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GEOGRAV

GEOGRAV

Name


  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


  GEOGREAD, 'egm96', egm96
  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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