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

The motion of the four Galilean moons of Jupiter is studied in this work. The moons had their positions with respect to the centre of the planet measured during one week of observation by means of telescopic charge coupled device images. It is shown that their movement can be well described as a simple harmonic motion. The revolution period and the orbital radius of each moon could be extracted from the various images and they were analysed in terms of Kepler’s third law and Newton’s law of universal gravitation. The mass of Jupiter could be evaluated within a 2% discrepancy using this simple method.