Physics

Physics

Problem

Satellite X orbits a planet with orbital radius RR. Satellite Y orbits the same planet with orbital radius 2R2R. Satellites X and Y have the same mass. What is the ratio centripetal acceleration of Xcentripetal acceleration of Y\frac{\text{centripetal acceleration of X}}{\text{centripetal acceleration of Y}}? A. 14\frac{1}{4} B. 12\frac{1}{2} C. 2 D. 4
Intuitive explanation

The key is recognizing that centripetal acceleration depends on orbital speed and radius, both of which change with distance from the planet. Use Kepler's third law to find how orbital speed scales with radius: satellites farther out move slower. Then apply ac=v2ra_c = \frac{v^2}{r} to see how acceleration drops as you move outward—it falls off faster than the radius increases.

Intuitive explanation

The key is recognizing that centripetal acceleration depends on orbital speed and radius, both of which change with distance from the planet. Use Kepler's third law to find how orbital speed scales with radius: satellites farther out move slower. Then apply ac=v2ra_c = \frac{v^2}{r} to see how acceleration drops as you move outward—it falls off faster than the radius increases.

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