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+.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