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A planet has a radius that is double the Earth's radius, and both have nearly the same average density. If vp and ve represent the escape velocities of the planet and Earth respectively, how are vp and ve related?

1. ve equals 1.5 times vp
2. vp equals 1.5 times ve
3. vp equals 2 times ve
4. ve equals 3 times vp

Correct answer: vp equals 2 times ve

Solution

Escape velocity is proportional to the square root of the radius of the planet, given the same average mass density. Since the planet's radius is twice that of Earth, the escape velocity of the planet will be √2 times that of Earth. Thus, vp = 2ve.

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