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Three asteroids of identical mass (M = 1.03×1012 kg) are orbiting their common center of mass...

Three asteroids of identical mass (M = 1.03×1012 kg) are orbiting their common center of mass in a perfect circle of radius R=75.8 km.

a. What is the period of orbit of one of these asteroids?

You are standing on one of the asteroids. You are standing on the side of the asteroid which faces out from the circle. Your goal is to jump up off the asteroid and escape the entire three asteroid system. The radius of the asteroid upon which you are standing is 710 meters.

b. If on Earth you can jump 1.01 meters, what final speed will you have when you escape the Asteroid cluster?

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