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An analytical theory for tesseral gravitational harmonics

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Abstract

An analytical method has been developed for the treatment of tesseral harmonic perturbations. The procedure is an iterative Lie transformation technique which avoids the typical eccentricity expansions as well as the numerical singularities normally associated with resonance conditions. At each iteration, terms of the perturbing potential become multiplied by the ratio of the satellite's orbital period to the earth's rotational period. Following a suitable number of iterations, the potential is deemed to be sufficiently small that it may be ignored, with the tesseral effects captured in the transformation.

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Authors and Affiliations

  1. Naval Research Laboratory, GRC International, Washington, D.C., 20375-5355, U.S.A.

    A. M. Segerman

  2. Naval Research Laboratory, Washington, D.C., 20375-5355, U.S.A.

    S. L. Coffey

Authors
  1. A. M. Segerman
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  2. S. L. Coffey
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Segerman, A.M., Coffey, S.L. An analytical theory for tesseral gravitational harmonics. Celestial Mechanics and Dynamical Astronomy 76, 139–156 (2000). https://doi.org/10.1023/A:1008345403145

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  • DOI: https://doi.org/10.1023/A:1008345403145

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