Newton, Isaac (1642–1727)

5. Gravity as a universal force of interaction

The systematic dependencies by means of which Keplerian phenomena become measures of celestial forces are one-body idealizations. Universal gravity entails interactions among bodies, producing perturbations that require corrections to the Keplerian phenomena. The Principia includes a successful treatment of two-body interactions and some promising, though limited, results on three-body effects in lunar motion. But the full significance of the inferences that could be drawn from universal gravity did not become clear until Clairaut’s analysis of the precession of the lunar orbit in 1749, and Laplace’s determination in 1785 of the roughly 880-year ‘Great Inequality’ in the motions of Jupiter and Saturn.

Such successful treatments of perturbations do more than provide corrections to Keplerian phenomena. They also show that Newtonian measurements of inverse-square centripetal forces continue to hold to high approximation in the presence of perturbations. Interactions with other bodies account for the precessions of all the planets except Mercury. Even in the case of Mercury, the famous 43 seconds-of-arc-per-century residual in its precession yields -2.000000157 as the measure of the exponent, instead of the exact -2 measured for the other planets. That such a small discrepancy came to be a problem at all testifies to the extraordinary level to which Newton’s theory of gravity demonstrates an ideal of empirical success.