Gravitation

Centripetal Force:

  • An object in circular motion keeps on changing its direction.
  • A force called Centripetal Force acts upon the object that keeps on  moving in a circular path.
  • The centripetal force is exerted from the centre of the path.
  • Without the Centripetal Force objects cannot move in circular paths, they will  always travel straight.
  • Example: The motion of the moon around the earth is due to the centripetal force. The centripetal force is due to the force of attraction of the earth. If there were no such force, the moon will travel in a uniform straight line motion.

 

Centripetal Force of Earth on Moon

 

Newton’s Observation:-

  • It is seen that a falling apple is attracted towards the earth. Does the apple attract the earth? If so, we do not see the earth moving towards an apple. Why?
  • According to the third law of motion, the apple does attract the earth. But according to the second law of motion, for a given force, acceleration is inversely proportional to the mass of an object .The mass of an apple is negligibly small compared to that of the earth. So, we do not see the earth moving towards the apple.
  • Extend the same argument for why the earth does not move towards the moon. In our solar system, all the planets go around the Sun. By arguing the same way, we can say that there exists a force between the Sun and the planets. From the above facts
  • Newton concluded that not only does the earth attract an apple and the moon, but all objects in the universe attract each other. This force of attraction between objects is called the gravitational force.

 

Gravitational Force of Earth

Universal law of Gravitation:

Statement:- ”:Every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them. ”  The force is along the line joining the centres of two objects.

 

 

Let two objects A and B of masses m1 and m2 lie at a distance r from each other as shown in Figure.  Let the force of attraction between two objects be F. According to the universal law of gravitation, the force between two objects is directly proportional to the product of their masses. That is,

From the above equation we can rewrite them as the following:

If we remove the proportionality we get proportionality constant G as the following:-

 

The above equation represents Newton’s Universal Law of gravitation:

Hence, 

 $G=\frac{Fr^2}{m_1m_2}$G=Fr2m1m2  

 

  • SI Unit: Nm² kg-²
  • Value of G = 6.673 × 10-11 Nm² kg-² (was found out by Henry Cavendish (1731- 1810))
  • The proportionality constant G is also known as the Universal Gravitational Constant.

 

Importance of Universal law Gravitation:

  1. The force that binds us to the earth;
  2. The moon moving around the earth;
  3. The planets are revolving around the Sun;
  4. The tides is due to moon and the Sun.