SAT Subject Physics Practice Question 53: Answer and Explanation

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Question: 53

10. Two satellites orbit the earth in circular orbits, each traveling at a constant speed. The radius of satellite A’s orbit is R, and the radius of satellite B’s orbit is 3R. Both satellites have the same mass. How does FA, the centripetal force on satellite A, compare with FB, the centripetal force on satellite B ?

A. FA = 9FB
B. FA = 3FB
C. FA = FB
D. FB = 3FA
E. FB = 9FA

Correct Answer: A

Explanation:

Since the centripetal force on each satellite is equal to the gravitational force it feels due to the earth, the question is equivalent to, “How does FA, the gravitational force on satellite A, compare to FB, the gravitational force on satellite B?” Because both satellites have the same mass, Newton’s law of gravitation tells us that the gravitational force is inversely proportional to r2. Since satellite B is 3 times farther from the center of the earth than satellite A, the gravitational force that satellite B feels is the gravitational force felt by satellite A. (Be careful if you tried to apply the formula Fc = for centripetal force and concluded that the answer was B. This is wrong because even though both satellites orbit at a constant speed, they don’t orbit at the same speed, so the formula for centripetal force cannot be used directly.)

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