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The mutual potential and gravitational torques of two bodies to fourth order

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Abstract

The mutual gravitational potential of two bodies of arbitrary shape is expressed to fourth order in an extension of MacCullagh's Formula for a single body. The expressions for the gravitational torques acting on each body are derived in a form convenient for use in the differential equations describing the rotational dynamics.

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References

  • Borderies, N.: 1978, ‘Mutual Gravitational Potential of N Solid Bodies’,Cel. Mech. 18, 295.

    Google Scholar 

  • Breedlove, W. J.: 1977, ‘A Numerical Study of the Effects of Fourth Degree Terms in the Earth-Moon Mutual Potential on Lunar Physical Librations’,Scientific Applications of Lunar Laser Ranging, J. D. Mulholland (ed.), 65–77, D. Reidel, Dordrecht.

    Google Scholar 

  • Burša, M.: 1973, ‘The Earth-Moon Potential Energy’,Studia Geoph. et Geod. 17, 272.

    Google Scholar 

  • Burša, M., 1974, ‘Moments of the Lunar Disturbing Force’,Studia Geoph. et Geod. 18, 207.

    Google Scholar 

  • Giacaglia, G. and Jefferys, W.: 1973, ‘Motion of a Space Station’,Cel. Mech. 4, 442.

    Google Scholar 

  • Giacaglia, G.: 1979,Transformations of Spherical Harmonics and Applications to Geodesy and Satellite Theory, Invited Paper, 9th Brazilian Congress in Cartography, Curitiba, Parona, Brazil, February 4–8.

  • MacCullagh, J.: 1855,Trans. of the Royal Irish Academy, XXII.

  • Meirovitch, L.: 1968, ‘On the Effect of Higher-Order Inertia Integrals on the Attitude Stability of Earth-pointing Satellites’,Journal of the Astronautical Sciences XV, No. 1, 14–18.

    Google Scholar 

  • Ramsey, A. S.: 1961,Newtonian Attraction, Cambridge University Press.

  • Williams, J.: 1977, ‘Present Achievements from Lunar Laser Ranging’,Scientific Applications of Lunar Laser Ranging, J. D. Mulholland (ed.), 37–50, D. Reidel, Dordrecht.

    Google Scholar 

  • Woolard, E.: 1953,Theory of the Rotation of the Earth Around Its Center of Mass, Astronomical Papers-American Ephemeris and Nautical Almanac Office, Vol. XV, Part I.

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Authors and Affiliations

  1. University of Texas at Austin, Austin, USA

    B. E. Schutz

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  1. B. E. Schutz
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Schutz, B.E. The mutual potential and gravitational torques of two bodies to fourth order. Celestial Mechanics 24, 173–181 (1981). https://doi.org/10.1007/BF01229194

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  • DOI: https://doi.org/10.1007/BF01229194

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