SAT Subject Physics Practice Question 168: Answer and Explanation

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Question: 168

14.

Two satellites orbit the earth. Their orbits are circular, and each satellite travels at a constant speed. If the mass of Satellite #2 is twice the mass of Satellite #1, which satellite’s speed is greater?

A. Satellite #1, by a factor of
B. Satellite #1, by a factor of 2
C. Satellite #2, by a factor of
D. Satellite #2, by a factor of 2
E. Neither; the satellites’ speeds are the same.

Correct Answer: A

Explanation:

Let m be the mass of a satellite orbiting the earth in a circular orbit of radius r at a constant speed of v. Since the centripetal force is provided by the gravitational force due to the earth (mass M), we can write . Solving for v gives us v = . This result tells us that the mass of the satellite is irrelevant; only the mass of the earth, M, remains in the formula. Since v is inversely proportional to the square root of r, the satellite that’s closer will have the greater speed. In this case, since Satellite #1 has the smaller orbit radius, it has the greater speed, and, since the radius of its orbit is