http://www.ck12.org Chapter 9. Newton’s Universal Law of Gravity
upon the Moon and other bodies of the solar system. As he expressed it, gravity acts between all objects according
to their mass. On Earth, only the force of gravity with the Earth itself is noticeable because the Earth is much more
massive than all other objects. However, there is a tiny gravitational force between all other objects as well. Newton
expressed the force of gravity as follows:
The Universal Law of GravityThe force,Fbetween two objects is directly proportional to the product of their massesm 1 m 2 and is inversely
proportional to the square of the distancer^2 between their centers:
F=Gm 1 m 2
r^2
whereGis a constant of proportionality called theuniversal gravitational constantand has a value ofG= 6. 67 ×
10 −^11 N·m
2
kg^2.
(Note: In using the Universal Law of Gravity we will assume that the mass of each body is concentrated at its
geometric center.)Check Your Understanding
What is the gravitational force between the two objects inFigure9.6 if each object has mass of 10.0kg and they are
separated by a distancer= 2 .00m?
FIGURE 9.6
According to Newton’s Universal Law of Gravity,
F=
Gm 1 m 2
r^2=
( 6. 67 × 10 −^11 N·m
2
kg^2 )(^10 .0kg)(^10 .0kg)
( 2 .00m)^2= 1. 6675 × 10 −^9 → 1. 67 × 10 −^9 N
This is an amazingly small force. It is a little bit larger than one-billionth of a Newton or about four-tenth of one-
billionth of a pound. Gravity is a very weak force unless there is a huge amount of mass involved, or the distance
between the masses is very small. In fact, gravity is the weakest of the four fundamental forces we discussed earlier.