Suppose you want to neutralize the gravitational attraction between the earth and the moon by placing equal amounts of charge on each. (a) Should the charges be both positive, both negative, or one positive and the other negative? Why? (b) Do you need to know the distance between the earth and the moon to find the magnitude of the charge? Why or why not? The masses of the earth and moon are

$5.98 \times 10 ^ { 24 }$

and

$7.35 \times 10 ^ { 22 } \mathrm { kg }$

respectively. Identical amounts of charge are placed on each body, such that the net force (gravitational plus electrical) on each is zero. What is the magnitude of the charge?

Solutions

Verified### Concept

The electrostatic force between 2 charges $q_1$ and $q_2$ is given by

$F=k \dfrac{\left|q_{1}\right|\left|q_{2}\right|}{r^{2}}$

The gravitational force between 2 masses $m$ and $M$ is given by

$F=G \dfrac{m M}{r^{2}}$

When the net force is zero, we have to find the charges on each body

**Given**

The mass of the Earth:

$M= 5.98 \cdot 10^{24} \ \text{kg}$

The mass of the Earth's Moon:

$m= 7.35 \cdot 10^{22} \ \text{kg}$

**The Problem**

Find the value of charges places on both Earth and Moon.