Corrections to the spacecraft orbital elements with Xephem 2.9.2

   Here are my corrections to the hyperbolic spacecraft elements in
spacecraft.edb (Pioneer 10, 11 and Voyager 1 and 2 for a total of 14 entries).
Ron Baake of JPL sent me the elliptical elements that he posted to the
newsgroups back in 1991, and I've checked and confirmed that the numbers in
the spacecraft.edb file match them exactly (even to the Update dates in the
comments). 

   The hyperbolic conic sections don't work because of two problems:

   First, the elements Ron gives include a, the elliptical semi-major axis
(which is negative for hyperbolic orbits).  However, the Xephem format for
hyperbolic orbits require q, the Perihelion distance.  They are related by the
following equation:

          q = -a*(e-1)

   The second problem is that Xephem wants T, the Epoch of Perihelion.
However, this isn't given in Ron's data.  He gives an Epoch and a Mean
Anomaly at that epoch.  The data in spacecraft.edb incorrectly use this
epoch as the Perihelion time.  However, using the given Mean Anomaly, one can
find the time difference between the epoch and the perihelion time:

                        3/2
       (t - T) = ( M * a   )/0.98563

 where (t - T) is the time difference between Epoch and Perihelion in days
          M    is the Mean anomaly in degrees
          a    is the semi-major axis in AU

   So, I converted the epoch time to Julian date using Xephem, subtracted
the time difference, and converted back to normal dates using Xephem.  The
corrected hyperbolic segments now work correctly, e.g. Voyager 2-6 is now
at Neptune on 8/25/1989 rather than in the inner solar system.  :-)

   I've also created sc_plus.edb with several new spacecraft.  They include
Mariner 9 and Viking 1 and 2 from JPL navigation publications, updated Galileo
elements from the JPL galileo web page and estimated conic sections for various
missions (Suisei, Mariner 10, Mars 5, Venera 13 and 15 and Vega 1) as 
calculated by Aron Wolf of JPL, generated from the planet positions and 
launch and encounter times.

Vance Haemmerle
Lunar & Planetary Lab
University of Arizona