 As Corollaries IV and V implied, for a given system of interacting bodies, their center of gravity is unmoved by the actions of the bodies among themselves, and will remain at rest or in uniform motion as long as the bodies are not disturbed by any external forces. This, as we noted, was as close as Newton could come to the notion of an inertial frame. Corollary VI shows that, in very special ideal circumstances—accelerative forces that act equally on all bodies within a system, and accelerate them all in parallel directions—an accelerating system of bodies will behave, internally, as if there were no external forces acting on it at all. Yet Newton’s discovery was not limited to the point made explicitly in Corollary VI. Rather, it was threefold. The second point was that there was in fact a force acting equally and in parallel lines, at least to a high approximation, on important systems of celestial bodies. The system of Jupiter and its satellites, for example, is obviously accelerating, as its center of gravity completes an approximately elliptical orbit around the Sun bound by accelerative forces toward the Sun’s center. But because the accelerations of all the bodies are nearly equal and parallel, their motions among themselves are nearly the same as if no such forces acted, and the system may be treated as the sort of system described in Corollary V. Evidently the accelerations are unequal, since Jupiter and the satellites are at varying distances from the sun, and they cannot be parallel since they are all directed at the center of the sun. But these differences of distance and direction are so small, in comparison with the distance of the entire system from the sun, that they may be neglected. And the same applies to the centripetal acceleration of Saturn’s system. 