Abstract
Lunisolar perturbations of an artificial satellite for general terms of the disturbing function were derived by Kaula (1962). However, his formulas use equatorial elements for the Moon and do not give a definite algorithm for computational procedures. As Kozai (1966, 1973) noted, both inclination and node of the Moon's orbit with respect to the equator of the Earth are not simple functions of time, while the same elements with respect to the ecliptic are well approximated by a constant and a linear function of time, respectively. In the present work, we obtain the disturbing function for the Lunar perturbations using ecliptic elements for the Moon and equatorial elements for the satellite. Secular, long-period, and short-period perturbations are then computed, with the expressions kept in closed form in both inclination and eccentricity of the satellite. Alternative expressions for short-period perturbations of high satellites are also given, assuming small values of the eccentricity. The Moon's position is specified by the inclination, node, argument of perigee, true (or mean) longitude, and its radius vector from the center of the Earth. We can then apply the results to numerical integration by using coordinates of the Moon from ephemeris tapes or to analytical representation by using results from lunar theory, with the Moon's motion represented by a precessing and rotating elliptical orbit.
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References
Bureau de Longitudes: 1971,Connaissance des Temps, Paris, p. xix.
Kaula, W. M.: 1961,Geophys. J. 5, 104.
Kaula, W. M.: 1962,Astron. J. 67, 300.
Kozai, Y.: 1966, ‘Lunar Perturbations with Short Periods’, SAO Spec. Rep. No. 235, Cambridge, Mass.
Kozai, Y.: 1973, ‘A New Method to Compute Lunisolar Perturbations in Satellite Motions’, SAO Special Report 349, Cambridge, Mass.
Lee, W. N.: 1971, ‘The Transformation of a series Expansion in Solid Spherical Harmonics under Translation and Rotation of Coordinates’, TE-47, MIT Measurement System Laboratory, Cambridge, Mass.
Plummer, H. C.: 1960,An Introductory Treatise on Dynamical Astronomy, Dover Reprint, New York.
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Giacaglia, G.E.O. Lunar perturbations of artificial satellites of the earth. Celestial Mechanics 9, 239–267 (1974). https://doi.org/10.1007/BF01260515
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DOI: https://doi.org/10.1007/BF01260515