The gravitational force between two bodies of masses m and M offset by a vector distance r is given by
where G is the gravitational constant. Like the electrostatic force, it is an inverse square law.
Newton Eric Weisstein's World of Biography showed that the gravitational force on a body of mass m from a spherically symmetric body of total mass M whose center is located a distance r away is equivalent to the force on m from a point mass M located a distance r away. This nontrivial fact can be proved using calculus, Eric Weisstein's World of Math and was one of the highlights of Newton's Eric Weisstein's World of Biography Principia Mathematica. Newton also showed that the gravitational force felt by a test particle at some point inside a spherically symmetric body (i.e., r < R, where r is the distance from the center of mass and R is the radius of the spherically symmetric body) is equivalent to the that due to a point mass at the center of mass with mass M(r), where M(r) is the total mass contained inside radius r.
Gravitational Acceleration, Gravitational Field, Gravitational Potential Energy, Gravity, Inverse Square Law, Sphere Gravitational Force
