From Phenomena to Metaphysics

Abstract

Newton’s methodology in his Principia provides the historical focus for the present methodological study. The background required to fully appreciate the methodology of Newton’s approach to universal gravitation, focused in Book 3 of the Principia, is deliciously complex and delightfully illuminated in the papers by Stein 1990a,b and Wilson 1970.¹ The essential steps are these: The appeal to the experimental work of Kepler and Galileo to establish certain phenomena, principally Kepler’s laws of planetary motion and the law of free fall at the surface of the earth. Next Newton’s basic laws of motion are applied to a certain idealised physical system, namely that of a small object (small in both spatial extent and mass) moving with respect to a much larger mass under the action of a force whose features are purely geometrically determined. The linear vector nature of the assumed forces allows construction of the centre of mass system, which separates out relative from common motions. It is then shown that one can obtain a sensitive equivalence between Kepler’s laws and the geometrical properties of the force, namely that it be directed always along the line of centres between the masses and that it vary inversely as the square of the distance between them. Various instances taken singly, and (less satisfyingly) for the moon. Moreover, Newton then argues that the value of this force for the moon is identical to the force required by Galileo’s law of free fall at the earth’s surface. Appeal is made again to the laws of motion (especially the third law) to argue that the satellites and falling bodies themselves are equally sources of gravitational force. The force is then generalised to a universal gravitation and shown to be applicable to the explanation of various other phenomena, e.g. Galileo’s law for pendulum motion, the tides, etc. while at the same time the corrections for inter-planetary interaction are suitably small, thus leaving the original conclusions drawn from Kepler’s laws intact.