GRAVITATION

INTRODUCTION

We are already familiar with the term ‘gravity’ and ‘gravitation’ from chapter 3 and 5, in which kinematics of freely falling objects under gravity and conservation force were discussed. Galileo studied the motion of falling bodies systematically. Newton was the first to realize that the weight of the object on the earth’s surface was due to the force of attraction between the objects and the earth. He also realized that this attraction is universal between any two objects in the universe. In 1660, at the age of 23 he discovered his famous law of universal gravitation and published in his book ‘Principal Mathematica’

In this chapter, we will study Newton’s law of gravitation and apply it to the study of the motion of planets and satellites.

NEWTON’S LAW OF UNIVERSAL GRAVITATION

Historically, in 1665, the college at Cambridge, where Sir Isaac Newton studied, was closed due to plague. So, he went to his home in Lincolnshire. One day, according to a popular story, while sitting under an apple tree he saw an apple falling to the earth. That incident set him to think about gravitation. It occurred to him that the force responsible for a body(or apple) to fall to earth is also responsible for providing centripetal force to keep the moon moving round the earth in a close orbit. Accelerations possessed by the moon and the falling body might have the same origin.

Newton also assumed that both centripetal acceleration and acceleration of free fall are directed towards the centre of the earth acting on the moon and the apple respectively.

The acceleration due to gravity g was known to be equal to 9.8 m/s². Centripetal acceleration was calculated by Newton using expression a=ŵ²r=4Π²r/T² and it was found to be 2.72×10-³m/s². In this calculation T- period of rotation of the moon – was taken as 27.3 days and r-earth-moon distance as 3.84×10^8m.

This expression shows that acceleration, and hence, force is inversely proportional to the square of its distances from the centre of the earth. Newton was able to justify this result only by assuming the mass of the earth to be concerned at centre of the earth.

These ideas generalized by Newton in his well known law of gravitation, are given in the statement below:

“Everybody in the universe attracts every other body which is directly proportional to the product of masses and inversely proportional to the square of  distance between their centre.