Newton's Law of Gravitation
Idea: Newton's Universal Law of Gravitation states that any two objects exert a gravitational force of attraction on each other. The direction of the force is along the line joing the objects (See Fig.(7.3)). The magnitude of the force is proportional to the product of the gravitational masses of the objects, and inversely proportional to the square of the distance between them. For the two objects in Figure 7.3:
Figure 7.3: Gravitational Force Between Two Masses
Note:
where kg is the mass of the Earth and m is the radius of the earth and
in agreement with the expression in Chapter 3.
Definition: Gravitional Potential Energy
Due to the gravitational force of attraction, any two objects with masses and located a distance r apart have the ability to do work. Hence they have potential energy. The gravitational potential energy of such objects is:
Note:
If we can approximate:
so that:
This agrees with the expression used in Chapter 5.