Force of Gravity Example – Newton’s Gravitational Force

Isaac Newton showed us the force of gravity between two objects is directly proportional to the mass of the two objects and inversely proportional to the distance between them. Expressed as a formula, the force of gravity is:

where
F_g is the  force of gravity
M is the mass of the first object
m is the mass of the second object
r is the distance between the centers of the two objects
and
G is the gravitational constant = 6.670 x 10^-11 N·m²/kg² in SI units.

This worked force of gravity example problem shows how to use this formula to find the force of gravity between two objects.

Example Problem:
The Earth has a mass of 5.972 x 10²⁴ kg and the Moon has a mass of 7.348 x 10²⁴ kg. The distance between them is 3.844 x 10⁸ m. What is the force of gravity between the Earth and the Moon?

Solution:

Using the formula for gravitational force, plug in the values given in the problem.

F_g = 1.981 x 10²² N

It takes a lot of force between the Moon and the Earth. For trivia’s sake, The force between the Earth and Moon due to gravity is 0.03 moles of Newtons.