Suppose an artificial satellite has been put into circular orbit about the Earth, at a distance from the center of the Earth equal to 1/4 the distance from the Earth's center to the Moon's center. In terms of the Moon's period T_m, what will be the period of the satellite? A) 16 T_m. B) 8 T_m. C) T_m. D) T_m/8. E) T_m/16.

Question

Quizplus · Accepted Answer

The period of an object in orbit depends only on the distance from the center of the object it is orbiting. Therefore, the period of the satellite will be the same as the period of an object in orbit at a distance from the center of the Earth equal to 1/4 the distance from the Earth's center to the Moon's center. Using Kepler's Third Law, we can calculate the period of the satellite: (T1/T2)^2 = (R1/R2)^3 where T1 and T2 are the periods of the two objects, R1 and R2 are their distances from the center of the Earth, and we can choose either the Earth or the Moon as the reference object. Let T2 be the period of the Moon, and let R1/R2 = 1/4. Then: (T1/T_m)^2 = (1/4)^3 T1/T_m = (1/4)^(3/2) = 1/8 T1 = T_m/8 Therefore, the period of the satellite is T_m/8, which is answer choice D.

Suppose an Artificial Satellite Has Been Put into Circular Orbit