Using simple harmonic motion to follow the Galilean moons testing Kepler's third law on a small system

摘要

The motion of the four Galilean moons of Jupiter is studied in this work. Themoons had their positions with respect to the centre of the planet measuredduring one week of observation by means of telescopic charge coupleddevice images. It is shown that their movement can be well described as asimple harmonic motion. The revolution period and the orbital radius of eachmoon could be extracted from the various images and they were analysed interms of Kepler's third law and Newton's law of universal gravitation. Themass of Jupiter could be evaluated within a 2% discrepancy using this simplemethod.