Law of Universal Gravitation

Published on Jul 15, 2016

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The story of discovery of gravity by Sir Isaac Newton is a celebrated tale. Though there are many versions of the tale, the essence of the story remains the same. Newton saw an apple falling from a tree and wondered why the apple would fall down instead of remaining suspended in air, moving sideways or flying upwards towards the sky.

After much contemplation Newton concluded that the earth draws the apple towards itself. He reasoned that there is a drawing power in all matter. He also believed that the total drawing power of the earth must be concentrated in its center, not in a lump on the side.

Everything attracts everything else

Newton described gravity as a phenomenon or force with which matter in the universe tends to attract other matter. Later Einstein’s general theory of relativity dictated that gravity is a result of the curvature of a fabric composed of space-time and not a force. Newton’s theory still holds true for daily use and even for applications which do not peculiarly require the general theory of relativity to reveal the true nature of things. Any two objects in the universe will attract each other with a force of gravitation or gravity.

Law of universal gravitation

Based on his initial ideas and hunches, Newton explored gravity to gain a deeper understanding and intuitively came up with a law of universal gravitation. The strength of this law can be understood from the fact that it has enabled space exploration, even though general theory of relativity is accepted as a superior and a more sound theory. According to the law of universal gravitation, every object in the universe attracts every other object with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In order to do away with the proportionality sign, there is a need for a constant. The constant used in the law of universal gravitation is ‘G’, conveniently called the gravitational constant.

Acceleration due to gravity or g

According to Newton’s second law of motion, acceleration of an object can be given by the force exerted on the object divided by the mass of the object. In a similar manner, from the law of universal gravitation, if we consider the attraction between earth and any other object near its surface, we can define the acceleration due to gravity or g. Thus, every object near the surface of the earth is attracted towards it with gravitational force and so it attains an acceleration proportional to the mass of the earth and inversely proportional to the square of the distance between the object and the center of the earth. Again, the proportionality sign can be replaced by an equal sign with the help of the gravitational constant ‘G’. All objects, irrespective of their own mass, when released from a certain height above the surface of the earth fall towards the earth with the same acceleration and hence take the same amount of time in reaching the surface of the earth. The only hiccup is air resistance which resists the motion of the object depending on the cross sectional area of the object.

 

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