  Recognizing that Newton's reasoning is approximative answers another complaint about the “deduction” of universal gravity: Newton invokes the proposition, if bodies move uniformly in concentric circular orbits whose periods vary as the 3/2 power of the radii, then the centripetal forces acting on these bodies vary as the inverse-square of the radii of the orbits, knowing full well that observation had established for centuries that the planets do not move uniformly in circular  orbits.[44] Newton does indeed invoke this proposition first to conclude (in Prop. 1) that, in modern parlance, there is an inverse-square centripetal acceleration field around Jupiter and Saturn and next to conclude (in Prop. 2) that there is an inverse-square centripetal acceleration field around the  Sun.[45] The orbits of the satellites of Jupiter were then considered to be circular, and hence Newton's inference from their motion was not so problematic. While, however, the orbits of Venus, Jupiter, and Saturn were considered to be very nearly circular, the motion in them had been known from before Ptolemy not to be uniform. Newton expressly concedes that his inference of the inverse-square from the 3/2 power rule for the planets is only approximate when, in the very next sentence, he remarks, “But this second part of the proposition is proved with the greatest exactness from the fact that the aphelia are at rest.” The absence of precession, however, can be used to infer the inverse-square only for each orbit individually, not a single, unified inverse-square centripetal acceleration field encompassing all of the orbits. Newton is accordingly using the 3/2 rule for circular orbits to establish that an inverse-square field holds around the Sun to at least a first approximation, and then using the absence of precession of the individual orbits to tighten the approximation.