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GEOGRAV

GEOGRAV

## Author

Craig B. Markwardt, NASA/GSFC Code 662, Greenbelt, MD 20770
craigm@lheamail.gsfc.nasa.gov
UPDATED VERSIONs can be found on my WEB PAGE:
http://cow.physics.wisc.edu/~craigm/idl/idl.html

## Purpose

Estimate gravitational potential and acceleration by harmonic expansion

## Major Topics

Physics, Gravity, Geodesy, Spacecraft Navigation

## Calling Sequence

GEOGRAV, GEOGMOD, R, PHI, A [, NMAX=NMAX, MMAX=MMAX, UNITS=UNITS]

## Description

GEOGRAV estimates the gravitational potential and acceleration due
to a non-point central body such as the Earth. The computation is
based on an expansion of the potential spherical harmonics. The
coefficients of the expansion, the Cnm and Snm, are assumed to be
known, and available in the GEOGMOD structure (see GEOGREAD).
Various gravity solutions are available.
The user specifies the geocentric position of interest, referred
to the earth-fixed coordinates. The result is the *inertial*
gravitational potential and acceleration, expressed in earth-fixed
coordinates (i.e., no fictitious potentials or accelerations are
applied). Users should normally rotate the acceleration into
inertial coordinates.
Users can restrict the degree and order of the potential
evaluation using the NMAX (order) and MMAX (degree) keywords.
Input *and* output units are specified using the UNITS keyword,
which is an integer value between 1 and 3. The allowed values are:
UNITS Accel. Pot. Position
1 (cgs) cm/s^2 (cm/s)^2 cm
2 (mks) m/s^2 (m/s)^2 m
3 (km) km/s^2 (km/s)^2 km
Note that the input coordinate units must match the desired output
units.

## Inputs

GEOGMOD - gravity model structure, as returned by GEOGREAD.
R - earth-fixed position(s) of interest. Either a 3-vector, for a
single evaluation, or a 3xN array, for evaluations of N
vectors.
PHI - upon return, the potential(s). Either a scalar or an
N-vector, depending on R.
A - upon return, the acceleration(s). Either a 3-vector or a 3xN
array, depending on R.

## Keyword Parameters

NMAX - maximum spherical harmonic order to evaluate
MMAX - maximum spherical harmonic degree to evaluate
UNITS - specifies input and output physical units (see above).
IMPLEMENTATION NOTE:
The computations in this routine are based on recursion relations
for fully-normalized associated Legendre polynomials. They should
be stable (and avoid underflow) for evaluations of high order
expansions.

## Example

GEOGRAV, egm96, r, phi, a
Read the gravity model "EGM96" and evaluate it at position "R" in
body coordinates. The potential and acceleration are returned in
PHI and A.

## References

Holmes, S. A. & Featherstone, W. E. 2002, "A unified approach to
the Clenshaw summation and the recursive computation of very
high degree and order normalised associated Legendre functions,"
J. Geodesy, 76, 279
McCarthy, D. D. (ed.) 1996: IERS Conventions, IERS T.N. 21.
http://maia.usno.navy.mil/conventions.html
Pines, S. 1973, "Uniform Representation of the Gravitational
Potential and its Derivatives," AIAA J., 11, 1508
Roithmayr, C. 1996, "Contributions of Spherical Harmonics to
Magnetic and Gravitational Fields," NASA Memo, NASA Johnson
Space Center, Houston, Texas, USA, 23 Jan 1996
(Republished as: NASA/TM2004213007, March 2004
URL: http://nssdcftp.gsfc.nasa.gov/models/geomagnetic/igrf/old_matlab_igrf/Contributions.pdf )
Seidelmann, P.K. 1992, *Explanatory Supplement to the Astronomical
Almanac*, ISBN 0-935702-68-7

## Modification History

Written and documented, 05 Jan 2004, CM
Documentation additions, CM, 26 Sep 2004
Add missing UNITIZE function, CM, 19 Nov 2004
Allow MMAX=0 case, CM, 2011-06-26

## Todo

Allow perturbations of the main coefficients, because of tides.
\$Id: geograv.pro,v 1.9 2012/02/19 22:44:40 cmarkwar Exp \$

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