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A brief history of gravitation:Copernicus to Newton
Somnath Datta
The article traces the contributions of the pioneers of the theory of gravitation, in particular the heliocentric model of Nicolaus Copernicus, planetary data collected by Tycho Brahe, Johannes Kepler's analysis of Tycho's data leading to the formulation of his three laws of planetary motion, and the ``falling of apple'' episode that gave Newton a sudden flash of a larger vision that unified the orbital motion of the moon, the orbital motion of the planets and the falling of terrestrial objects downward, into one single law of universal gravitation. Based on the model of the heliocentric universe the geocentric paths of Venus and Mars have been constructed in two ways, using a geometrical method, and plotting the relevant parametric equations. The orbital radius $R$ and the time period $T$ of each planet's revolution around the sun has been calculated from the observed value of the angle of its maximum deviation from the sun and the measured value of its synodic period. Kepler's laws of planetary motion have been reviewed and the third law has been checked using the calculated values of $T$ and $R$. The role played by the 3rd Law of planetary motion in shaping Newton's law of universal gravitation has been highlighted. How the inverse square nature of the law of gravitation relates the orbital motion of the moon to the falling of an apple has been worked out in mathematical details.