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A satellite moves in a circular orbit at constant speed, with Earth's gravity supplying the centripetal force at every instant. How much work does this centripetal force do on the satellite over one complete orbit?
AZero, because the force is always perpendicular to the velocity
BA large positive amount, equal to its full kinetic energy
CA negative amount, since gravity always opposes the motion
DIt depends on how fast the satellite is moving
Answer & Solution
Correct answer: A. Zero, because the force is always perpendicular to the velocity
1. Centripetal force is always perpendicular to the path, and hence to the object's velocity, since it points toward the center of curvature while the velocity is tangent to the circle.
2. Work is defined as W = F d cos theta, and when theta is 90 degrees, cos theta is zero, so a force perpendicular to the displacement does zero work.
3. Because gravity is acting as the centripetal force here, and it stays perpendicular to the velocity throughout a circular orbit, it does zero work on the satellite over any portion of the orbit, including a full revolution.
4. The satellite's kinetic energy therefore never changes from this force, its speed stays constant, so gravity is not removing energy either, and the result does not depend on how fast the satellite happens to be moving, since the perpendicularity holds at any speed.
_Source: OpenStax College Physics (CC BY 4.0), Ch 6 "Uniform Circular Motion and Gravitation", section 6.3 Centripetal Force_
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