The Use of Brown’s Lunar Theory in Lunar Satellite Perturbations by Sun and Earth
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.
KeywordsSatellite Orbit Lunar Satellite Disturbing Function Planetary Equation Full Orbit
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