An astronaut is in equilibrium when he is positioned 140 km from the center of asteroid X and 581 km from the center of asteroid Y, along the straight line joining the centers of the asteroids. What is the ratio of the masses X/Y of the asteroids?
A) 0.0581
B) 17.2
C) 0.241
D) 4.15

Question

Quizplus · Accepted Answer

The gravitational force between the astronaut and asteroid X is equal to the gravitational force between the astronaut and asteroid Y. Therefore, the ratio of the masses of the asteroids is equal to the ratio of the squares of the distances between the astronaut and the asteroids.$$M_X/M_Y = (140 km/581 km)^2 = 0.0581$$

An Astronaut Is in Equilibrium When He Is Positioned 140