pro baryvel, dje, deq, dvelh, dvelb ;+ ; 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 ; ; 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. ; ; PROCEDURE CALLED: ; Function PREMAT() -- computes precession matrix ; ; 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 ; ; EXAMPLE: ; Compute the radial velocity of the Earth toward Altair on 15-Feb-1994 ; ; IDL> jdcnv, 1994, 2, 15, 0, jd ;==> JD = 2449398.5 ; IDL> baryvel, jd, 2000, vh, vb ; ==> vh = [-17.07809, -22.80063, -9.885281] ;Heliocentric km/s ; ==> vb = [-17.08083, -22.80471, -9.886582] ;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 ;- On_Error,2 if N_params() LT 4 then begin print,'Syntax: BARYVEL, dje, deq, dvelh, dvelb' print,' dje - input Julian ephemeris date' print,' deq - input epoch of mean equinox of dvelh and dvelb' print,' dvelh - output vector(3) heliocentric velocity comp in km/s' print,' dvelb - output vector(3) barycentric velocity comp in km/s' return endif ;Define constants dc2pi = 2*!DPI cc2pi = 2*!PI dc1 = 1.0D0 dcto = 2415020.0D0 dcjul = 36525.0D0 ;days in julian year dcbes = 0.313D0 dctrop = 365.24219572D0 ;days in tropical year (...572 insig) dc1900 = 1900.0D0 AU = 1.4959787D8 ;Constants dcfel(i,k) of fast changing elements. dcfel = [1.7400353D00, 6.2833195099091D02, 5.2796D-6 $ ,6.2565836D00, 6.2830194572674D02, -2.6180D-6 $ ,4.7199666D00, 8.3997091449254D03, -1.9780D-5 $ ,1.9636505D-1, 8.4334662911720D03, -5.6044D-5 $ ,4.1547339D00, 5.2993466764997D01, 5.8845D-6 $ ,4.6524223D00, 2.1354275911213D01, 5.6797D-6 $ ,4.2620486D00, 7.5025342197656D00, 5.5317D-6 $ ,1.4740694D00, 3.8377331909193D00, 5.6093D-6 ] dcfel = reform(dcfel,3,8) ;constants dceps and ccsel(i,k) of slowly changing elements. dceps = [4.093198D-1, -2.271110D-4, -2.860401D-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 = reform(ccsel,3,17) ;Constants of the arguments of the short-period perturbations. dcargs = [5.0974222D0, -7.8604195454652D2 $ ,3.9584962D0, -5.7533848094674D2 $ ,1.6338070D0, -1.1506769618935D3 $ ,2.5487111D0, -3.9302097727326D2 $ ,4.9255514D0, -5.8849265665348D2 $ ,1.3363463D0, -5.5076098609303D2 $ ,1.6072053D0, -5.2237501616674D2 $ ,1.3629480D0, -1.1790629318198D3 $ ,5.5657014D0, -1.0977134971135D3 $ ,5.0708205D0, -1.5774000881978D2 $ ,3.9318944D0, 5.2963464780000D1 $ ,4.8989497D0, 3.9809289073258D1 $ ,1.3097446D0, 7.7540959633708D1 $ ,3.5147141D0, 7.9618578146517D1 $ ,3.5413158D0, -5.4868336758022D2 ] dcargs = reform(dcargs,2,15) ;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 = reform(ccamps,5,15) ;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 = reform(ccsec,3,4) ;Sidereal rates. dcsld = 1.990987D-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 = [5.1679830D0, 8.3286911095275D3 $ ,5.4913150D0, -7.2140632838100D3 $ ,5.9598530D0, 1.5542754389685D4 ] dcargm = reform(dcargm,2,3) ;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 = reform(ccampm,4,3) ;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 = 0.99999696D0 ;Time arguments. dt = (dje - dcto) / dcjul tvec = [1d0, dt, dt*dt] ;Values of all elements for the instant(aneous?) dje. temp = (tvec # dcfel) mod dc2pi dml = temp[0] forbel = temp[1:7] g = forbel[0] ;old fortran equivalence deps = total(tvec*dceps) mod dc2pi sorbel = (tvec # ccsel) mod dc2pi e = sorbel[0] ;old fortran equivalence ;Secular perturbations in longitude. dummy=cos(2.0) sn = sin((tvec[0:1] # ccsec[1:2,*]) mod cc2pi) ;Periodic perturbations of the emb (earth-moon barycenter). pertl = total(ccsec[0,*] * sn) + dt*ccsec3*sn[2] pertld = 0.0 pertr = 0.0 pertrd = 0.0 for k=0,14 do begin a = (dcargs[0,k]+dt*dcargs[1,k]) mod dc2pi cosa = cos(a) sina = sin(a) pertl = pertl + ccamps[0,k]*cosa + ccamps[1,k]*sina pertr = pertr + ccamps[2,k]*cosa + ccamps[3,k]*sina if k lt 11 then begin pertld = pertld + (ccamps[1,k]*cosa-ccamps[0,k]*sina)*ccamps[4,k] pertrd = pertrd + (ccamps[3,k]*cosa-ccamps[2,k]*sina)*ccamps[4,k] endif endfor ;Elliptic part of the motion of the emb. phi = (e*e/4d0)*(((8d0/e)-e)*sin(g) +5*sin(2*g) +(13/3d0)*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) mod 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 = 0,2 do begin a = (dcargm[0,k] + dt*dcargm[1,k]) mod dc2pi sina = sin(a) cosa = cos(a) pertl = pertl + ccampm[0,k]*sina pertld = pertld + ccampm[1,k]*cosa pertp = pertp + ccampm[2,k]*cosa pertpd = pertpd - ccampm[3,k]*sina endfor ;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=0,3 do begin plon = forbel[k+3] pomg = sorbel[k+1] pecc = sorbel[k+9] tl = (plon + 2.0*pecc*sin(plon-pomg)) mod 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]) endfor ;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 eq 0 then begin dvelh = AU * ([dxhd, dyahd, dzahd]) dvelb = AU * ([dxbd, dyabd, dzabd]) return endif ;General precession from epoch dje to deq. deqdat = (dje-dcto-dcbes) / dctrop + dc1900 prema = premat(deqdat,deq, /FK4) dvelh = AU * ( prema # [dxhd, dyahd, dzahd] ) dvelb = AU * ( prema # [dxbd, dyabd, dzabd] ) return end