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If a small planet were discovered whose orbital period was twice that of
Earth, how many times farther from the Sun would this planet be?
10 years ago

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Steve
consider that T^2 = kr^3
That means that T^2/r^3 is constant

T^2/r^3 = (2T)^2/(xr)^3 = 4T^2/x^3r^3
So, 4/x^3 = 1, and x = ∛4

That is, our small planet's orbital radius is ∛4 times earth's.
10 years ago

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