# Question 7.11: A NEAR-EARTH ASTEROID GOAL Use gravitational potential energ...

**A NEAR-EARTH ASTEROID**

**GOAL** Use gravitational potential energy to calculate the work done by gravity on a falling object.

**PROBLEM** An asteroid with mass m=1.00 \times 10^9 \mathrm{~kg} comes from deep space, effectively from infinity, and falls toward Earth. (**a**) Find the change in potential energy when it reaches a point 4.00 \times 10^8 \mathrm{~m} 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?

**STRATEGY** Part (**a**) requires simple substitution into the definition of gravitational potential energy. To find the work done by the force of gravity, recall that the work done on an object by a conservative force is just the negative of the change in potential energy. Part (**b**) can be solved with conservation of energy, and part (**c**) is an application of the work-energy theorem.

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