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 TOWARDS NEWTON'S THEORIES

TOWARDS NEWTON’S THEORIES

Newton was born on the same day of Galileo’s death. This was the time of great scientific developments. Tycho Brahe’s observations of planetary motions were used extensively by Johannes Kepler to formulate the three laws, famously called the Kepler’s laws of planetary motions. A vivid account of Kepler’s laws is given in the book - ‘Ideas And Opinions Of Albert Einstein’.

The first law says that planets move in elliptical orbit with the Sun at one of its foci. Well, it is irrelevant to ask why the Sun is only at that focus and not on other. Symmetry principle allows it to be on any focus – but not both, except for quantum mechanical probabilities. The second law says that the line joining the Sun and the planet sweeps out equal areas in equal intervals of time. It is like a restatement of the law of conservation of angular momentum. We will see a proof of the second and the first laws in the next section. The third law states the relation between time period and distance from the Sun (it is square of time period of orbit and cube of semi-major axis proportionality relation). Look at the Exercise for this relation.

 There were other discoveries during this era and the most important development was made by Rene Descartes (the Father of modern philosophy) and Fermat. Rene devised something known as the Cartesian coordinate and, it was probably the most important development in mathematics when it comes to analytical part. Coordinate system is a very handy tool for studying the nature as it provides us with the most important tool, the coordinate axis (the only thing, using which, one can measure something). The pre-existing system of axiomatic geometry could not be used to study curves.But coordinate system enabled mathematicians to do so.In analytical system, you have a well defined address for a point which is its beautiful feature in contrast to axiomatic system. More important insights related to vectors and perpendicularity are obtained in this

structure.And Mathematics would becompletely aloof from physics had there not been an analytical system since in physical law, different points of space represent different properties and relativity holds much importance in it. For example, the inverse square law definition that a point at distance r from gravitational body faces a force proportional to the inverse of r’s square reflects the nature of force at this point and its difference from other points.The present theories on vector calculus could not have existed had it been only for Projective (another successful geometry by Desargues) and axiomaitic geometry. It can be said that it was coordinate geometry which created the modern physics. This geometry was developed further by Gauss and Riemann (other mathematicians like Bolyai and Nicholai Lobachevsky developed the axiomatic form of the same Non-Euclidean geometry which, by no means, could be used for analytical purpose like development of relativity) into the world of hyperdimensions where curved spaces played important role.

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