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 co¬ordinates and of the velocities of a satellite is obtained in the form of a trigonometric series in four arguments with numerical coef¬ficients. At the earlier stages of the computation we are not com¬pelled to use Hansen's basic W-function:We make use of the fic¬titious 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 pref¬erence given to the method of iteration was motivated by the cir¬cumstance that input information must not necessarily be limited to the choice of the rotating ellipse as an intermediary orbit. A sys¬tematic investigation of the orbital stability of lunar satellites can be based on the development given herein.
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