def icrsFromFK4(fk4P, fk4V, fk4Epoch):
"""
Converts mean catalog FK4 equatorial coordinates to ICRS coordinates.
Uses the approximation that ICRS is FK5 J2000.
Inputs:
- fk4Epoch TDB date of fk4 coordinates (Besselian epoch)
note: TDT will always do and UTC is usually adequate
- fk4P(3) mean catalog fk4 cartesian position (au)
- fk4V(3) mean FK4 cartesian velocity (au per Besselian year),
i.e. proper motion and radial velocity
Returns a tuple containg:
- icrsP(3) mean ICRS cartesian position (au), a numpy.array
- icrsV(3) mean ICRS cartesian velocity (au/year), a numpy.array
Error Conditions:
none
Warnings:
The FK4 date is in Besselian years.
The FK4 proper motion is in au/Besselian year,
whereas the FK5 J2000 proper motion is in au/Julian year.
The FK4 system refers to a specific set of precession constants;
not all Besselian-epoch data was precessed using these constants
(especially data for epochs before B1950).
References:
P.T. Wallace's routine FK425
"""
fk4P = numpy.asarray(fk4P, dtype=float)
fk4V = numpy.asarray(fk4V, dtype=float)
# compute new precession constants
# note: ETrms and PreBn both want Besselian date
eTerms = llv.etrms(fk4Epoch)
precMat = llv.prebn(fk4Epoch, 1950.0)
# subtract e-terms from position. As a minor approximation,
# we don't bother to subtract variation in e-terms from proper motion.
magP = RO.MathUtil.vecMag(fk4P)
meanFK4P = fk4P - (eTerms * magP)
# correct position for velocity (PM and rad. vel.) to B1950
tempP = meanFK4P + fk4V * (1950.0 - fk4Epoch)
# precess position and velocity to B1950
b1950P = numpy.dot(precMat, tempP)
b1950V = numpy.dot(precMat, fk4V)
# convert position and velocity to ICRS (actually FK5 J2000.0)
icrsP = numpy.dot(_MatPP, b1950P) + numpy.dot(_MatPV, b1950V)
icrsV = numpy.dot(_MatVP, b1950P) + numpy.dot(_MatVV, b1950V)
return (icrsP, icrsV)
def icrsFromFK4 (fk4P, fk4V, fk4Epoch):
"""
Converts mean catalog FK4 equatorial coordinates to ICRS coordinates.
Uses the approximation that ICRS is FK5 J2000.
Inputs:
- fk4Epoch TDB date of fk4 coordinates (Besselian epoch)
note: TDT will always do and UTC is usually adequate
- fk4P(3) mean catalog fk4 cartesian position (au)
- fk4V(3) mean FK4 cartesian velocity (au per Besselian year),
i.e. proper motion and radial velocity
Returns a tuple containg:
- icrsP(3) mean ICRS cartesian position (au), a numpy.array
- icrsV(3) mean ICRS cartesian velocity (au/year), a numpy.array
Error Conditions:
none
Warnings:
The FK4 date is in Besselian years.
The FK4 proper motion is in au/Besselian year,
whereas the FK5 J2000 proper motion is in au/Julian year.
The FK4 system refers to a specific set of precession constants;
not all Besselian-epoch data was precessed using these constants
(especially data for epochs before B1950).
References:
P.T. Wallace's routine FK425
"""
fk4P = numpy.asarray(fk4P, dtype = float)
fk4V = numpy.asarray(fk4V, dtype = float)
# compute new precession constants
# note: ETrms and PreBn both want Besselian date
eTerms = llv.etrms (fk4Epoch)
precMat = llv.prebn (fk4Epoch, 1950.0)
# subtract e-terms from position. As a minor approximation,
# we don't bother to subtract variation in e-terms from proper motion.
magP = RO.MathUtil.vecMag(fk4P)
meanFK4P = fk4P - (eTerms * magP)
# correct position for velocity (PM and rad. vel.) to B1950
tempP = meanFK4P + fk4V * (1950.0 - fk4Epoch)
# precess position and velocity to B1950
b1950P = numpy.dot(precMat, tempP)
b1950V = numpy.dot(precMat, fk4V)
# convert position and velocity to ICRS (actually FK5 J2000.0)
icrsP = numpy.dot(_MatPP, b1950P) + numpy.dot(_MatPV, b1950V)
icrsV = numpy.dot(_MatVP, b1950P) + numpy.dot(_MatVV, b1950V)
return (icrsP, icrsV)
def fk4FromICRS(icrsP, icrsV, fk4Epoch):
"""
Converts mean fk4 equatorial coordinates to ICRS coordinates.
Uses the approximation that ICRS is FK5 J2000.
Inputs:
- icrsP(3) ICRS cartesian position (au)
- icrsV(3) ICRS cartesian velocity (au per Julian year),
i.e. proper motion and radial velocity
- fk4Epoch date of fk4 coordinates (Besselian epoch)
note: tdt will always do and utc is usually adequate
Returns a tuple containing:
- fk4P(3) FK4 cartesian position (au), a numpy.array
- fk4V(3) FK4 cartesian velocity (au/Besselian year), a numpy.array
Error Conditions:
none
Warnings:
The FK4 system refers to a specific set of precession constants,
and not all Besselian-epoch data was precessed using these constants
(especially data for epochs before B1950).
Details:
One approximation is used:
- Velocity is not corrected for time-variation in the e-terms.
This introduces errors on the order of a milliarcsecond per century.
References:
P.T. Wallace's FK524 routine
"""
eTerms = llv.etrms(fk4Epoch)
precMat = llv.prebn(1950.0, fk4Epoch)
# convert position and velocity from J2000.0 to B1950
b1950P = numpy.dot(_MatPP, icrsP) + numpy.dot(_MatPV, icrsV)
b1950V = numpy.dot(_MatVP, icrsP) + numpy.dot(_MatVV, icrsV)
# correct position for velocity (pm and rad. vel.) to fk4Epoch
tempP = b1950P + b1950V * (fk4Epoch - 1950.0)
# precess position and velocity to B1950
meanFK4P = numpy.dot(precMat, tempP)
fk4V = numpy.dot(precMat, b1950V)
# add e-terms to mean position, iterating thrice (should be plenty!)
# to get mean catalog place. As a minor approximation,
# we don't bother to add variation in e-terms to the velocity.
fk4P = meanFK4P.copy()
for iterNum in range(3):
magP = RO.MathUtil.vecMag(fk4P)
fk4P = meanFK4P + eTerms * magP
return (fk4P, fk4V)
def fk4FromICRS(icrsP, icrsV, fk4Epoch):
"""
Converts mean fk4 equatorial coordinates to ICRS coordinates.
Uses the approximation that ICRS is FK5 J2000.
Inputs:
- icrsP(3) ICRS cartesian position (au)
- icrsV(3) ICRS cartesian velocity (au per Julian year),
i.e. proper motion and radial velocity
- fk4Epoch date of fk4 coordinates (Besselian epoch)
note: tdt will always do and utc is usually adequate
Returns a tuple containing:
- fk4P(3) FK4 cartesian position (au), a numpy.array
- fk4V(3) FK4 cartesian velocity (au/Besselian year), a numpy.array
Error Conditions:
none
Warnings:
The FK4 system refers to a specific set of precession constants,
and not all Besselian-epoch data was precessed using these constants
(especially data for epochs before B1950).
Details:
One approximation is used:
- Velocity is not corrected for time-variation in the e-terms.
This introduces errors on the order of a milliarcsecond per century.
References:
P.T. Wallace's FK524 routine
"""
eTerms = llv.etrms (fk4Epoch)
precMat = llv.prebn (1950.0, fk4Epoch)
# convert position and velocity from J2000.0 to B1950
b1950P = numpy.dot(_MatPP, icrsP) + numpy.dot(_MatPV, icrsV)
b1950V = numpy.dot(_MatVP, icrsP) + numpy.dot(_MatVV, icrsV)
# correct position for velocity (pm and rad. vel.) to fk4Epoch
tempP = b1950P + b1950V * (fk4Epoch - 1950.0)
# precess position and velocity to B1950
meanFK4P = numpy.dot (precMat, tempP)
fk4V = numpy.dot (precMat, b1950V)
# add e-terms to mean position, iterating thrice (should be plenty!)
# to get mean catalog place. As a minor approximation,
# we don't bother to add variation in e-terms to the velocity.
fk4P = meanFK4P.copy()
for iterNum in range(3):
magP = RO.MathUtil.vecMag(fk4P)
fk4P = meanFK4P + eTerms * magP
return (fk4P, fk4V)
def icrsFromFixedFK4(fk4P, fk4Date):
"""
Converts mean catalog fk4 coordinates to ICRS for a fixed star.
Uses the approximation that ICRS = FK5 J2000.
Inputs:
- fk4Date TDB date of fk4 coordinates (Besselian epoch)
note: TDT will always do and UTC is usually adequate
- fk4P(3) mean catalog fk4 cartesian position (au)
Returns:
- icrsP(3) ICRS cartesian position (au), a numpy.array
Error Conditions:
none
Warnings:
The FK4 date is in Besselian years.
The star is assumed fixed on the celestial sphere. That is a bit
different than assuming it has zero proper motion because
FK4 system has slight ficticious proper motion.
The FK4 system refers to a specific set of precession constants;
not all Besselian-epoch data was precessed using these constants
(especially data for epochs before B1950).
References:
P.T. Wallace's routine FK45Z
"""
# compute new precession constants
# note: ETrms and PreBn both want Besselian date
eTerms = llv.etrms (fk4Date)
precMat = llv.prebn (fk4Date, 1950.0)
# subtract e-terms from position. As a minor approximation,
# we don't bother to subtract variation in e-terms from proper motion.
magP = RO.MathUtil.vecMag(fk4P)
meanFK4P = fk4P - (eTerms * magP)
# precess position to B1950, assuming zero fk4 pm
# (we'll correct for the fictious fk4 pm later)
b1950P = numpy.dot(precMat, meanFK4P)
# convert position to ICRS (actually FK5 J2000)
# but still containing fk4 fictitious pm;
# compute fictitious pm.
tempP = numpy.dot(_MatPP, b1950P)
ficV = numpy.dot(_MatVP, b1950P)
# correct ICRS position for fk4 fictitious pm
# (subtract over period fk4Date to J2000)
period = 2000.0 - Tm.epJFromMJD (llv.epb2d (fk4Date))
return tempP - ficV * period
