Two planets in space gravitationally attract each other. If both the masses and distances are doubled, the force between them is
A)one-quarter.
B)half as much.
C)twice as much.
D)four times as much.
E)none of the above

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 their centers. If both masses and the distance are doubled, the new force $F'$ becomes $F' = G\frac{(2m_1)(2m_2)}{(2r)^2} = G\frac{4m_1m_2}{4r^2} = G\frac{m_1m_2}{r^2} = F$. Thus, the force remains unchanged.

Two Planets in Space Gravitationally Attract Each Other