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Classical Mechanics

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The Mass of Jupiter

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In astronomy, the masses of object's are calculated by observing the orbit of an object orbiting that mass. This question will ask you to duplicate that research using the orbit of the moon Io around the planet Jupiter. Assume that Io orbits in a uniform circular orbit with a period of 1.76 days at a radius of 422,000 km.

What is the mass of Jupiter?

Note, you will need to use the physics of circular motion as well as Newton's law of gravity. You may assume that the mass of Jupiter is much greater than the mass of Io.

A

$1.31 \times 10^{16} kg$

B

$1.99 \times 10^{21} kg$

C

$4.92 \times 10^{23} kg$

D

$1.92 \times 10^{27} kg$

E

$4.92 \times 10^{30} kg$