, Volume 3, Issue 1, pp 3-66

A semi-analytic theory for the motion of a lunar satellite

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A semi-analytical solution to the problem of the motion of a satellite of the moon is presented. Perturbative effects which are considered include those due to the attraction of the moon, earth, and sun, the non-sphericity of the moon's gravitational field, coupling of lower-order terms, solar radiation pressure, and physical libration. Short-period terms and intermediate-period terms, terms with the period of the moon's longitude, are produced by means of von Zeipel's method; it is proposed to obtain the secular perturbations, and those depending only on the argument of perilune, by numerical integration of the equations of motions. The short-period terms and intermediate-period terms are developed up to second order, where first order is 10−2. The secular perturbations and perturbations dependent on the argument of perilune are obtained to third order.