFrom and eqTo must be non-nil, although they may point to the same
// struct. EqTo is returned for convenience.
func Position(eqFrom, eqTo *coord.Equatorial, epochFrom, epochTo float64, mα unit.HourAngle, mδ unit.Angle) *coord.Equatorial {
p := NewPrecessor(epochFrom, epochTo)
t := epochTo - epochFrom
eqTo.RA = unit.RAFromRad(eqFrom.RA.Rad() + mα.Rad()*t)
eqTo.Dec = eqFrom.Dec + mδ*unit.Angle(t)
return p.Precess(eqTo, eqTo)
}
// Position computes the apparent position of an object.
//
// Position is computed for equatorial coordinates in eqFrom, considering
// proper motion, precession, nutation, and aberration. Result is in
// eqTo. EqFrom and eqTo must be non-nil, but may point to the same struct.
func Position(eqFrom, eqTo *coord.Equatorial, epochFrom, epochTo float64, mα sexa.HourAngle, mδ sexa.Angle) *coord.Equatorial {
precess.Position(eqFrom, eqTo, epochFrom, epochTo, mα, mδ)
jd := base.JulianYearToJDE(epochTo)
Δα1, Δδ1 := Nutation(eqTo.RA, eqTo.Dec, jd)
Δα2, Δδ2 := Aberration(eqTo.RA, eqTo.Dec, jd)
eqTo.RA += Δα1 + Δα2
eqTo.Dec += Δδ1 + Δδ2
return eqTo
}
// ProperMotion3D takes the 3D equatorial coordinates of an object
// at one epoch and computes its coordinates at a new epoch, considering
// proper motion and radial velocity.
//
// Radial distance (r) must be in parsecs, radial velocitiy (mr) in
// parsecs per year.
//
// Both eqFrom and eqTo must be non-nil, although they may point to the same
// struct. EqTo is returned for convenience.
func ProperMotion3D(eqFrom, eqTo *coord.Equatorial, epochFrom, epochTo, r, mr float64, mα base.HourAngle, mδ base.Angle) *coord.Equatorial {
sα, cα := math.Sincos(eqFrom.RA)
sδ, cδ := math.Sincos(eqFrom.Dec)
x := r * cδ * cα
y := r * cδ * sα
z := r * sδ
mrr := mr / r
zmδ := z * mδ.Rad()
mx := x*mrr - zmδ*cα - y*mα.Rad()
my := y*mrr - zmδ*sα + x*mα.Rad()
mz := z*mrr + r*mδ.Rad()*cδ
t := epochTo - epochFrom
xp := x + t*mx
yp := y + t*my
zp := z + t*mz
eqTo.RA = math.Atan2(yp, xp)
eqTo.Dec = math.Atan2(zp, math.Hypot(xp, yp))
return eqTo
}