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Gravitational force & its derivation.
Gravitation: Everybody in this universe attracts every other body with a force known as force of gravitation. Gravitation is the force of attraction between any two bodies in the universe. The attraction between the sun and the earth, the attraction between a table and a chair lying in a room, the attraction between the earth and a satellite revolving around it, etc; are all examples of gravitation.
The gravitational force plays an important role in nature as is clear from the following examples:
1. All the planets revolve around the sun due to the gravitational force between the sun and the planets. Thus the gravitational force is responsible for the existence of the solar system.
2. The motion of the moon around the earth is due to the gravitational force between the moon and the earth.
3. Tides in oceans are formed due to the gravitational force between the moon and the water in oceans.
Newton's universal law of gravitation: This law states that everybody in this universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The direction of the force is along the line joining the centers of two bodies.

As shown in figure consider two bodies A and B of masses m1 and m2. Let r be that distance between their centres. If F is the force with which the two bodies attract each other, then according to the law of gravitation,

Where G is a proportionality constant, called universal gravitational constant.


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