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diff --git a/math/slalib/doc/el2ue.hlp b/math/slalib/doc/el2ue.hlp new file mode 100644 index 00000000..9271fff6 --- /dev/null +++ b/math/slalib/doc/el2ue.hlp @@ -0,0 +1,133 @@ +.help el2ue Jun99 "Slalib Package" +.nf + + SUBROUTINE slELUE (DATE, JFORM, EPOCH, ORBINC, ANODE, + : PERIH, AORQ, E, AORL, DM, + : U, JSTAT) + + - - - - - - + E L U E + - - - - - - + + Transform conventional osculating orbital elements into "universal" form. + + Given: + DATE d epoch (TT MJD) of osculation (Note 3) + JFORM i choice of element set (1-3, Note 6) + EPOCH d epoch (TT MJD) of the elements + ORBINC d inclination (radians) + ANODE d longitude of the ascending node (radians) + PERIH d longitude or argument of perihelion (radians) + AORQ d mean distance or perihelion distance (AU) + E d eccentricity + AORL d mean anomaly or longitude (radians, JFORM=1,2 only) + DM d daily motion (radians, JFORM=1 only) + + Returned: + U d(13) universal orbital elements (Note 1) + + (1) combined mass (M+m) + (2) total energy of the orbit (alpha) + (3) reference (osculating) epoch (t0) + (4-6) position at reference epoch (r0) + (7-9) velocity at reference epoch (v0) + (10) heliocentric distance at reference epoch + (11) r0.v0 + (12) date (t) + (13) universal eccentric anomaly (psi) of date, approx + + JSTAT i status: 0 = OK + -1 = illegal JFORM + -2 = illegal E + -3 = illegal AORQ + -4 = illegal DM + -5 = numerical error + + Called: slUEPV, slPVUE + + Notes + + 1 The "universal" elements are those which define the orbit for the + purposes of the method of universal variables (see reference). + They consist of the combined mass of the two bodies, an epoch, + and the position and velocity vectors (arbitrary reference frame) + at that epoch. The parameter set used here includes also various + quantities that can, in fact, be derived from the other + information. This approach is taken to avoiding unnecessary + computation and loss of accuracy. The supplementary quantities + are (i) alpha, which is proportional to the total energy of the + orbit, (ii) the heliocentric distance at epoch, (iii) the + outwards component of the velocity at the given epoch, (iv) an + estimate of psi, the "universal eccentric anomaly" at a given + date and (v) that date. + + 2 The companion routine is slUEPV. This takes the set of numbers + that the present routine outputs and uses them to derive the + object's position and velocity. A single prediction requires one + call to the present routine followed by one call to slUEPV; + for convenience, the two calls are packaged as the routine + slPLNE. Multiple predictions may be made by again calling the + present routine once, but then calling slUEPV multiple times, + which is faster than multiple calls to slPLNE. + + 3 DATE is the epoch of osculation. It is in the TT timescale + (formerly Ephemeris Time, ET) and is a Modified Julian Date + (JD-2400000.5). + + 4 The supplied orbital elements are with respect to the J2000 + ecliptic and equinox. The position and velocity parameters + returned in the array U are with respect to the mean equator and + equinox of epoch J2000, and are for the perihelion prior to the + specified epoch. + + 5 The universal elements returned in the array U are in canonical + units (solar masses, AU and canonical days). + + 6 Three different element-format options are available: + + Option JFORM=1, suitable for the major planets: + + EPOCH = epoch of elements (TT MJD) + ORBINC = inclination i (radians) + ANODE = longitude of the ascending node, big omega (radians) + PERIH = longitude of perihelion, curly pi (radians) + AORQ = mean distance, a (AU) + E = eccentricity, e (range 0 to <1) + AORL = mean longitude L (radians) + DM = daily motion (radians) + + Option JFORM=2, suitable for minor planets: + + EPOCH = epoch of elements (TT MJD) + ORBINC = inclination i (radians) + ANODE = longitude of the ascending node, big omega (radians) + PERIH = argument of perihelion, little omega (radians) + AORQ = mean distance, a (AU) + E = eccentricity, e (range 0 to <1) + AORL = mean anomaly M (radians) + + Option JFORM=3, suitable for comets: + + EPOCH = epoch of perihelion (TT MJD) + ORBINC = inclination i (radians) + ANODE = longitude of the ascending node, big omega (radians) + PERIH = argument of perihelion, little omega (radians) + AORQ = perihelion distance, q (AU) + E = eccentricity, e (range 0 to 10) + + 7 Unused elements (DM for JFORM=2, AORL and DM for JFORM=3) are + not accessed. + + 8 The algorithm was originally adapted from the EPHSLA program of + D.H.P.Jones (private communication, 1996). The method is based + on Stumpff's Universal Variables. + + Reference: Everhart & Pitkin, Am.J.Phys. 51, 712 (1983). + + P.T.Wallace Starlink 18 February 1999 + + Copyright (C) 1999 Rutherford Appleton Laboratory + Copyright (C) 1995 Association of Universities for Research in Astronomy Inc. + +.fi +.endhelp |