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# Kepler watch

1. Planet A and planet B are in circular orbits around a distant star. Planet A is 5.5 times farther from the star than is planet B.

What is the ratio of their speeds Va/Vb?

So I know that (rA/rB)^3 is equal to (Ta/Tb)^2 and I can find the ratio of their periods (basically, (5.5/1)^1.5). How do I go from here?

On another note, is this question actually Keplerish? Should I just be assuming that they both take the same time to finish one orbit and do circular geometry?
2. omega = 2*pi/T
v = omega*r
So you should be able to get v ratios.

They don't take the same time to finish an orbit, if they did, ratio of T would be 1 which it isn't.
3. mv^2/r = GMm/r^2

so

v^2 = GM/r

so

v1^2/v2^2 = r1/r2

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Updated: October 9, 2009
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