The Use of Brown’s Lunar Theory in Lunar Satellite Perturbations by Sun and Earth

  • A. E. Roy
Conference paper
Part of the COSPAR-IAU-IAG/IUGG-IUTAM book series (IUTAM)


In order to compute the lunar potential’s effect on the orbit of an artificial lunar satellite it is necessary to calculate and subtract perturbations by Earth and Sun to a high degree of accuracy. The present paper describes how the first- and second-order Earth-solar changes in the elements of the selenocentric Keplerian satellite orbit are obtained by making use of Brown’s lunar theory. Values are given of the accuracy attained by comparing changes in the orbital elements of a typical lunar satellite (of semi-major axis 1.25 times the Moon’s radius, eccentricity O.17 and orbital inclination 30°) calculated from the first-order analytical theory and from numerical integration of the Gauss-Lagrange planetary equations. It is found for example that during two full orbits, the maximum errors in the semi-major axis and periselenium distance are of order 8 cm at most while angular accuracy is equally satisfactory.


Satellite Orbit Lunar Satellite Disturbing Function Planetary Equation Full Orbit 
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  1. 1.
    Brumberg, V. A.: General Perturbations of the Elements of Artificial Lunar Satellites. Bull. Inst. Theor. Astron. Leningrad 8 (1962) 705.MathSciNetGoogle Scholar
  2. 2.
    Kozai, Y.: Motion of a Lunar Orbiter. Publ. Astron. Soc. Japan 15 (1963) 301.Google Scholar
  3. 3.
    Kaula, W. M.: Calculation of Perturbations of Lunar Orbiters. App. III in IMP D and E Feasibility study. Publ. X-672-64-4, NASA Goddard Space Flight Center, 1964.Google Scholar
  4. 4.
    Oesterwinter, C.: Motion of a lunar satellite. Astron. J. 71 (1966) 987.CrossRefGoogle Scholar
  5. 5.
    Tolson, E. H., Gapcynski, J. P.: An Analysis of the Lunar Gravitational Field as obtained from Lunar Orbiter Tracking Data. Presented at the IQSY/COSPAR Assemblies, July 1967.Google Scholar
  6. 6.
    Roy, A. E.: The Theory of the Motion of an Artificial Lunar Satellite. I. Development of the Disturbing function. Icarus 9 (1968) 82.Google Scholar
  7. 7.
    Roy, A. E.: The Theory of the Motion of an Artificial Lunar Satellite. II. The First-order and Second-order Theories. Icarus 9 (1968) 133.Google Scholar
  8. 8.
    Brown, E. W.: Tables of the Motion of the Moon. New Haven: Yale Univ. Press 1919.zbMATHGoogle Scholar

Copyright information

© Springer Verlag, Berlin/Heidelberg 1970

Authors and Affiliations

  • A. E. Roy
    • 1
  1. 1.Department of AstronomyGlasgow UniversityGlasgowUK

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