This is the polar form of a conic with a given
eccentricity e. For planet, we get 0<e<1, i.e., an ellipse.Newton did extensive research in optics and
also in various branches of mathematics. We will not go into the details;
you must be very familiar to calculus.
Newton’s inverse square law was very
controversial. Many scientists did not like his idea of action at a
distance. The controversy was not to be resolved till the 20th
century, when the mathematical techniques were powerful enough to develop a
Now, consider some philosophical aspects of
Newton’s time. One problem was the motion of bodies. Does a body move
relative to another body or relative to absolute space? Newton said it’s
relative to space. Suppose there were two objects – a bucket and the water
in bucket. If bucket started rotating, the water would start moving in water
slowly. If you stopped the bucket, the water would still be moving
irrespective of when you stopped the bucket. Then, there is no relation
between the rotation of water and the bucket. Clearly, the water must be
moving relative to something else, which, as Newton said, is absolute space.
It is called Newton’s bucket experiment. Motion of absolute space finally
ended when Einstein put forward his ideas. Einstein did not consider any
absolute space. Space would be distorted by matter. Matter and space worked
in symbiosis in his model. Matter moved relative to anything; there was no
particular frame of view. So, it was called the theory of relativity. We
will consider this theory meanwhile.