Express law of gravitation in vector form. What are its implications?

Vector Form of Newton’s Law of Gravitation

Consider two particles, A and B, with masses m₁ and m₂, separated by a distance r, as shown in the figure.

In vector form, Newton’s law of gravitation describes the gravitational force between these two particles. The force is attractive, meaning that particle m₁ is pulled towards m₂, and vice versa.

The negative sign in the equation signifies that the force is directed opposite to the position vector, confirming that gravitational force is always attractive.

This law further implies that the gravitational forces acting between two particles form an action-reaction pair. These forces are directed along the line joining the centers of the two particles, making gravitational force a central force.