Suppose the Earth and the Moon carried positive charges of...

Suppose the Earth and the Moon carried positive charges of equal magnitude. How large would the charge need to be to produce an electrostatic repulsion equal to $1.00 \%$ of the gravitational attraction between the two bodies?

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Key Concepts

Newton's Law of Universal Gravitation

This principle describes the gravitational attraction between two masses. It states that any two bodies exert a force on each other that is proportional to the product of their masses and inversely proportional to the square of the distance between them. It is fundamental in calculating the gravitational force acting between the Earth and the Moon.

Coulomb's Law

This law governs the electrostatic force between two charged objects. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Coulomb's Law is essential for determining the magnitude of the repulsive force when both bodies carry similarly signed charges.

Force Equilibrium and Comparison

This concept involves equating and comparing two different forces—in this case, equating a specified fraction of gravitational force with the electrostatic force. By setting the electrostatic force equal to 1.00% of the gravitational force, one can solve for the magnitude of the charge needed. This application of forcing balance is critical for problems that require modifying one force to achieve a particular effect relative to another.

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