Planetary Motion

Abstract

Newton begins this section with a discussion of the observed angular elongation of the Medician stars, the four moons of Jupiter which had recently been discovered by Galileo. The angular elongation of a satellite’s orbit is the number of degrees (minutes, seconds, thirds, etc.) through which an earth bound observer must turn his or her telescope in order for its cross-hairs to traverse the semi-diameter of the satellite’s orbit. This angle can be readily converted into miles or kilometers if the distance from the earth to the satellite is known by some other means. Is there a discernible relationship between the diameter of Jupiter’s satellites’ orbits and their orbital periods? According to Kepler’s third law of planetary motion, the ratio of the orbital periods of any two of the five primary planets about the sun are as the sesquiplicate ratio of the semi-major axes of the ellipses which describe their orbits. Do the satellites of Jupiter and of Saturn also obey Kepler’s third law of planetary motion? And how are these phænomena connected to Newton’s mathematical demonstrations enumerated in Book I.

All astronomers agree that their periodic times are in the sesquiplicate proportion of the semi-diameters of their orbits.

—Isaac Newton