Consider two planets in space that gravitationally attract each other. If the masses of both planets are doubled, and the distance between them is also doubled, then the force between them is
A) twice as much.
B) one quarter.
C) four times as much.
D) half as much.
E) none of these

Question

Quizplus · Accepted Answer

The gravitational force between two masses is given by Newton's law of universal gravitation, $F = G\frac{m_1m_2}{r^2}$, where $F$ is the gravitational force, $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between the centers of the two masses. If the masses of both planets are doubled, the numerator of the fraction becomes 4 times larger because both $m_1$ and $m_2$ are doubled ($2m_1 \times 2m_2 = 4m_1m_2$). If the distance between them is also doubled, the denominator of the fraction becomes 4 times larger because the distance squared ($r^2$) becomes $4r^2$ when $r$ is doubled. Thus, the increase in the numerator is exactly offset by the increase in the denominator, resulting in the gravitational force remaining unchanged.

Consider Two Planets in Space That Gravitationally Attract Each Other