Mars is about 1.5 times as far from the sun as the earth and its mass is about 0.1 times the earth's mass. Relative to the gravitational force the sun exerts on the earth, the force it exerts on Mars is about
A) 0.0044 as much.
B) 0.0067 as much.
C) 0.044 as much.
D) 0.067 as much.

Question

Quizplus · Accepted Answer

The gravitational force between two objects is directly proportional to their masses and inversely proportional to the distance between them squared.

So, the ratio of the gravitational force exerted by the sun on Mars to that on Earth is:

(force on Mars/force on Earth) = (mass of Mars/mass of Earth) × (distance from the sun to the Earth/distance from the sun to Mars)²

Plugging in the given values, we get:

(force on Mars/force on Earth) = (0.1/1) × (1.5/1)² = 0.044

Therefore, the force the sun exerts on Mars relative to the force it exerts on Earth is about 0.044, or 4.4% as much.

Hence, the best choice is C.

Mars Is About 1