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A satellite moves at constant speed v in a circular orbit around the Earth. An object of mass m is ejected from the satellite so that it just barely escapes Earth's gravity. What is the kinetic energy of the object at the moment of ejection?

1. 3/2 m v²
2. m v²
3. 2 m v²
4. 1/2 m v²

Correct answer: m v²

Solution

At the orbital radius, escape speed v_esc = sqrt(2) * v_orbit = sqrt(2) v. The kinetic energy needed to just escape is (1/2) m v_esc² = (1/2) m (2 v²) = m v².

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