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On the computation of the spherical harmonic terms needed during the numerical integration of the orbital motion of an artificial satellite

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Abstract

A method is presented for the accurate and efficient computation of the forces and their first derivatives arising from any number of zonal and tesseral terms in the Earth's gravitational potential. The basic formulae are recurrence relations between some solid spherical harmonics,V n,m, associated with the standard polynomial ones.

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Reference

  • DeWitt, R. N.: 1962, Derivatives of Expressions Describing the Gravitational Field of the Earth, U.S. Naval Weapons Laboratory, Technical Memorandum No. K-35/62.

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Authors and Affiliations

  1. Lockheed Missiles and Space Company, Sunnyvale, Calif, USA

    Leland E. Cunningham

  2. Astronomy Dept., University of California, Berkeley, Calif., USA

    Leland E. Cunningham

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  1. Leland E. Cunningham
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Cunningham, L.E. On the computation of the spherical harmonic terms needed during the numerical integration of the orbital motion of an artificial satellite. Celestial Mechanics 2, 207–216 (1970). https://doi.org/10.1007/BF01229495

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  • DOI: https://doi.org/10.1007/BF01229495

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