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GEO2GEODETIC

## Name

GEO2GEODETIC

## Purpose

Convert from geographic/planetographic to geodetic coordinates

## Explanation

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=])

## Input

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
used.

## Output

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

None

## Restrictions

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.

## Examples

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
POLAR_RADIUS

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