ABSTRACT
We were introduced to Newton’s law of gravity briefly earlier in the discussion of the concept of force in Chapter 2. Because it is another fundamental principle, let us revisit it and take a close look. This law states that “between any two particles there is a force of attraction that is directly proportional to the product of the masses of the particles and inversely proportional to the square of their distance apart.” The justification for regarding this law as one of our fundamental principles lies in its universality. Newton was led to formulate this law through a study of planetary motion. Before the time of Newton, Kepler, based on Tycho’s observational record of Mars’ motion, had found that the motions of the planets followed certain empirical laws: the celebrated three laws of planetary motion. These laws express certain regularities found in the observed data, but they are descriptive only of the motion of planets about the sun and do not explain why planets revolve about the sun. Newton showed that if he assumed the law of gravitation, then, with the aid of his laws of motion, the motion of the planets could be described and Kepler’s laws derived (Chapter 7). Newton next showed that his laws could be applied to the motion of the moon around the Earth and to bodies falling near the Earth’s surface; he compared the accelerations toward the Earth’s center in the two cases and found that they satisfied the inverse square law. In his work, Newton first assumed and later proved that if the mass of a large sphere is symmetrically distributed, then the gravitational attraction on an external particle is the same as if the mass of the sphere were concentrated at its center. We shall consider this theorem later.
