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diff --git a/math/slalib/doc/ue2el.hlp b/math/slalib/doc/ue2el.hlp new file mode 100644 index 00000000..6eb0996a --- /dev/null +++ b/math/slalib/doc/ue2el.hlp @@ -0,0 +1,167 @@ +.help ue2el Jun99 "Slalib Package" +.nf + + SUBROUTINE slUEEL (U, JFORMR, + : JFORM, EPOCH, ORBINC, ANODE, PERIH, + : AORQ, E, AORL, DM, JSTAT) + + - - - - - - + U E E L + - - - - - - + + Transform universal elements into conventional heliocentric + osculating elements. + + Given: + 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 + + JFORMR i requested element set (1-3; Note 3) + + Returned: + JFORM d element set actually returned (1-3; Note 4) + EPOCH d epoch of elements (TT MJD) + 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) + JSTAT i status: 0 = OK + -1 = illegal combined mass + -2 = illegal JFORMR + -3 = position/velocity out of range + + Notes + + 1 The "universal" elements are those which define the orbit for the + purposes of the method of universal variables (see reference 2). + 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 universal elements are with respect to the mean equator and + equinox of epoch J2000. The orbital elements produced are with + respect to the J2000 ecliptic and mean equinox. + + 3 Three different element-format options are supported: + + 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 + 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 + 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 + + 4 It may not be possible to generate elements in the form + requested through JFORMR. The caller is notified of the form + of elements actually returned by means of the JFORM argument: + + JFORMR JFORM meaning + + 1 1 OK - elements are in the requested format + 1 2 never happens + 1 3 orbit not elliptical + + 2 1 never happens + 2 2 OK - elements are in the requested format + 2 3 orbit not elliptical + + 3 1 never happens + 3 2 never happens + 3 3 OK - elements are in the requested format + + 5 The arguments returned for each value of JFORM (cf Note 6: JFORM + may not be the same as JFORMR) are as follows: + + JFORM 1 2 3 + EPOCH t0 t0 T + ORBINC i i i + ANODE Omega Omega Omega + PERIH curly pi omega omega + AORQ a a q + E e e e + AORL L M - + DM n - - + + where: + + t0 is the epoch of the elements (MJD, TT) + T " epoch of perihelion (MJD, TT) + i " inclination (radians) + Omega " longitude of the ascending node (radians) + curly pi " longitude of perihelion (radians) + omega " argument of perihelion (radians) + a " mean distance (AU) + q " perihelion distance (AU) + e " eccentricity + L " longitude (radians, 0-2pi) + M " mean anomaly (radians, 0-2pi) + n " daily motion (radians) + - means no value is set + + 6 At very small inclinations, the longitude of the ascending node + ANODE becomes indeterminate and under some circumstances may be + set arbitrarily to zero. Similarly, if the orbit is close to + circular, the true anomaly becomes indeterminate and under some + circumstances may be set arbitrarily to zero. In such cases, + the other elements are automatically adjusted to compensate, + and so the elements remain a valid description of the orbit. + + References: + + 1 Sterne, Theodore E., "An Introduction to Celestial Mechanics", + Interscience Publishers Inc., 1960. Section 6.7, p199. + + 2 Everhart, E. & Pitkin, E.T., Am.J.Phys. 51, 712, 1983. + + Called: slPVEL + + P.T.Wallace Starlink 18 March 1999 + + Copyright (C) 1999 Rutherford Appleton Laboratory + Copyright (C) 1995 Association of Universities for Research in Astronomy Inc. + +.fi +.endhelp |