How fat is Jupiter

Classical Mechanics Level 3

Astronomers determine masses of distant objects by observing their smaller companions. For example, they can measure the period of a planet orbiting around a distant star, measure the radius of its circular orbit, and then employ Newtonian physics to determine the mass of the star.

Callisto is one of the Jupiter's moons. Its period of revolution is \(16.7~\mbox{days}\), and the radius of its circular trajectory is \(1.9 \times 10^6~\mbox{km}\). What is Jupiter's mass in kg?

Details and assumptions

  • The mass of Callisto is much smaller than the mass of Jupiter.

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