On a modification of Hansen's lunar theory

Abstract

In this article a modification of Hansen's lunar theory is given in a form that permits a purely numerical treatment of solar perturbations of planetary satellites or of perturbations caused by the earth in the motion of hypothetical lunar satellites. The development of the coordinates and of the velocities of a satellite is obtained in the form of a trigonometric series in four arguments with numerical coefficients. At the earlier stages of the computation we are not compelled to use Hansen's basic W function. We make use of the fictitious mean anomaly and the replacement ‘bar’ operation, two characteristic features of Hansen's theory, to set up a process of iteration in a convenient form, rather than to compute W. The preference given to the method of iteration was motivated by the circumstance that an input information must not necessarily be limited to the choice of the rotating ellipse as an intermediary orbit. A systematic investigation of the orbital stability of lunar satellites can be based on the development given in this article.