def __precess(self, ra0, dec0, equinox1, equinox2, doprint=False, fk4=False, radian=False):
scal = True
if isinstance(ra0, ndarray):
ra = ra0.copy()
dec = dec0.copy()
scal = False
else:
ra = array([ra0])
dec = array([dec0])
npts = ra.size
if not radian:
ra_rad = deg2rad(ra) # Convert to double precision if not already
dec_rad = deg2rad(dec)
else:
ra_rad = ra
dec_rad = dec
a = cos(dec_rad)
x = zeros((npts, 3))
x[:, 0] = a * np.cos(ra_rad)
x[:, 1] = a * np.sin(ra_rad)
x[:, 2] = np.sin(dec_rad)
# Use PREMAT function to get precession matrix from Equinox1 to Equinox2
r = premat(equinox1, equinox2, fk4=fk4)
x2 = transpose(dot(transpose(r), transpose(x))) # rotate to get
# output direction cosines
ra_rad = zeros(npts) + arctan2(x2[:, 1], x2[:, 0])
dec_rad = zeros(npts) + arcsin(x2[:, 2])
if not radian:
ra = rad2deg(ra_rad)
ra = ra + (ra < 0.) * 360.e0 # RA between 0 and 360 degrees
dec = rad2deg(dec_rad)
else:
ra = ra_rad
dec = dec_rad
ra = ra + (ra < 0.) * 2.0e0 * pi
if doprint:
print 'Equinox (%.2f): %f,%f' % (equinox2, ra, dec)
if scal:
ra, dec = ra[0], dec[0]
return ra, dec
def precess(ra0, dec0, equinox1, equinox2, doprint=False, fk4=False, radian=False):
"""
NAME:
PRECESS
PURPOSE:
Precess coordinates from EQUINOX1 to EQUINOX2.
EXPLANATION:
For interactive display, one can use the procedure ASTRO which calls
PRECESS or use the /PRINT keyword. The default (RA,DEC) system is
FK5 based on epoch J2000.0 but FK4 based on B1950.0 is available via
the /FK4 keyword.
Use BPRECESS and JPRECESS to convert between FK4 and FK5 systems
CALLING SEQUENCE:
PRECESS, ra, dec, [ equinox1, equinox2, /PRINT, /FK4, /RADIAN ]
INPUT - OUTPUT:
RA - Input right ascension (scalar or vector) in DEGREES, unless the
/RADIAN keyword is set
DEC - Input declination in DEGREES (scalar or vector), unless the
/RADIAN keyword is set
The input RA and DEC are modified by PRECESS to give the
values after precession.
OPTIONAL INPUTS:
EQUINOX1 - Original equinox of coordinates, numeric scalar. If
omitted, then PRECESS will query for EQUINOX1 and EQUINOX2.
EQUINOX2 - Equinox of precessed coordinates.
OPTIONAL INPUT KEYWORDS:
/PRINT - If this keyword is set and non-zero, then the precessed
coordinates are displayed at the terminal. Cannot be used
with the /RADIAN keyword
/FK4 - If this keyword is set and non-zero, the FK4 (B1950.0) system
will be used otherwise FK5 (J2000.0) will be used instead.
/RADIAN - If this keyword is set and non-zero, then the input and
output RA and DEC vectors are in radians rather than degrees
RESTRICTIONS:
Accuracy of precession decreases for declination values near 90
degrees. PRECESS should not be used more than 2.5 centuries from
2000 on the FK5 system (1950.0 on the FK4 system).
EXAMPLES:
(1) The Pole Star has J2000.0 coordinates (2h, 31m, 46.3s,
89d 15' 50.6"); compute its coordinates at J1985.0
IDL> precess, ten(2,31,46.3)*15, ten(89,15,50.6), 2000, 1985, /PRINT
====> 2h 16m 22.73s, 89d 11' 47.3"
(2) Precess the B1950 coordinates of Eps Ind (RA = 21h 59m,33.053s,
DEC = (-56d, 59', 33.053") to equinox B1975.
IDL> ra = ten(21, 59, 33.053)*15
IDL> dec = ten(-56, 59, 33.053)
IDL> precess, ra, dec ,1950, 1975, /fk4
PROCEDURE:
Algorithm from Computational Spherical Astronomy by Taff (1983),
p. 24. (FK4). FK5 constants from "Astronomical Almanac Explanatory
Supplement 1992, page 104 Table 3.211.1.
PROCEDURE CALLED:
Function PREMAT - computes precession matrix
REVISION HISTORY
Written, Wayne Landsman, STI Corporation August 1986
Correct negative output RA values February 1989
Added /PRINT keyword W. Landsman November, 1991
Provided FK5 (J2000.0) I. Freedman January 1994
Precession Matrix computation now in PREMAT W. Landsman June 1994
Added /RADIAN keyword W. Landsman June 1997
Converted to IDL V5.0 W. Landsman September 1997
Correct negative output RA values when /RADIAN used March 1999
Work for arrays, not just vectors W. Landsman September 2003
Convert to Python Sergey Koposov July 2010
"""
scal = True
if isinstance(ra0, ndarray):
ra = ra0.copy()
dec = dec0.copy()
scal = False
else:
ra=array([ra0])
dec=array([dec0])
npts = ra.size
if not radian:
ra_rad = deg2rad(ra) #Convert to double precision if not already
dec_rad = deg2rad(dec)
else:
ra_rad = ra
dec_rad = dec
a = cos(dec_rad)
x = zeros((npts, 3))
x[:,0] = a * cos(ra_rad)
x[:,1] = a * sin(ra_rad)
x[:,2] = sin(dec_rad)
# Use PREMAT function to get precession matrix from Equinox1 to Equinox2
r = premat(equinox1, equinox2, fk4=fk4)
x2 = transpose(dot(transpose(r), transpose(x))) #rotate to get output direction cosines
ra_rad = zeros(npts) + arctan2(x2[:,1], x2[:,0])
dec_rad = zeros(npts) + arcsin(x2[:,2])
if not radian:
ra = rad2deg(ra_rad)
ra = ra + (ra < 0.) * 360.e0 #RA between 0 and 360 degrees
dec = rad2deg(dec_rad)
else:
ra = ra_rad
dec = dec_rad
ra = ra + (ra < 0.) * 2.0e0 * pi
if doprint:
print( 'Equinox (%.2f): %f,%f' % (equinox2, ra, dec))
if scal:
ra, dec = ra[0], dec[0]
return ra, dec
def baryvel(dje, deq=0):
"""
NAME:
BARYVEL
PURPOSE:
Calculates heliocentric and barycentric velocity components of Earth.
EXPLANATION:
BARYVEL takes into account the Earth-Moon motion, and is useful for
radial velocity work to an accuracy of ~1 m/s.
CALLING SEQUENCE:
dvel_hel, dvel_bary = baryvel(dje, deq)
INPUTS:
DJE - (scalar) Julian ephemeris date.
DEQ - (scalar) epoch of mean equinox of dvelh and dvelb. If deq=0
then deq is assumed to be equal to dje.
OUTPUTS:
DVELH: (vector(3)) heliocentric velocity component. in km/s
DVELB: (vector(3)) barycentric velocity component. in km/s
The 3-vectors DVELH and DVELB are given in a right-handed coordinate
system with the +X axis toward the Vernal Equinox, and +Z axis
toward the celestial pole.
OPTIONAL KEYWORD SET:
JPL - if /JPL set, then BARYVEL will call the procedure JPLEPHINTERP
to compute the Earth velocity using the full JPL ephemeris.
The JPL ephemeris FITS file JPLEPH.405 must exist in either the
current directory, or in the directory specified by the
environment variable ASTRO_DATA. Alternatively, the JPL keyword
can be set to the full path and name of the ephemeris file.
A copy of the JPL ephemeris FITS file is available in
http://idlastro.gsfc.nasa.gov/ftp/data/
PROCEDURES CALLED:
Function PREMAT() -- computes precession matrix
JPLEPHREAD, JPLEPHINTERP, TDB2TDT - if /JPL keyword is set
NOTES:
Algorithm taken from FORTRAN program of Stumpff (1980, A&A Suppl, 41,1)
Stumpf claimed an accuracy of 42 cm/s for the velocity. A
comparison with the JPL FORTRAN planetary ephemeris program PLEPH
found agreement to within about 65 cm/s between 1986 and 1994
If /JPL is set (using JPLEPH.405 ephemeris file) then velocities are
given in the ICRS system; otherwise in the FK4 system.
EXAMPLE:
Compute the radial velocity of the Earth toward Altair on 15-Feb-1994
using both the original Stumpf algorithm and the JPL ephemeris
IDL> jdcnv, 1994, 2, 15, 0, jd ;==> JD = 2449398.5
IDL> baryvel, jd, 2000, vh, vb ;Original algorithm
==> vh = [-17.07243, -22.81121, -9.889315] ;Heliocentric km/s
==> vb = [-17.08083, -22.80471, -9.886582] ;Barycentric km/s
IDL> baryvel, jd, 2000, vh, vb, /jpl ;JPL ephemeris
==> vh = [-17.07236, -22.81126, -9.889419] ;Heliocentric km/s
==> vb = [-17.08083, -22.80484, -9.886409] ;Barycentric km/s
IDL> ra = ten(19,50,46.77)*15/!RADEG ;RA in radians
IDL> dec = ten(08,52,3.5)/!RADEG ;Dec in radians
IDL> v = vb[0]*cos(dec)*cos(ra) + $ ;Project velocity toward star
vb[1]*cos(dec)*sin(ra) + vb[2]*sin(dec)
REVISION HISTORY:
Jeff Valenti, U.C. Berkeley Translated BARVEL.FOR to IDL.
W. Landsman, Cleaned up program sent by Chris McCarthy (SfSU) June 1994
Converted to IDL V5.0 W. Landsman September 1997
Added /JPL keyword W. Landsman July 2001
Documentation update W. Landsman Dec 2005
Converted to Python S. Koposov 2009-2010
"""
#Define constants
dc2pi = 2 * pi
cc2pi = 2 * pi
dc1 = 1.0e0
dcto = 2415020.0e0
dcjul = 36525.0e0 #days in Julian year
dcbes = 0.313e0
dctrop = 365.24219572e0 #days in tropical year (...572 insig)
dc1900 = 1900.0e0
au = 1.4959787e8
#Constants dcfel(i,k) of fast changing elements.
dcfel = array([
1.7400353e00, 6.2833195099091e02, 5.2796e-6, 6.2565836e00,
6.2830194572674e02, -2.6180e-6, 4.7199666e00, 8.3997091449254e03,
-1.9780e-5, 1.9636505e-1, 8.4334662911720e03, -5.6044e-5, 4.1547339e00,
5.2993466764997e01, 5.8845e-6, 4.6524223e00, 2.1354275911213e01,
5.6797e-6, 4.2620486e00, 7.5025342197656e00, 5.5317e-6, 1.4740694e00,
3.8377331909193e00, 5.6093e-6
])
dcfel = reshape(dcfel, (8, 3))
#constants dceps and ccsel(i,k) of slowly changing elements.
dceps = array([4.093198e-1, -2.271110e-4, -2.860401e-8])
ccsel = array([
1.675104e-2, -4.179579e-5, -1.260516e-7, 2.220221e-1, 2.809917e-2,
1.852532e-5, 1.589963e00, 3.418075e-2, 1.430200e-5, 2.994089e00,
2.590824e-2, 4.155840e-6, 8.155457e-1, 2.486352e-2, 6.836840e-6,
1.735614e00, 1.763719e-2, 6.370440e-6, 1.968564e00, 1.524020e-2,
-2.517152e-6, 1.282417e00, 8.703393e-3, 2.289292e-5, 2.280820e00,
1.918010e-2, 4.484520e-6, 4.833473e-2, 1.641773e-4, -4.654200e-7,
5.589232e-2, -3.455092e-4, -7.388560e-7, 4.634443e-2, -2.658234e-5,
7.757000e-8, 8.997041e-3, 6.329728e-6, -1.939256e-9, 2.284178e-2,
-9.941590e-5, 6.787400e-8, 4.350267e-2, -6.839749e-5, -2.714956e-7,
1.348204e-2, 1.091504e-5, 6.903760e-7, 3.106570e-2, -1.665665e-4,
-1.590188e-7
])
ccsel = reshape(ccsel, (17, 3))
#Constants of the arguments of the short-period perturbations.
dcargs = array([
5.0974222e0, -7.8604195454652e2, 3.9584962e0, -5.7533848094674e2,
1.6338070e0, -1.1506769618935e3, 2.5487111e0, -3.9302097727326e2,
4.9255514e0, -5.8849265665348e2, 1.3363463e0, -5.5076098609303e2,
1.6072053e0, -5.2237501616674e2, 1.3629480e0, -1.1790629318198e3,
5.5657014e0, -1.0977134971135e3, 5.0708205e0, -1.5774000881978e2,
3.9318944e0, 5.2963464780000e1, 4.8989497e0, 3.9809289073258e1,
1.3097446e0, 7.7540959633708e1, 3.5147141e0, 7.9618578146517e1,
3.5413158e0, -5.4868336758022e2
])
dcargs = reshape(dcargs, (15, 2))
#Amplitudes ccamps(n,k) of the short-period perturbations.
ccamps = array([
-2.279594e-5, 1.407414e-5, 8.273188e-6, 1.340565e-5, -2.490817e-7,
-3.494537e-5, 2.860401e-7, 1.289448e-7, 1.627237e-5, -1.823138e-7,
6.593466e-7, 1.322572e-5, 9.258695e-6, -4.674248e-7, -3.646275e-7,
1.140767e-5, -2.049792e-5, -4.747930e-6, -2.638763e-6, -1.245408e-7,
9.516893e-6, -2.748894e-6, -1.319381e-6, -4.549908e-6, -1.864821e-7,
7.310990e-6, -1.924710e-6, -8.772849e-7, -3.334143e-6, -1.745256e-7,
-2.603449e-6, 7.359472e-6, 3.168357e-6, 1.119056e-6, -1.655307e-7,
-3.228859e-6, 1.308997e-7, 1.013137e-7, 2.403899e-6, -3.736225e-7,
3.442177e-7, 2.671323e-6, 1.832858e-6, -2.394688e-7, -3.478444e-7,
8.702406e-6, -8.421214e-6, -1.372341e-6, -1.455234e-6, -4.998479e-8,
-1.488378e-6, -1.251789e-5, 5.226868e-7, -2.049301e-7, 0.e0,
-8.043059e-6, -2.991300e-6, 1.473654e-7, -3.154542e-7, 0.e0,
3.699128e-6, -3.316126e-6, 2.901257e-7, 3.407826e-7, 0.e0, 2.550120e-6,
-1.241123e-6, 9.901116e-8, 2.210482e-7, 0.e0, -6.351059e-7,
2.341650e-6, 1.061492e-6, 2.878231e-7, 0.e0
])
ccamps = reshape(ccamps, (15, 5))
#Constants csec3 and ccsec(n,k) of the secular perturbations in longitude.
ccsec3 = -7.757020e-8
ccsec = array([
1.289600e-6, 5.550147e-1, 2.076942e00, 3.102810e-5, 4.035027e00,
3.525565e-1, 9.124190e-6, 9.990265e-1, 2.622706e00, 9.793240e-7,
5.508259e00, 1.559103e01
])
ccsec = reshape(ccsec, (4, 3))
#Sidereal rates.
dcsld = 1.990987e-7 #sidereal rate in longitude
ccsgd = 1.990969e-7 #sidereal rate in mean anomaly
#Constants used in the calculation of the lunar contribution.
cckm = 3.122140e-5
ccmld = 2.661699e-6
ccfdi = 2.399485e-7
#Constants dcargm(i,k) of the arguments of the perturbations of the motion
# of the moon.
dcargm = array([
5.1679830e0, 8.3286911095275e3, 5.4913150e0, -7.2140632838100e3,
5.9598530e0, 1.5542754389685e4
])
dcargm = reshape(dcargm, (3, 2))
#Amplitudes ccampm(n,k) of the perturbations of the moon.
ccampm = array([
1.097594e-1, 2.896773e-7, 5.450474e-2, 1.438491e-7, -2.223581e-2,
5.083103e-8, 1.002548e-2, -2.291823e-8, 1.148966e-2, 5.658888e-8,
8.249439e-3, 4.063015e-8
])
ccampm = reshape(ccampm, (3, 4))
#ccpamv(k)=a*m*dl,dt (planets), dc1mme=1-mass(earth+moon)
ccpamv = array([8.326827e-11, 1.843484e-11, 1.988712e-12, 1.881276e-12])
dc1mme = 0.99999696e0
#Time arguments.
dt = (dje - dcto) / dcjul
tvec = array([1e0, dt, dt * dt])
#Values of all elements for the instant(aneous?) dje.
temp = (transpose(dot(transpose(tvec), transpose(dcfel)))) % dc2pi
dml = temp[0]
forbel = temp[1:8]
g = forbel[0] #old fortran equivalence
deps = (tvec * dceps).sum() % dc2pi
sorbel = (transpose(dot(transpose(tvec), transpose(ccsel)))) % dc2pi
e = sorbel[0] #old fortran equivalence
#Secular perturbations in longitude.
dummy = cos(2.0)
sn = sin((transpose(dot(transpose(tvec[0:2]), transpose(ccsec[:, 1:3])))) %
cc2pi)
#Periodic perturbations of the emb (earth-moon barycenter).
pertl = (ccsec[:, 0] * sn).sum() + dt * ccsec3 * sn[2]
pertld = 0.0
pertr = 0.0
pertrd = 0.0
for k in range(0, 15):
a = (dcargs[k, 0] + dt * dcargs[k, 1]) % dc2pi
cosa = cos(a)
sina = sin(a)
pertl = pertl + ccamps[k, 0] * cosa + ccamps[k, 1] * sina
pertr = pertr + ccamps[k, 2] * cosa + ccamps[k, 3] * sina
if k < 11:
pertld = pertld + (ccamps[k, 1] * cosa -
ccamps[k, 0] * sina) * ccamps[k, 4]
pertrd = pertrd + (ccamps[k, 3] * cosa -
ccamps[k, 2] * sina) * ccamps[k, 4]
#Elliptic part of the motion of the emb.
phi = (e * e / 4e0) * (((8e0 / e) - e) * sin(g) + 5 * sin(2 * g) +
(13 / 3e0) * e * sin(3 * g))
f = g + phi
sinf = sin(f)
cosf = cos(f)
dpsi = (dc1 - e * e) / (dc1 + e * cosf)
phid = 2 * e * ccsgd * ((1 + 1.5 * e * e) * cosf + e *
(1.25 - 0.5 * sinf * sinf))
psid = ccsgd * e * sinf / sqrt(dc1 - e * e)
#Perturbed heliocentric motion of the emb.
d1pdro = dc1 + pertr
drd = d1pdro * (psid + dpsi * pertrd)
drld = d1pdro * dpsi * (dcsld + phid + pertld)
dtl = (dml + phi + pertl) % dc2pi
dsinls = sin(dtl)
dcosls = cos(dtl)
dxhd = drd * dcosls - drld * dsinls
dyhd = drd * dsinls + drld * dcosls
#Influence of eccentricity, evection and variation on the geocentric
# motion of the moon.
pertl = 0.0
pertld = 0.0
pertp = 0.0
pertpd = 0.0
for k in range(0, 3):
a = (dcargm[k, 0] + dt * dcargm[k, 1]) % dc2pi
sina = sin(a)
cosa = cos(a)
pertl = pertl + ccampm[k, 0] * sina
pertld = pertld + ccampm[k, 1] * cosa
pertp = pertp + ccampm[k, 2] * cosa
pertpd = pertpd - ccampm[k, 3] * sina
#Heliocentric motion of the earth.
tl = forbel[1] + pertl
sinlm = sin(tl)
coslm = cos(tl)
sigma = cckm / (1.0 + pertp)
a = sigma * (ccmld + pertld)
b = sigma * pertpd
dxhd = dxhd + a * sinlm + b * coslm
dyhd = dyhd - a * coslm + b * sinlm
dzhd = -sigma * ccfdi * cos(forbel[2])
#Barycentric motion of the earth.
dxbd = dxhd * dc1mme
dybd = dyhd * dc1mme
dzbd = dzhd * dc1mme
for k in range(0, 4):
plon = forbel[k + 3]
pomg = sorbel[k + 1]
pecc = sorbel[k + 9]
tl = (plon + 2.0 * pecc * sin(plon - pomg)) % cc2pi
dxbd = dxbd + ccpamv[k] * (sin(tl) + pecc * sin(pomg))
dybd = dybd - ccpamv[k] * (cos(tl) + pecc * cos(pomg))
dzbd = dzbd - ccpamv[k] * sorbel[k + 13] * cos(plon - sorbel[k + 5])
#Transition to mean equator of date.
dcosep = cos(deps)
dsinep = sin(deps)
dyahd = dcosep * dyhd - dsinep * dzhd
dzahd = dsinep * dyhd + dcosep * dzhd
dyabd = dcosep * dybd - dsinep * dzbd
dzabd = dsinep * dybd + dcosep * dzbd
#Epoch of mean equinox (deq) of zero implies that we should use
# Julian ephemeris date (dje) as epoch of mean equinox.
if deq == 0:
dvelh = au * (array([dxhd, dyahd, dzahd]))
dvelb = au * (array([dxbd, dyabd, dzabd]))
return (dvelh, dvelb)
#General precession from epoch dje to deq.
deqdat = (dje - dcto - dcbes) / dctrop + dc1900
prema = premat(deqdat, deq, fk4=True)
dvelh = au * (transpose(
dot(transpose(prema), transpose(array([dxhd, dyahd, dzahd])))))
dvelb = au * (transpose(
dot(transpose(prema), transpose(array([dxbd, dyabd, dzabd])))))
return (dvelh, dvelb)
def precess(ra0,
dec0,
equinox1,
equinox2,
doprint=False,
fk4=False,
radian=False):
"""
NAME:
PRECESS
PURPOSE:
Precess coordinates from EQUINOX1 to EQUINOX2.
EXPLANATION:
For interactive display, one can use the procedure ASTRO which calls
PRECESS or use the /PRINT keyword. The default (RA,DEC) system is
FK5 based on epoch J2000.0 but FK4 based on B1950.0 is available via
the /FK4 keyword.
Use BPRECESS and JPRECESS to convert between FK4 and FK5 systems
CALLING SEQUENCE:
PRECESS, ra, dec, [ equinox1, equinox2, /PRINT, /FK4, /RADIAN ]
INPUT - OUTPUT:
RA - Input right ascension (scalar or vector) in DEGREES, unless the
/RADIAN keyword is set
DEC - Input declination in DEGREES (scalar or vector), unless the
/RADIAN keyword is set
The input RA and DEC are modified by PRECESS to give the
values after precession.
OPTIONAL INPUTS:
EQUINOX1 - Original equinox of coordinates, numeric scalar. If
omitted, then PRECESS will query for EQUINOX1 and EQUINOX2.
EQUINOX2 - Equinox of precessed coordinates.
OPTIONAL INPUT KEYWORDS:
/PRINT - If this keyword is set and non-zero, then the precessed
coordinates are displayed at the terminal. Cannot be used
with the /RADIAN keyword
/FK4 - If this keyword is set and non-zero, the FK4 (B1950.0) system
will be used otherwise FK5 (J2000.0) will be used instead.
/RADIAN - If this keyword is set and non-zero, then the input and
output RA and DEC vectors are in radians rather than degrees
RESTRICTIONS:
Accuracy of precession decreases for declination values near 90
degrees. PRECESS should not be used more than 2.5 centuries from
2000 on the FK5 system (1950.0 on the FK4 system).
EXAMPLES:
(1) The Pole Star has J2000.0 coordinates (2h, 31m, 46.3s,
89d 15' 50.6"); compute its coordinates at J1985.0
IDL> precess, ten(2,31,46.3)*15, ten(89,15,50.6), 2000, 1985, /PRINT
====> 2h 16m 22.73s, 89d 11' 47.3"
(2) Precess the B1950 coordinates of Eps Ind (RA = 21h 59m,33.053s,
DEC = (-56d, 59', 33.053") to equinox B1975.
IDL> ra = ten(21, 59, 33.053)*15
IDL> dec = ten(-56, 59, 33.053)
IDL> precess, ra, dec ,1950, 1975, /fk4
PROCEDURE:
Algorithm from Computational Spherical Astronomy by Taff (1983),
p. 24. (FK4). FK5 constants from "Astronomical Almanac Explanatory
Supplement 1992, page 104 Table 3.211.1.
PROCEDURE CALLED:
Function PREMAT - computes precession matrix
REVISION HISTORY
Written, Wayne Landsman, STI Corporation August 1986
Correct negative output RA values February 1989
Added /PRINT keyword W. Landsman November, 1991
Provided FK5 (J2000.0) I. Freedman January 1994
Precession Matrix computation now in PREMAT W. Landsman June 1994
Added /RADIAN keyword W. Landsman June 1997
Converted to IDL V5.0 W. Landsman September 1997
Correct negative output RA values when /RADIAN used March 1999
Work for arrays, not just vectors W. Landsman September 2003
Convert to Python Sergey Koposov July 2010
"""
scal = True
if isinstance(ra0, ndarray):
ra = ra0.copy()
dec = dec0.copy()
scal = False
else:
ra = array([ra0])
dec = array([dec0])
npts = ra.size
if not radian:
ra_rad = deg2rad(ra) #Convert to double precision if not already
dec_rad = deg2rad(dec)
else:
ra_rad = ra
dec_rad = dec
a = cos(dec_rad)
x = zeros((npts, 3))
x[:, 0] = a * cos(ra_rad)
x[:, 1] = a * sin(ra_rad)
x[:, 2] = sin(dec_rad)
# Use PREMAT function to get precession matrix from Equinox1 to Equinox2
r = premat(equinox1, equinox2, fk4=fk4)
x2 = transpose(dot(transpose(r),
transpose(x))) #rotate to get output direction cosines
ra_rad = zeros(npts) + arctan2(x2[:, 1], x2[:, 0])
dec_rad = zeros(npts) + arcsin(x2[:, 2])
if not radian:
ra = rad2deg(ra_rad)
ra = ra + (ra < 0.) * 360.e0 #RA between 0 and 360 degrees
dec = rad2deg(dec_rad)
else:
ra = ra_rad
dec = dec_rad
ra = ra + (ra < 0.) * 2.0e0 * pi
if doprint:
print 'Equinox (%.2f): %f,%f' % (equinox2, ra, dec)
if scal:
ra, dec = ra[0], dec[0]
return ra, dec
def precess(ra, dec, equinox1, equinox2, FK4 = None,radian=False):
"""
NAME:
PRECESS
PURPOSE:
Precess coordinates from EQUINOX1 to EQUINOX2.
EXPLANATION:
For interactive display, one can use the procedure ASTRO which calls
PRECESS or use the /PRINT keyword. The default (RA,DEC) system is
FK5 based on epoch J2000.0 but FK4 based on B1950.0 is available via
the /FK4 keyword.
CALLING SEQUENCE:
PRECESS, ra, dec, [ equinox1, equinox2, /PRINT, /FK4, /RADIAN ]
INPUT - OUTPUT:
RA - Input right ascension (scalar or vector) in DEGREES, unless the
/RADIAN keyword is set
DEC - Input declination in DEGREES (scalar or vector), unless the
/RADIAN keyword is set
The input RA and DEC are modified by PRECESS to give the
values after precession.
OPTIONAL INPUTS:
EQUINOX1 - Original equinox of coordinates, numeric scalar. If
omitted, then PRECESS will query for EQUINOX1 and EQUINOX2.
EQUINOX2 - Equinox of precessed coordinates.
OPTIONAL INPUT KEYWORDS:
FK4 - If this keyword is set, the FK4 (B1950.0) system
will be used otherwise FK5 (J2000.0) will be used instead.
RADIAN - If this keyword is set and non-zero, then the input and
output RA and DEC vectors are in radians rather than degrees
RESTRICTIONS:
Accuracy of precession decreases for declination values near 90
degrees. PRECESS should not be used more than 2.5 centuries from
2000 on the FK5 system (1950.0 on the FK4 system).
EXAMPLES:
(1) The Pole Star has J2000.0 coordinates (2h, 31m, 46.3s,
89d 15' 50.6") compute its coordinates at J1985.0
In [1]: ra, dec = precess(ten(2,31,46.3)*15, ten(89,15,50.6), 2000, 1985)
====> 2h 16m 22.73s, 89d 11' 47.3"
(2) Precess the B1950 coordinates of Eps Ind (RA = 21h 59m,33.053s,
DEC = (-56d, 59', 33.053") to equinox B1975.
In [2]: ra = ten(21, 59, 33.053)*15
In [3]: dec = ten(-56, 59, 33.053)
In [4]: ra,dec = precess(ra, dec ,1950, 1975, /fk4)
PROCEDURE:
Algorithm from Computational Spherical Astronomy by Taff (1983),
p. 24. (FK4). FK5 constants from "Astronomical Almanac Explanatory
Supplement 1992, page 104 Table 3.211.1.
PROCEDURE CALLED:
Function PREMAT - computes precession matrix
REVISION HISTORY
Written, Wayne Landsman, STI Corporation August 1986
Correct negative output RA values February 1989
Added /PRINT keyword W. Landsman November, 1991
Provided FK5 (J2000.0) I. Freedman January 1994
Precession Matrix computation now in PREMAT W. Landsman June 1994
Added /RADIAN keyword W. Landsman June 1997
Converted to IDL V5.0 W. Landsman September 1997
Converted to Python April 2014
"""
import numpy as np
from premat import premat
deg_to_rad = np.pi/180.
#Is RA a vector or scalar?
try:
npts = np.min( [len(ra), len(dec)] )
except:
npts = 1
if not radian:
ra_rad = ra*deg_to_rad
dec_rad = dec*deg_to_rad
else:
ra_rad= float(ra) ; dec_rad = float(dec)
sec_to_rad = deg_to_rad/3600
a = np.cos(dec_rad)
x = np.zeros((3,npts))
x[0,:] = a*np.cos(ra_rad)
x[1,:] = a*np.sin(ra_rad)
x[2,:] = np.sin(dec_rad)
# Use PREMAT function to get precession matrix from Equinox1 to Equinox2
r = premat(equinox1, equinox2, fk4 = FK4)
x2 = np.dot(r,x) #rotate to get output direction cosines
ra_rad = np.arctan2(x2[1,:],x2[0,:])
dec_rad = np.arcsin(x2[2,:])
if not radian:
ra = ra_rad/deg_to_rad
ra = ra + (ra < 0.)*360. #RA between 0 and 360 degrees
dec = dec_rad/deg_to_rad
else:
ra = ra_rad ; dec = dec_rad
return (ra, dec)
def baryvel(dje, deq=0):
"""
NAME:
BARYVEL
PURPOSE:
Calculates heliocentric and barycentric velocity components of Earth.
EXPLANATION:
BARYVEL takes into account the Earth-Moon motion, and is useful for
radial velocity work to an accuracy of ~1 m/s.
CALLING SEQUENCE:
dvel_hel, dvel_bary = baryvel(dje, deq)
INPUTS:
DJE - (scalar) Julian ephemeris date.
DEQ - (scalar) epoch of mean equinox of dvelh and dvelb. If deq=0
then deq is assumed to be equal to dje.
OUTPUTS:
DVELH: (vector(3)) heliocentric velocity component. in km/s
DVELB: (vector(3)) barycentric velocity component. in km/s
The 3-vectors DVELH and DVELB are given in a right-handed coordinate
system with the +X axis toward the Vernal Equinox, and +Z axis
toward the celestial pole.
OPTIONAL KEYWORD SET:
JPL - if /JPL set, then BARYVEL will call the procedure JPLEPHINTERP
to compute the Earth velocity using the full JPL ephemeris.
The JPL ephemeris FITS file JPLEPH.405 must exist in either the
current directory, or in the directory specified by the
environment variable ASTRO_DATA. Alternatively, the JPL keyword
can be set to the full path and name of the ephemeris file.
A copy of the JPL ephemeris FITS file is available in
http://idlastro.gsfc.nasa.gov/ftp/data/
PROCEDURES CALLED:
Function PREMAT() -- computes precession matrix
JPLEPHREAD, JPLEPHINTERP, TDB2TDT - if /JPL keyword is set
NOTES:
Algorithm taken from FORTRAN program of Stumpff (1980, A&A Suppl, 41,1)
Stumpf claimed an accuracy of 42 cm/s for the velocity. A
comparison with the JPL FORTRAN planetary ephemeris program PLEPH
found agreement to within about 65 cm/s between 1986 and 1994
If /JPL is set (using JPLEPH.405 ephemeris file) then velocities are
given in the ICRS system; otherwise in the FK4 system.
EXAMPLE:
Compute the radial velocity of the Earth toward Altair on 15-Feb-1994
using both the original Stumpf algorithm and the JPL ephemeris
IDL> jdcnv, 1994, 2, 15, 0, jd ;==> JD = 2449398.5
IDL> baryvel, jd, 2000, vh, vb ;Original algorithm
==> vh = [-17.07243, -22.81121, -9.889315] ;Heliocentric km/s
==> vb = [-17.08083, -22.80471, -9.886582] ;Barycentric km/s
IDL> baryvel, jd, 2000, vh, vb, /jpl ;JPL ephemeris
==> vh = [-17.07236, -22.81126, -9.889419] ;Heliocentric km/s
==> vb = [-17.08083, -22.80484, -9.886409] ;Barycentric km/s
IDL> ra = ten(19,50,46.77)*15/!RADEG ;RA in radians
IDL> dec = ten(08,52,3.5)/!RADEG ;Dec in radians
IDL> v = vb[0]*cos(dec)*cos(ra) + $ ;Project velocity toward star
vb[1]*cos(dec)*sin(ra) + vb[2]*sin(dec)
REVISION HISTORY:
Jeff Valenti, U.C. Berkeley Translated BARVEL.FOR to IDL.
W. Landsman, Cleaned up program sent by Chris McCarthy (SfSU) June 1994
Converted to IDL V5.0 W. Landsman September 1997
Added /JPL keyword W. Landsman July 2001
Documentation update W. Landsman Dec 2005
Converted to Python S. Koposov 2009-2010
"""
#Define constants
dc2pi = 2 * pi
cc2pi = 2 * pi
dc1 = 1.0e0
dcto = 2415020.0e0
dcjul = 36525.0e0 #days in Julian year
dcbes = 0.313e0
dctrop = 365.24219572e0 #days in tropical year (...572 insig)
dc1900 = 1900.0e0
au = 1.4959787e8
#Constants dcfel(i,k) of fast changing elements.
dcfel = array([1.7400353e00, 6.2833195099091e02, 5.2796e-6, 6.2565836e00, 6.2830194572674e02, -2.6180e-6, 4.7199666e00, 8.3997091449254e03, -1.9780e-5, 1.9636505e-1, 8.4334662911720e03, -5.6044e-5, 4.1547339e00, 5.2993466764997e01, 5.8845e-6, 4.6524223e00, 2.1354275911213e01, 5.6797e-6, 4.2620486e00, 7.5025342197656e00, 5.5317e-6, 1.4740694e00, 3.8377331909193e00, 5.6093e-6])
dcfel = reshape(dcfel, (8, 3))
#constants dceps and ccsel(i,k) of slowly changing elements.
dceps = array([4.093198e-1, -2.271110e-4, -2.860401e-8])
ccsel = array([1.675104e-2, -4.179579e-5, -1.260516e-7, 2.220221e-1, 2.809917e-2, 1.852532e-5, 1.589963e00, 3.418075e-2, 1.430200e-5, 2.994089e00, 2.590824e-2, 4.155840e-6, 8.155457e-1, 2.486352e-2, 6.836840e-6, 1.735614e00, 1.763719e-2, 6.370440e-6, 1.968564e00, 1.524020e-2, -2.517152e-6, 1.282417e00, 8.703393e-3, 2.289292e-5, 2.280820e00, 1.918010e-2, 4.484520e-6, 4.833473e-2, 1.641773e-4, -4.654200e-7, 5.589232e-2, -3.455092e-4, -7.388560e-7, 4.634443e-2, -2.658234e-5, 7.757000e-8, 8.997041e-3, 6.329728e-6, -1.939256e-9, 2.284178e-2, -9.941590e-5, 6.787400e-8, 4.350267e-2, -6.839749e-5, -2.714956e-7, 1.348204e-2, 1.091504e-5, 6.903760e-7, 3.106570e-2, -1.665665e-4, -1.590188e-7])
ccsel = reshape(ccsel, (17, 3))
#Constants of the arguments of the short-period perturbations.
dcargs = array([5.0974222e0, -7.8604195454652e2, 3.9584962e0, -5.7533848094674e2, 1.6338070e0, -1.1506769618935e3, 2.5487111e0, -3.9302097727326e2, 4.9255514e0, -5.8849265665348e2, 1.3363463e0, -5.5076098609303e2, 1.6072053e0, -5.2237501616674e2, 1.3629480e0, -1.1790629318198e3, 5.5657014e0, -1.0977134971135e3, 5.0708205e0, -1.5774000881978e2, 3.9318944e0, 5.2963464780000e1, 4.8989497e0, 3.9809289073258e1, 1.3097446e0, 7.7540959633708e1, 3.5147141e0, 7.9618578146517e1, 3.5413158e0, -5.4868336758022e2])
dcargs = reshape(dcargs, (15, 2))
#Amplitudes ccamps(n,k) of the short-period perturbations.
ccamps = array([-2.279594e-5, 1.407414e-5, 8.273188e-6, 1.340565e-5, -2.490817e-7, -3.494537e-5, 2.860401e-7, 1.289448e-7, 1.627237e-5, -1.823138e-7, 6.593466e-7, 1.322572e-5, 9.258695e-6, -4.674248e-7, -3.646275e-7, 1.140767e-5, -2.049792e-5, -4.747930e-6, -2.638763e-6, -1.245408e-7, 9.516893e-6, -2.748894e-6, -1.319381e-6, -4.549908e-6, -1.864821e-7, 7.310990e-6, -1.924710e-6, -8.772849e-7, -3.334143e-6, -1.745256e-7, -2.603449e-6, 7.359472e-6, 3.168357e-6, 1.119056e-6, -1.655307e-7, -3.228859e-6, 1.308997e-7, 1.013137e-7, 2.403899e-6, -3.736225e-7, 3.442177e-7, 2.671323e-6, 1.832858e-6, -2.394688e-7, -3.478444e-7, 8.702406e-6, -8.421214e-6, -1.372341e-6, -1.455234e-6, -4.998479e-8, -1.488378e-6, -1.251789e-5, 5.226868e-7, -2.049301e-7, 0.e0, -8.043059e-6, -2.991300e-6, 1.473654e-7, -3.154542e-7, 0.e0, 3.699128e-6, -3.316126e-6, 2.901257e-7, 3.407826e-7, 0.e0, 2.550120e-6, -1.241123e-6, 9.901116e-8, 2.210482e-7, 0.e0, -6.351059e-7, 2.341650e-6, 1.061492e-6, 2.878231e-7, 0.e0])
ccamps = reshape(ccamps, (15, 5))
#Constants csec3 and ccsec(n,k) of the secular perturbations in longitude.
ccsec3 = -7.757020e-8
ccsec = array([1.289600e-6, 5.550147e-1, 2.076942e00, 3.102810e-5, 4.035027e00, 3.525565e-1, 9.124190e-6, 9.990265e-1, 2.622706e00, 9.793240e-7, 5.508259e00, 1.559103e01])
ccsec = reshape(ccsec, (4, 3))
#Sidereal rates.
dcsld = 1.990987e-7 #sidereal rate in longitude
ccsgd = 1.990969e-7 #sidereal rate in mean anomaly
#Constants used in the calculation of the lunar contribution.
cckm = 3.122140e-5
ccmld = 2.661699e-6
ccfdi = 2.399485e-7
#Constants dcargm(i,k) of the arguments of the perturbations of the motion
# of the moon.
dcargm = array([5.1679830e0, 8.3286911095275e3, 5.4913150e0, -7.2140632838100e3, 5.9598530e0, 1.5542754389685e4])
dcargm = reshape(dcargm, (3, 2))
#Amplitudes ccampm(n,k) of the perturbations of the moon.
ccampm = array([1.097594e-1, 2.896773e-7, 5.450474e-2, 1.438491e-7, -2.223581e-2, 5.083103e-8, 1.002548e-2, -2.291823e-8, 1.148966e-2, 5.658888e-8, 8.249439e-3, 4.063015e-8])
ccampm = reshape(ccampm, (3, 4))
#ccpamv(k)=a*m*dl,dt (planets), dc1mme=1-mass(earth+moon)
ccpamv = array([8.326827e-11, 1.843484e-11, 1.988712e-12, 1.881276e-12])
dc1mme = 0.99999696e0
#Time arguments.
dt = (dje - dcto) / dcjul
tvec = array([1e0, dt, dt * dt])
#Values of all elements for the instant(aneous?) dje.
temp = (transpose(dot(transpose(tvec), transpose(dcfel)))) % dc2pi
dml = temp[0]
forbel = temp[1:8]
g = forbel[0] #old fortran equivalence
deps = (tvec * dceps).sum() % dc2pi
sorbel = (transpose(dot(transpose(tvec), transpose(ccsel)))) % dc2pi
e = sorbel[0] #old fortran equivalence
#Secular perturbations in longitude.
dummy = cos(2.0)
sn = sin((transpose(dot(transpose(tvec[0:2]), transpose(ccsec[:,1:3])))) % cc2pi)
#Periodic perturbations of the emb (earth-moon barycenter).
pertl = (ccsec[:,0] * sn).sum() + dt * ccsec3 * sn[2]
pertld = 0.0
pertr = 0.0
pertrd = 0.0
for k in range(0, 15):
a = (dcargs[k,0] + dt * dcargs[k,1]) % dc2pi
cosa = cos(a)
sina = sin(a)
pertl = pertl + ccamps[k,0] * cosa + ccamps[k,1] * sina
pertr = pertr + ccamps[k,2] * cosa + ccamps[k,3] * sina
if k < 11:
pertld = pertld + (ccamps[k,1] * cosa - ccamps[k,0] * sina) * ccamps[k,4]
pertrd = pertrd + (ccamps[k,3] * cosa - ccamps[k,2] * sina) * ccamps[k,4]
#Elliptic part of the motion of the emb.
phi = (e * e / 4e0) * (((8e0 / e) - e) * sin(g) + 5 * sin(2 * g) + (13 / 3e0) * e * sin(3 * g))
f = g + phi
sinf = sin(f)
cosf = cos(f)
dpsi = (dc1 - e * e) / (dc1 + e * cosf)
phid = 2 * e * ccsgd * ((1 + 1.5 * e * e) * cosf + e * (1.25 - 0.5 * sinf * sinf))
psid = ccsgd * e * sinf / sqrt(dc1 - e * e)
#Perturbed heliocentric motion of the emb.
d1pdro = dc1 + pertr
drd = d1pdro * (psid + dpsi * pertrd)
drld = d1pdro * dpsi * (dcsld + phid + pertld)
dtl = (dml + phi + pertl) % dc2pi
dsinls = sin(dtl)
dcosls = cos(dtl)
dxhd = drd * dcosls - drld * dsinls
dyhd = drd * dsinls + drld * dcosls
#Influence of eccentricity, evection and variation on the geocentric
# motion of the moon.
pertl = 0.0
pertld = 0.0
pertp = 0.0
pertpd = 0.0
for k in range(0, 3):
a = (dcargm[k,0] + dt * dcargm[k,1]) % dc2pi
sina = sin(a)
cosa = cos(a)
pertl = pertl + ccampm[k,0] * sina
pertld = pertld + ccampm[k,1] * cosa
pertp = pertp + ccampm[k,2] * cosa
pertpd = pertpd - ccampm[k,3] * sina
#Heliocentric motion of the earth.
tl = forbel[1] + pertl
sinlm = sin(tl)
coslm = cos(tl)
sigma = cckm / (1.0 + pertp)
a = sigma * (ccmld + pertld)
b = sigma * pertpd
dxhd = dxhd + a * sinlm + b * coslm
dyhd = dyhd - a * coslm + b * sinlm
dzhd = -sigma * ccfdi * cos(forbel[2])
#Barycentric motion of the earth.
dxbd = dxhd * dc1mme
dybd = dyhd * dc1mme
dzbd = dzhd * dc1mme
for k in range(0, 4):
plon = forbel[k + 3]
pomg = sorbel[k + 1]
pecc = sorbel[k + 9]
tl = (plon + 2.0 * pecc * sin(plon - pomg)) % cc2pi
dxbd = dxbd + ccpamv[k] * (sin(tl) + pecc * sin(pomg))
dybd = dybd - ccpamv[k] * (cos(tl) + pecc * cos(pomg))
dzbd = dzbd - ccpamv[k] * sorbel[k + 13] * cos(plon - sorbel[k + 5])
#Transition to mean equator of date.
dcosep = cos(deps)
dsinep = sin(deps)
dyahd = dcosep * dyhd - dsinep * dzhd
dzahd = dsinep * dyhd + dcosep * dzhd
dyabd = dcosep * dybd - dsinep * dzbd
dzabd = dsinep * dybd + dcosep * dzbd
#Epoch of mean equinox (deq) of zero implies that we should use
# Julian ephemeris date (dje) as epoch of mean equinox.
if deq == 0:
dvelh = au * (array([dxhd, dyahd, dzahd]))
dvelb = au * (array([dxbd, dyabd, dzabd]))
return (dvelh,dvelb)
#General precession from epoch dje to deq.
deqdat = (dje - dcto - dcbes) / dctrop + dc1900
prema = premat(deqdat, deq, fk4=True)
dvelh = au * (transpose(dot(transpose(prema), transpose(array([dxhd, dyahd, dzahd])))))
dvelb = au * (transpose(dot(transpose(prema), transpose(array([dxbd, dyabd, dzabd])))))
return (dvelh, dvelb)
