Newton's Law of Gravitation

For masses m and M that are separated by a distance r, the gravitation force of one mass on the other is:

Fg = -
G m M

G is the universal gravitational constant that measures the "strength" of the gravitational interaction:   G = 6.67 x 10-11 N m2 / kg2

Important points:

  1. The minus sign indicates that the force is attractive; there is no anti-gravity!
  2. The unit vector indicates that the force is colinear with the line connecting the two masses.
  3. The force decreases as the inverse square of the separation between the two masses.

For an object of mass m on the Earth's surface, the gravitational force is:
Fg = -
G Me m
  ≡ - m g

This formula defines the gravitational acceleration g.