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      Convert from geographic/planetographic to geodetic coordinates


      Converts from geographic (latitude, longitude, altitude) to geodetic
      (latitude, longitude, altitude). In geographic coordinates, the
          Earth is assumed a perfect sphere with a radius equal to its equatorial
              radius. The geodetic (or ellipsoidal) coordinate system takes into
              account the Earth's oblateness.
      Geographic and geodetic longitudes are identical.
              Geodetic latitude is the angle between local zenith and the equatorial plane.
              Geographic and geodetic altitudes are both the closest distance between
              the satellite and the ground.
      The PLANET keyword allows a similar transformation for the other
      planets (planetographic to planetodetic coordinates).
      The EQUATORIAL_RADIUS and POLAR_RADIUS keywords allow the
      transformation for any ellipsoid.
      Latitudes and longitudes are expressed in degrees, altitudes in km.
      REF: Stephen P. Keeler and Yves Nievergelt, "Computing geodetic
      coordinates", SIAM Rev. Vol. 40, No. 2, pp. 300-309, June 1998
      Planetary constants from "Allen's Astrophysical Quantities",
      Fourth Ed., (2000)

Calling Sequence

      ecoord=geo2geodetic(gcoord,[ PLANET=,EQUATORIAL_RADIUS=, POLAR_RADIUS=])


      gcoord = a 3-element array of geographic [latitude,longitude,altitude],
                or an array [3,n] of n such coordinates.

Optional Keyword Input

      PLANET = keyword specifying planet (default is Earth). The planet
                may be specified either as an integer (1-9) or as one of the
                (case-independent) strings 'mercury','venus','earth','mars',
                'jupiter','saturn','uranus','neptune', or 'pluto'
      EQUATORIAL_RADIUS : Self-explanatory. In km. If not set, PLANET's
                value is used.
      POLAR_RADIUS : Self-explanatory. In km. If not set, PLANET's value is


      a 3-element array of geodetic/planetodetic [latitude,longitude,altitude],
        or an array [3,n] of n such coordinates, double precision.

Common Blocks



      Whereas the conversion from geodetic to geographic coordinates is given
      by an exact, analytical formula, the conversion from geographic to
      geodetic isn't. Approximative iterations (as used here) exist, but tend
      to become less good with increasing eccentricity and altitude.
      The formula used in this routine should give correct results within
      six digits for all spatial locations, for an ellipsoid (planet) with
      an eccentricity similar to or less than Earth's.
      More accurate results can be obtained via calculus, needing a
      non-determined amount of iterations.
      In any case,
          IDL> PRINT,geodetic2geo(geo2geodetic(gcoord)) - gcoord
      is a pretty good way to evaluate the accuracy of geo2geodetic.pro.


      Locate the geographic North pole, altitude 0., in geodetic coordinates
      IDL> geo=[90.d0,0.d0,0.d0]
      IDL> geod=geo2geodetic(geo); convert to equivalent geodetic coordinates
      IDL> PRINT,geod
      90.000000 0.0000000 21.385000
      As above, but for the case of Mars
      IDL> geod=geo2geodetic(geo,PLANET='Mars')
      IDL> PRINT,geod
      90.000000 0.0000000 18.235500

Modification History

      Written by Pascal Saint-Hilaire (shilaire@astro.phys.ethz.ch), May 2002
      Generalized for all solar system planets by Robert L. Marcialis
              (umpire@lpl.arizona.edu), May 2002
      Modified 2002/05/18, PSH: added keywords EQUATORIAL_RADIUS and

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