From fa080de7afc95aa1c19a6e6fc0e0708ced2eadc4 Mon Sep 17 00:00:00 2001
From: Joseph Hunkeler <jhunkeler@gmail.com>
Date: Wed, 8 Jul 2015 20:46:52 -0400
Subject: Initial commit

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+.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
-- 
cgit 

