[Proj] Geodesics on Saturn's moons

Charles Karney ckarney at sarnoff.com
Wed Apr 1 05:39:11 EST 2009

I've updated my geodesic routines.  For documentation go to


The code itself (C++ classes and the Geod utility) is available at


The main changes are:

    * code has been sped up modestly (about 25-30%) by trimming the
      orders of the series used and by improving the starting guesses
      for Newton's method for the inverse problem.

    * a prolate spheroid can be specified by a negative reciprocal

    * the Geod utility accepts the following new options (type Geod -h,
      for details):
      -e a r, to set the ellipsoid parameters,
      -b, to report azi2 as a back azimuth,
      -a, to accept and report distances in terms of arc length on the
          auxiliary sphere.

Example: to determine a geodesic for a pair of points on Tethys, one of
Saturn's moons (which is prolate on account of tidal forces?), do

    echo 30N 0E 28S 180W | ./Geod -e 529300 -47.7 -i -p 0
    44.80204 136.31245 1660275

Still to do:

    * More documentation (probably at least a month off)
    * More thorough analysis of Newton's method for inverse problem

Charles Karney <ckarney at sarnoff.com>
Sarnoff Corporation, Princeton, NJ 08543-5300

URL: http://charles.karney.info
Tel: +1 609 734 2312
Fax: +1 609 734 2662

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