 Thus the situation described by Corollary VI, in Newton’s analysis, emerges as a limiting case of an orbiting system under an inverse-square force. As the size of the orbit is arbitrarily increased, the accelerations toward the center become indistinguishable from equal and parallel accelerations. Evidently, Newton’s proposition provides, characteristically, a general method for treating a variety of possible configurations. But it enabled Newton to address the specific physical fact of the variation in the Sun’s gravity, and its consequences for the superposition upon it of lesser gravitating systems. At the distance of Jupiter or Saturn, a revolving system can be a very nearly regular Keplerian system. As the distance to the Sun decreases, however, differences in magnitude and direction of the accelerations become significant, and at the distance of the Earth-Moon system the motions become nearly intractable. The decisive factor is the proportion between the size of the orbiting system and its distance from the center of attraction. 