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AP® Physics C: Mechanics

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Moons Collide: New Circular Orbit?

APPHMC-FSPIUR

Two identical, small moons are traveling in elliptical orbits around a planet (mass $M$, radius $R$). They crash into each other and stick together (losing no mass) and then settle into a stable circular orbit of radius $r$ where $r>>R.$

If the planets originally each have a mass of $m$, what is the orbital speed of the new, circular orbit?

A

$v=\sqrt {\cfrac {GMm}{r}}$

B

$v=\sqrt {\cfrac {2GMm}{r}}$

C

$v=\sqrt {\cfrac {GM}{r}}$

D

$v=\sqrt {\cfrac {Gm}{r}}$

E

$v=\sqrt {\cfrac {2Gm}{r}}$