pro xyz,date,x,y,z,xvel,yvel,zvel,equinox=equinox ;+ ; NAME: ; XYZ ; PURPOSE: ; Calculate geocentric X,Y, and Z and velocity coordinates of the Sun ; EXPLANATION: ; Calculates geocentric X,Y, and Z vectors and velocity coordinates ; (dx, dy and dz) of the Sun. (The positive X axis is directed towards ; the equinox, the y-axis, towards the point on the equator at right ; ascension 6h, and the z axis toward the north pole of the equator). ; Typical position accuracy is <1e-4 AU (15000 km). ; ; CALLING SEQUENCE: ; XYZ, date, x, y, z, [ xvel, yvel, zvel, EQUINOX = ] ; ; INPUT: ; date: reduced julian date (=JD - 2400000), scalar or vector ; ; OUTPUT: ; x,y,z: scalars or vectors giving heliocentric rectangular coordinates ; (in A.U) for each date supplied. Note that sqrt(x^2 + y^2 ; + z^2) gives the Earth-Sun distance for the given date. ; xvel, yvel, zvel: velocity vectors corresponding to X, Y and Z. ; ; OPTIONAL KEYWORD INPUT: ; EQUINOX: equinox of output. Default is 1950. ; ; EXAMPLE: ; What were the rectangular coordinates and velocities of the Sun on ; Jan 22, 1999 0h UT (= JD 2451200.5) in J2000 coords? NOTE: ; Astronomical Almanac (AA) is in TDT, so add 64 seconds to ; UT to convert. ; ; IDL> xyz,51200.5+64.d/86400.d,x,y,z,xv,yv,zv,equinox = 2000 ; ; Compare to Astronomical Almanac (1999 page C20) ; X (AU) Y (AU) Z (AU) ; XYZ: 0.51456871 -0.76963263 -0.33376880 ; AA: 0.51453130 -0.7697110 -0.3337152 ; abs(err): 0.00003739 0.00007839 0.00005360 ; abs(err) ; (km): 5609 11759 8040 ; ; NOTE: Velocities in AA are for Earth/Moon barycenter ; (a very minor offset) see AA 1999 page E3 ; X VEL (AU/DAY) YVEL (AU/DAY) Z VEL (AU/DAY) ; XYZ: -0.014947268 -0.0083148382 -0.0036068577 ; AA: -0.01494574 -0.00831185 -0.00360365 ; abs(err): 0.000001583 0.0000029886 0.0000032077 ; abs(err) ; (km/sec): 0.00265 0.00519 0.00557 ; ; PROCEDURE CALLS: ; PRECESS_XYZ ; REVISION HISTORY ; Original algorithm from Almanac for Computers, Doggett et al. USNO 1978 ; Adapted from the book Astronomical Photometry by A. Henden ; Written W. Landsman STX June 1989 ; Correct error in X coefficient W. Landsman HSTX January 1995 ; Added velocities, more terms to positions and EQUINOX keyword, ; some minor adjustments to calculations ; P. Plait/ACC March 24, 1999 ;- On_error,2 if (n_params() eq 0) then begin print,'Syntax - XYZ, date, x, y, z, [ xvel, yvel, zvel, EQUINOX= ]' print,' (date is REDUCED Julian date (JD - 2400000.0) )' return endif picon = !DPI/180.0d t = (date - 15020.0d0)/36525.0d0 ;Relative Julian century from 1900 ; NOTE: longitude arguments below are given in *equinox* of date. ; Precess these to equinox 1950 to give everything an even footing. ; Compute argument of precession from equinox of date back to 1950 pp = (1.396041d + 0.000308d*(t + 0.5d))*(t-0.499998d) ; Compute mean solar longitude, precessed back to 1950 el = 279.696678D + 36000.76892D*t + 0.000303d*t*t - pp ; Compute Mean longitude of the Moon c = 270.434164d + 480960.d*t + 307.883142d*t - 0.001133d*t*t - pp ; Compute longitude of Moon's ascending node n = 259.183275d - 1800.d*t - 134.142008d*t + 0.002078d*t*t - pp ; Compute mean solar anomaly g = 358.475833d + 35999.04975d*t - 0.00015d*t*t ; Compute the mean jupiter anomaly j = 225.444651d + 2880.0d*t + 154.906654d*t*t ; Compute mean anomaly of Venus v = 212.603219d + 58320.d*t + 197.803875d*t + 0.001286d*t*t ; Compute mean anomaly of Mars m = 319.529425d + 19080.d*t + 59.8585d*t + 0.000181d*t*t ; Convert degrees to radians for trig functions el = el*picon g = g*picon j = j*picon c = c*picon v = v*picon n = n*picon m = m*picon ; Calculate X,Y,Z using trigonometric series X = 0.999860d*cos(el) \$ - 0.025127d*cos(g - el) \$ + 0.008374d*cos(g + el) \$ + 0.000105d*cos(g + g + el) \$ + 0.000063d*t*cos(g - el) \$ + 0.000035d*cos(g + g - el) \$ - 0.000026d*sin(g - el - j) \$ - 0.000021d*t*cos(g + el) \$ + 0.000018d*sin(2.d*g + el - 2.d*v) \$ + 0.000017d*cos(c) \$ - 0.000014d*cos(c - 2.d*el) \$ + 0.000012d*cos(4.d*g + el - 8.d*m + 3.d*j) \$ - 0.000012d*cos(4.d*g - el - 8.d*m + 3.d*j) \$ - 0.000012d*cos(g + el - v) \$ + 0.000011d*cos(2.d*g + el - 2.d*v) \$ + 0.000011d*cos(2.d*g - el - 2.d*j) Y = 0.917308d*sin(el) \$ + 0.023053d*sin(g - el) \$ + 0.007683d*sin(g + el) \$ + 0.000097d*sin(g + g + el) \$ - 0.000057d*t*sin(g - el) \$ - 0.000032d*sin(g + g - el) \$ - 0.000024d*cos(g - el - j) \$ - 0.000019d*t*sin(g + el) \$ - 0.000017d*cos(2.d0*g + el - 2.d0*v) \$ + 0.000016d*sin(c) \$ + 0.000013d*sin(c - 2.d0*el ) \$ + 0.000011d*sin(4.d0*g + el - 8.d0*m + 3.d0*j) \$ + 0.000011d*sin(4.d0*g - el - 8.d0*m + 3.d0*j) \$ - 0.000011d*sin(g + el - v) \$ + 0.000010d*sin(2.d0*g + el - 2.d0*v ) \$ - 0.000010d*sin(2.d0*g - el - 2.d0*j ) Z = 0.397825d*sin(el) \$ + 0.009998d*sin(g-el) \$ + 0.003332d*sin(g+el) \$ + 0.000042d*sin(g+g+el) \$ - 0.000025d*t*sin(g-el) \$ - 0.000014d*sin(g+g-el) \$ - 0.000010d*cos(g-el-j) ;Precess_to new equator? if keyword_set(equinox) then precess_xyz, x, y, z, 1950, equinox if N_params() LE 3 then return XVEL = -0.017200d * sin(el) \$ -0.000288d * sin(g + el) \$ -0.000005d * sin(2.d0*g + el) \$ -0.000004d * sin(c) \$ +0.000003d * sin(c - 2.d0*el) \$ +0.000001d *t * sin(g+el) \$ -0.000001d * sin(2.d0*g-el) YVEL = 0.015780 * cos(el) \$ +0.000264 * cos(g + el) \$ +0.000005 * cos(2.d0*g + el) \$ +0.000004 * cos(c) \$ +0.000003 * cos(c - 2.d0*el) \$ -0.000001 * t * cos(g + el) ZVEL = 0.006843 * cos(el) \$ +0.000115 * cos(g + el) \$ +0.000002 * cos(2.d0*g + el) \$ +0.000002 * cos(c) \$ +0.000001 * cos(c - 2.d0*el) ;Precess to new equator? if keyword_set(equinox) then precess_xyz, xvel, yvel, zvel, 1950, equinox return end