Newton's law of universal gravitation

Gravity is an attractive force between all matter: any two objects with mass attract each other. Newton's law of universal gravitation gives the magnitude of this force for two point masses, where each object's mass is treated as concentrated at a single point.

For point masses $$m_1$$ and $$m_2$$ separated by a distance $$r$$, the magnitude of the gravitational force is:

Here, $$F$$ is the force on each mass, $$r$$ is the distance between the two point masses, and $$G$$ is the gravitational constant.

How mass and separation affect the force

The force is proportional to the product of the masses. If one mass doubles while the other mass and the separation stay the same, the force doubles.

The force is inversely proportional to the square of the separation. If the distance doubles while the masses stay the same, the force falls to one-quarter of its original value.

The forces on the two masses

Each mass experiences a force of the same magnitude, directed towards the other mass. The forces therefore act in opposite directions along the line joining the masses, even if the masses are different.