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      SUBROUTINE slPVUE (PV, DATE, PMASS, U, JSTAT)

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      P V U E
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  Construct a universal element set based on an instantaneous position
  and velocity.

  Given:
     PV        d(6)   heliocentric x,y,z,xdot,ydot,zdot of date,
                      (AU,AU/s; Note 1)
     DATE      d      date (TT Modified Julian Date = JD-2400000.5)
     PMASS     d      mass of the planet (Sun=1; Note 2)

  Returned:
     U         d(13)  universal orbital elements (Note 3)

                 (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 PMASS
                              -2 = too close to Sun
                              -3 = too slow

  Notes

  1  The PV 6-vector can be with respect to any chosen inertial frame,
     and the resulting universal-element set will be with respect to
     the same frame.  A common choice will be mean equator and ecliptic
     of epoch J2000.

  2  The mass, PMASS, is important only for the larger planets.  For
     most purposes (e.g. asteroids) use 0D0.  Values less than zero
     are illegal.

  3  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.

  Reference:  Everhart, E. & Pitkin, E.T., Am.J.Phys. 51, 712, 1983.

  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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