.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.

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