  The group of propositions following the deduction of universal gravity gives indications of the evidential strategy that lies behind the leap to taking this law to be exact. Immediately upon concluding first that the planets would sweep out equal areas in equal times in exact ellipses and then that the orbits would be exactly stationary were it not for the gravitational interactions among the planets, Newton calls attention to the easiest to observe deviations from this idealization, the then still mysterious vagaries in the motions of Jupiter and Saturn which Newton attributes to their gravitational interaction. Because, according to the theory, the idealization would hold exactly in the specified circumstances, these and all other deviations must result from further forces not taken into account in the idealized case. Identifying these forces and showing that, according to the theory, they do produce the deviations is a way for ongoing research to marshal continuing evidence to bear on the theory of gravity. To put the point differently, the initial idealizations that Newton identifies can serve as the starting point for a process of successive approximations that should yield increasingly close agreement with the complex true motions. These idealizations are especially well suited for this purpose precisely because, according to the theory, they would hold exactly were no other forces at work, and hence every deviation from them should be physically telling, and not just, for example, an accidental feature of a curve-fit. Pursuit of such a research program of successive approximations promises to yield either further evidence for the theory of gravity when the program is successful or the exceptions Newton speaks of in Rule 4 that require the theory to be revised.