Question

Question: (a) what equal positive charges would have to be placed on Earth and on the Moon to neutralize their gravitational attraction? (b) Why don’t you need to know the lunar distance to solve this problem? (c) How many kilograms of hydrogen ions (that is, protons) would be needed to provide the positive charge calculated in (a)?

Short answer

1. The value of equal positive charges to be placed on Earth and on the Moon to neutralize their gravitational attraction is$5.7\times {10}^{13}C$.
2. As the distance gets cancelled due to both their electric and gravitational charges, we don’t need to know the lunar distance to solve this problem.
3. The amount of hydrogen ions needed to provide the positive charge calculated in (a) is$6.0\times {10}^{5}kg$

Step-by-step solution

The given data

Positive charges are needed to be placed on Earth and on the moon to neutralize their gravitational attraction.

Understanding the concept of gravitational force and electric force 

Using the concept of both gravitational and electrostatic force from Coulomb's law, we can get the value of the positive charge of the particle. Again, we can get the number of hydrogen ions using the concept of the net charge

Formulae:

The magnitude of the electrostatic force between any two particles$F=k\frac{\left|q_1\right|\left|q_2\right|}{r^2}\left(i\right)$

The magnitude of gravitational force $F=G\frac{Mm}{r^2}\left(ii\right)$

The number of electrons present, $n=qle\left(ii\right)$

Calculation of the positive charge

The magnitudes of the gravitational and electrical forces must be the same. Thus, using equations (i) and (ii), we can get the value of the net positive charge as given: $(q$

is the charge on either body, $r$is the centre - to- centre separation of Earth and Moon, $G$is the universal gravitational constant, $M$is the mass of Earth, and m is the mass of the Moon.)