M 2. Newton's generalization of Kepler's third law can be written in a simple way if we use units that compare everythin

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M 2 Newton S Generalization Of Kepler S Third Law Can Be Written In A Simple Way If We Use Units That Compare Everythin 1 (158.09 KiB) Viewed 98 times

M 2. Newton's generalization of Kepler's third law can be written in a simple way if we use units that compare everything to the Earth's orbit around the Sun: P2= where P is the orbital period in Earth-years, a is the semi-major axis in AU, and M is the mass of the central object measured in solar masses (i.e., the Sun's mass in these units is 1.) Remember that this generalized version of the law can be applied to orbital motion around central objects other than the Sun. Using the following data about the Galilean satellites of Jupiter, find the approximate mass of Jupiter in solar masses. (3pts) Period (days) Semi-major axis (AU) lo 1.769 0.0028 Europa 3.551 0.0045 Ganymede 7.155 0.0072 Callisto 16.69 0.0126 Hint 1: You can get an answer using only one of the moons, but you might want to use at least two and compare the results. Are they about the same? a³ p2. Hint 2: You can rearrange the equation to get the mass: M = Hint 3: Make sure you are using the right units!