Propagation of Errors in Orbits Computed from Density Layer Models

  1. Soren W. Henriksen,
  2. Armando Mancini and
  3. Bernard H. Chovitz
  1. Foster Morrison

Published Online: 15 MAR 2013

DOI: 10.1029/GM015p0111

The Use of Artificial Satellites for Geodesy

The Use of Artificial Satellites for Geodesy

How to Cite

Morrison, F. (2013) Propagation of Errors in Orbits Computed from Density Layer Models, in The Use of Artificial Satellites for Geodesy (eds S. W. Henriksen, A. Mancini and B. H. Chovitz), American Geophysical Union, Washington, D. C.. doi: 10.1029/GM015p0111

Author Information

  1. Geodetic Research and Development Laboratory, Rockville, Maryland 20852

Publication History

  1. Published Online: 15 MAR 2013
  2. Published Print: 1 JAN 1972

ISBN Information

Print ISBN: 9780875900155

Online ISBN: 9781118663646

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Keywords:

  • Density layer models;
  • Fourier coefficients;
  • Gravitational attraction;
  • Gravity;
  • Mean anomaly

Summary

Errors arise in computations of the gravitational force due to a simple density layer from the need to approximate the layer; these are essentially quadrature errors. These errors in turn cause errors in orbits computed from such a model for the geopotential. To model the quadrature errors, a disturbing potential is defined that is the difference between the potential of a pair of equal mass points and that of a single point lying midway between them and equal to their sum. The total error is constructed by the superposition of a number of such disturbing functions. Two categories of errors exist: the use of too coarse a grid of mass points to simulate the density layer, and use of grids of varying coarseness for regions of the layer close to or remote from the satellite. Procedures are given for preventing biases introduced by these quadrature errors from distorting a solution for geodetic parameters.