A discussion of Pontecoulant's solution of the three-body problem of the lunar theory. This solution is applied to the motion of a lunar satellite perturbed by the earth to obtain an estimate of the changes caused in the radial coordinate. It is found that the maximum decrease in nominal perilunar radius depends on the ratio of the angular velocities of the perturbing body and the satellite, and on an eccentricity parameter. For a satellite with an orbital period approximately one-fifteenth that of the moon and with an eccentricity parameter of 0.2, this decrease amounts to about 3 percent of the perilunar radius.
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