The Earth is about 81 times as massive as the Moon. Suppose the earth and Moon are 10 distance units apart. If you were an astronaut between the Earth and Moon at how many distance units from the Earth will the gravitational attraction on you from the two bodies be equal and opposite?
A) 81 units
B) 9 units
C) 19 units
D) 1 unit

Question

Quizplus · Accepted Answer

The gravitational force is inversely proportional to the square of the distance from the mass causing the attraction. Let $x$ be the distance from the Earth where the gravitational forces are equal. Since the Earth is 81 times as massive as the Moon, and if we consider the total distance between the Earth and Moon to be 10 units, the forces will balance when the distance from the Earth is such that $x^2$ is to $(10-x)^2$ as 1 is to 81, because the force is proportional to the mass and inversely proportional to the square of the distance. Solving this proportion gives $x = 1$ unit from the Earth.

The Earth Is About 81 Times as Massive as the Moon