# 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

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