The theory of the motion of an artificial lunar satellite I. Development of the disturbing function

Abstract

The orbit of an artificial lunar satellite under the attraction of the Moon, Earth, and Sun is studied by the method of the variation of arbitrary constants. Expressions for the first-order changes, both secular and periodic, in the elements of the selenocentric Keplerian orbit of the satellite are given where the disturbing function is due to the Earth and the Sun taken to be point masses and the second harmonic of the Moon's gravitational field. The second-order changes in the elements are also given, as far as the secular and most important long-period terms are concerned. The Earth's selenocentric orbit, as given by Brown's lunar theory, is used so that changes in the Earth-Moon system due to the Sun are taken into account. It is found that the Sun, through these changes, can produce periodic inequalities in the satellite orbit greater than those directly produced by the solar attraction. The effects of the Sun and Earth on the satellite are given to an accurary such that observational data from a close lunar orbiter may be used to provide values of the principal moments of inertia of the Moon to 1 part in 20 000. Depending upon their size and effects, secular or periodic, upon the satellite's orbit, higher harmonics in the Moon's gravitational field can be evaluated to a lesser degree of accuracy.