I guess most of us are aware of the“apple incident” that led to the developments of the laws of motion. Basically,this in a way led to the development of calculus as well!

As an extension to newton’s observations from this incident, he pondered over the fact that the attractive force that resulted in the apple falling on earth’s surface may be the same attractive force between the moon and the earth, and in fact, he also thought that this very force acts between any two bodies in the universe!

Thus, he formulated the “law of gravitation”, which states:“Any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.”

Now, there was no controversy as such with the first statement i.e. Any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses. But the second statement: inversely proportional to the square of the distance between them,did arise some doubts.

The question that arose was, “Which distance is to be measured?” The distance between centres of both bodies, or the distance between surface of one to the centre of the other, or the distance between their surfaces.

To overcome this, newton calculated the force of attraction between earth and every single point on the moon(don’t ask how); and eventually added them to get the resultant (integration).

And hence, integral calculus was born.

After integrating, what he observed was quite astonishing.The value that he got was almost the same as the one that he calculated when the distance was taken as the distance between their centres.

All this he did, sitting under a tree with just books and papers! Great man, Sir Isaac Newton.

## Answer ( 1 )

I guess most of us are aware of the“apple incident” that led to the developments of the laws of motion. Basically,this in a way led to the development of calculus as well!

As an extension to newton’s observations from this incident, he pondered over the fact that the attractive force that resulted in the apple falling on earth’s surface may be the same attractive force between the moon and the earth, and in fact, he also thought that this very force acts between any two bodies in the universe!

Thus, he formulated the “law of gravitation”, which states:“Any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.”

Now, there was no controversy as such with the first statement i.e. Any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses. But the second statement: inversely proportional to the square of the distance between them,did arise some doubts.

The question that arose was, “Which distance is to be measured?” The distance between centres of both bodies, or the distance between surface of one to the centre of the other, or the distance between their surfaces.

To overcome this, newton calculated the force of attraction between earth and every single point on the moon(don’t ask how); and eventually added them to get the resultant (integration).

And hence, integral calculus was born.

After integrating, what he observed was quite astonishing.The value that he got was almost the same as the one that he calculated when the distance was taken as the distance between their centres.

All this he did, sitting under a tree with just books and papers! Great man, Sir Isaac Newton.

PS: THIS WAS TOLD TO ME BY MY MATHS TEACHER.