The Earth is about 81 times as massive as the Moon. Suppose the earth and Moon are 240,000 miles apart. If you were an astronaut between the Earth and Moon at what distance from the Earth will the gravitational attraction on you from the two bodies be equal and opposite?
A) 216,000 mi
B) 2963 mi
C) 24,000 km
D) 24,000 miles

Question

Quizplus · Accepted Answer

The gravitational force is equal when the ratio of distances from the two bodies is the square root of the ratio of their masses. Since the Earth is about 81 times as massive as the Moon, the square root of 81 is 9. This means you should be 1 part from the Moon and 9 parts from the Earth for the forces to balance. Since the total distance is 240,000 miles, dividing this by 10 (1 part + 9 parts) gives 24,000 miles from the Moon, which is the same distance from the Earth where the forces balance, making option D correct.

The Earth Is About 81 Times as Massive as the Moon