The radius of the Moon is R. A satellite orbiting the Moon in a circular orbit has an acceleration due to the Moon's gravity of 0.14 m/s². The acceleration due to gravity at the Moon's surface is 1.62 m/s². The height of the satellite above the Moon's surface is A) 3.4R. B) 0.42R. C) 11R. D) 2.4R. E) 1.7R.

Question

Quizplus · Accepted Answer

The acceleration of the orbiting satellite is given by:

a = GM_m/R^2

where G is the gravitational constant, M_m is the mass of the Moon, and R is the distance between the center of the Moon and the satellite.

We are given the acceleration, a = 0.14 m/s^2 and the acceleration due to gravity at the Moon's surface, g = 1.62 m/s^2.

From these, we can find the ratio of the distances from the center of the Moon:

a/g = GM_m/R^2 / GM_m/R_m^2

where R_m is the radius of the Moon.

Simplifying, we get:

R/R_m = √(g/a)

Plugging in the values, we get:

R/R_m = √(1.62/0.14) = 2.42

Therefore, the distance from the center of the Moon to the satellite is 2.42 times the radius of the Moon. Subtracting the radius of the Moon, we get the height of the satellite above the surface:

h = R(2.42 - 1) = 1.42R

Therefore, the answer is closest to choice D, 2.4R.

The Radius of the Moon Is R