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

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Io, a satellite of Jupiter, has an orbital period of 1.77 days and an orbital radius of $4.22 X 10^{5}$ $4.22 X 10^5$ 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.

Explanation:

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

$T^{2} = \frac{G . M}{4 π} r^{3}$ $T^2 = (G.M)/(4pi)r^3$ 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.

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

1 Answer

Explanation:

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Io, a satellite of Jupiter, has an orbital period of 1.77 days and an orbital radius of 4.22X1054.22 X 10^5 km. From these data, how would you determine the mass of Jupiter?

1 Answer

Explanation:

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