Planet A and Planet B are in circular orbits around a distant star. Planet A is 6.0 times farther from the star than Planet B. Find the ratio of their speeds. Va/Vb.

Question

Physics

Adolfo Parks

17 May, 13:57

Planet A and Planet B are in circular orbits around a distant star. Planet A is 6.0 times farther from the star than Planet B. Find the ratio of their speeds. Va/Vb.

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Answers (1)

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Aaron Byrd · Answer 1

The answer is easy if you know the physics.

a/a' = (r/R) ^2 = (r/9r) ^2 = 1/81; so that a = a'/81.

A's radial acceleration must be 1/81 of B's. And each acceleration is a = v^2/R and a' = V^2/r, where v and V are the tangential speeds you want the ratio for.

a = v^2/R = v^2/9r = V^2/81r = a'/81 In which case v^2/V^2 = 9/81 = 1/9; so that 1/3 = Va/Vb ANS