def test_premat(self): fn = "premat.test" good, dat = self.getData(fn) self.assertEqual(good, True) err = 0 for i in xrange(len(dat[::,0])): r = numpy.reshape(dat[i,2:11], (3,3)) if dat[i,11] == 0: m = at.premat(dat[i,0], dat[i,1]) else: m = at.premat(dat[i,0], dat[i,1], FK4=True) if (r-m).max() > self.p: print "test_premat - Error detected" err += 1 self.assertEqual(err, 0)
def baryvel(dje, deq): """ Calculate helio- and barycentric velocity. .. note:: The "JPL" option present in IDL is not provided here. Parameters ---------- dje : float Julian ephemeris date deq : float Epoch of mean equinox of helio- and barycentric velocity output. If `deq` is zero, `deq` is assumed to be equal to `dje`. Returns ------- dvelh : array Heliocentric velocity vector [km/s]. dvelb : array Barycentric velocity vector [km/s]. Notes ----- .. note:: This function was ported from the IDL Astronomy User's Library. :IDL - Documentation: pro baryvel, dje, deq, dvelh, dvelb, JPL = JPL 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: BARYVEL, dje, deq, dvelh, dvelb, [ JPL = ] 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 """ # Define constants dc2pi = 2 * np.pi cc2pi = 2 * np.pi dc1 = 1.0 dcto = 2415020.0 dcjul = 36525.0 # days in Julian year dcbes = 0.313 dctrop = 365.24219572 # days in tropical year (...572 insig) dc1900 = 1900.0 AU = 1.4959787e8 # Constants dcfel(i,k) of fast changing elements. dcfel = [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 = np.resize(dcfel, (8,3)) # constants dceps and ccsel(i,k) of slowly changing elements. dceps = [4.093198e-1, -2.271110e-4, -2.860401e-8 ] ccsel = [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 = np.resize(ccsel, (17,3)) # Constants of the arguments of the short-period perturbations. dcargs = [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 = np.resize(dcargs, (15,2)) # Amplitudes ccamps(n,k) of the short-period perturbations. ccamps = \ [-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 = np.resize(ccamps, (15,5)) # Constants csec3 and ccsec(n,k) of the secular perturbations in longitude. ccsec3 = -7.757020e-8 ccsec = [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 = np.resize(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 = [5.1679830e0, 8.3286911095275e3 \ ,5.4913150e0, -7.2140632838100e3 \ ,5.9598530e0, 1.5542754389685e4 ] dcargm = np.resize(dcargm, (3,2)) # Amplitudes ccampm(n,k) of the perturbations of the moon. ccampm = [ 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 = np.resize(ccampm, (3,4)) # ccpamv(k)=a*m*dl,dt (planets), dc1mme=1-mass(earth+moon) ccpamv = [8.326827e-11, 1.843484e-11, 1.988712e-12, 1.881276e-12] dc1mme = 0.99999696e0 # Time arguments. dt = (dje - dcto) / dcjul tvec = np.array([1e0, dt, dt*dt]) # Values of all elements for the instant(aneous?) dje. temp = idlMod(np.dot(dcfel, tvec), dc2pi) dml = temp[0] forbel = temp[1:8] g = forbel[0] # old fortran equivalence deps = idlMod(np.sum(tvec*dceps), dc2pi) sorbel = idlMod(np.dot(ccsel, tvec), dc2pi) e = sorbel[0] # old fortran equivalence # Secular perturbations in longitude. dummy = np.cos(2.0) sn = np.sin(idlMod(np.dot(ccsec[::,1:3], tvec[0:2]), cc2pi)) # Periodic perturbations of the emb (earth-moon barycenter). pertl = np.sum(ccsec[::,0] * sn) + (dt * ccsec3 * sn[2]) pertld = 0.0 pertr = 0.0 pertrd = 0.0 for k in xrange(15): a = idlMod((dcargs[k,0] + dt*dcargs[k,1]), dc2pi) cosa = np.cos(a) sina = np.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)*np.sin(g) +5*np.sin(2*g) +(13/3e0)*e*np.sin(3*g)) f = g + phi sinf = np.sin(f) cosf = np.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 / np.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 = idlMod((dml + phi + pertl), dc2pi) dsinls = np.sin(dtl) dcosls = np.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 xrange(3): a = idlMod((dcargm[k,0] + dt*dcargm[k,1]), dc2pi) sina = np.sin(a) cosa = np.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 = np.sin(tl) coslm = np.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*np.cos(forbel[2]) # Barycentric motion of the earth. dxbd = dxhd*dc1mme dybd = dyhd*dc1mme dzbd = dzhd*dc1mme for k in xrange(4): plon = forbel[k+3] pomg = sorbel[k+1] pecc = sorbel[k+9] tl = idlMod((plon + 2.0*pecc*np.sin(plon-pomg)), cc2pi) dxbd = dxbd + ccpamv[k]*(np.sin(tl) + pecc*np.sin(pomg)) dybd = dybd - ccpamv[k]*(np.cos(tl) + pecc*np.cos(pomg)) dzbd = dzbd - ccpamv[k]*sorbel[k+13]*np.cos(plon - sorbel[k+5]) # Transition to mean equator of date. dcosep = np.cos(deps) dsinep = np.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 * np.array([dxhd, dyahd, dzahd]) dvelb = AU * np.array([dxbd, dyabd, dzabd]) return dvelh, dvelb # General precession from epoch dje to deq. deqdat = (dje-dcto-dcbes) / dctrop + dc1900 prema = np.transpose(premat(deqdat, deq, FK4=True)) dvelh = AU * np.dot( [dxhd, dyahd, dzahd], prema ) dvelb = AU * np.dot( [dxbd, dyabd, dzabd], prema ) return dvelh, dvelb