Chapter 13, Problem 36A

If the moon were twice as massive, would the attractive force of Earth on the moon be twice as large? Of the moon on Earth?

To determine

Whether the attractive force of Earth on the moon and also that of moon on Earth twice as large, if the moon were twice as massive.

Explanation of Solution

Introduction:

The force of gravity is one of the fundamental forces in nature, which is responsible for the attractive force between any two objects that are having mass. This force is always attractive because it continuously attempts to pull the bodies together and never tries to push them away from each other. This is the weakest among the four fundamental forces in nature − Strong nuclear force, Electromagnetic force, weak nuclear force, and gravitational force.

The gravitational force $\left(F\right)$ experienced by an object of mass $\left(m\right)$ falling towards the Earth can be written as,

  $F=\frac{GMm}{d^2}$ $\left(1\right)$

Where $\text{ G}$ is gravitational constant, $\text{ G}=6.673\times {10}^{-11}\text{ N}{\text{.m}}^2/{\text{kg}}^2$

  $M$ is mass of the Earth,

  $m$ is mass of an object,

  $d$ is distance between the Earth and an object.

If the moon were twice as massive, then the attractive force of Earth on the moon is twice as large, because the gravitational force is directly related to mass of both the objects under consideration (equation 1). In the same way the attractive force of moon on the Earth also get doubled, if the moon were twice as massive.