Suppose that a comet goes around the sun in an elliptical orbit such that the comet at the farthest point in its orbit is 3 times as far from the sun as it is when it is at its closest point. How many times stronger is the gravitational force on the comet due to the sun when it is at its closest point than when it is at its farthest?
A) $\left|\overrightarrow{F_{g}}\right|$ is the same at both positions.
B) $\sqrt{3}$ times stronger
C) 3 times stronger
D) 9 times stronger
E) 27 times stronger
F) The answer depends on the relative masses of the comet and the sun.

Question

Quizplus · Accepted Answer

The gravitational force between two objects is given by Newton's law of universal gravitation, $F_g = G\frac{m_1m_2}{r^2}$, where $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between their centers. Since the distance at the closest point is 1/3 of the distance at the farthest point, the gravitational force at the closest point is $(\frac{1}{1/3})^2 = 3^2 = 9$ times stronger than at the farthest point.

Suppose That a Comet Goes Around the Sun in an Elliptical