The motion of the planets , the moon and the Sun was the interesting subject among the students of Trinity College at Cambridge in England. Issac Newton was also one among these students. In 1666, the college was closed for an indefinite period due to plague. Newton was 23 years old then ,he went to his home in Lincolnshire. Issac Newton continued to think about the planetary motion and motion of the moon.
One day Newton sat under an apple tree and had tea with his friends. He saw an apple falling to ground. This incident made him think about falling bodies. He concluded that the same force of gravitation which attracts the apple to the Earth might also be responsible for attracting the moon and keeping it in its orbit. The centripetal acceleration of the moon in its orbit and the downward acceleration of a body falling on the Earth might have the same origin.Newton calculated the centripetal acceleration by assuming the moon's orbit to be circular as shown in figure:
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Acceleration due to gravity on the Earth's surface , g = 9.8`m/sec^2`
Centripetal acceleration on the moon, ac =`v^2/r`
where r is the radius of the orbit of the moon(3.84 x 108 m) and `upsilon` is the speed of the Moon.
He calculated the centripetal acceleration ac= 2.7 x 10-3 `m/sec^2`
Newton assumed that both the moon and the apple are accelerated towards the center of the Earth. But their motions differ, because , the moon has a tangential velocity whereas the apple does not have.
Newton found that ac was less than g and hence concluded that force produced due to gravitational attraction of the Earth decreases with increase in distance from the center of the Earth.He assumed that this acceleration and therefore the force was inversely proportional to the square of the distance from the center of the Earth.
He found that the value of ac was about `1/3600` of the value of g, since the radius of the lunar orbit r is nearly 60 times the radius if the Earth R.
Newton realized that this force of attraction was a case of universal attraction between any tow bodies present anywhere in the universe and proposed the universal gravitational law.
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The law states that every particle of matter in the universe attracts every other particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Mathematically given as F = G`(m_1m_2)/r^2`
where m1 and m2 are the masses of the two bodies, r is the distance between their centres.
The gravitational force between Sun and Earth is very large.
By Using this Angular Acceleration Formula you can solve your problems.