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An asteroid with mass 1*109 (to power 9) kg comes from deep space, effectively from infinity, and falls toward Earth.
(a) Find the change in potential energy when it reaches a point 4* 108 (to power 8) from the center of the Earth (just beyond the orbital radius of the Moon). In addition,find the work done by the force of gravity.
(b) Calculate the asteroid's speed at that point, assuming it was initially at rest when it was arbitrarily far away.
(c) How much work would have to be done on the asteroid by some other agent so the asteroid would be traveling at only half the speed found in(b) at the same point?
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