Io, a satellite of Jupiter, has an orbital period of 1.77 days and an orbital radius of $4.22 X 10^5$ km. From these data, how would you determine the mass of Jupiter?

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Answer 1 · 2017-09-27T21:43:40

Use Kepler's 3rd law.

It states that the orbital period, T is related to the distance, r as:

$T^2 = (G.M)/(4pi)r^3$ where G is the universal gravitational constant (a very small number for reasons physicists still find hard to explain.)

Rearranging for M should give Jupiter's mass.

Io, a satellite of Jupiter, has an orbital period of 1.77 days and an orbital radius of 4.22 X 10^54.22 X 10^5 km. From these data, how would you determine the mass of Jupiter?