# Modern Physics/The Law of Gravitation

## Law of Gravitation[edit]

Of Newton's accomplishments, the discovery of the universal law of gravitation ranks as one of his greatest. Imagine two masses, *M*_{1} and *M*_{2}, separated by a distance *r*. The gravitational force has the magnitude

where *G* is the *gravitational constant*:

The force is always attractive, and acts along the line joining the centre of the two masses.

## Vector Notation[edit]

Let's say that we have two masses, M and m, separated by a distance r, and a distance vector **R**. The relationship between **R** and r is given by:

We will also change our force into a force vector, acting in the direction of **R**:

And this gives us our final vector equation:

Notice that since the ratio between **R** and r is normalized, the addition of these terms does not alter the equation, only the direction in which the force is acting.