Fundamentals of Astrodynamics by Roger R. Bate

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In 1665 Newton was a student at the University of Cambridge when an outbreak of the plague forced the university to close down for 2 years. Those 2 years were to be the most creative period in Newton's life. The 23-year-old genius conceived the law of gravitation, the laws of motion and developed the fundamental concepts of the differential calculus during the long vacation of 1666, but owing to some small discrepancies in his explanation of the moon's motion he tossed his papers aside. The world was not to learn of his momentous discoveries until some 20 years later!

To Edmund Halley, discoverer of Halley's comet, is due the credit for bringing Newton's discoveries before the world. One day in 1685 Halley and two of his contemporaries, Christopher Wren and Robert Hooke, were discussing the theory of Descartes which explained the motion of the planets by means of whirlpools and eddies which swept the planets around the sun. Dissatisfied with this explanation, they speculated whether a force. "similar to magnetism " and falling off inversely with the square of distance might not require the planets to move in precisely elliptical paths. Hooke thought that this should be easy to prove whereupon Wren offered Hooke 40 shillings if he could produce the proof with in 2 weeks. The 2 weeks passed and nothing more was heard from Hooke.

Several months later Halley was visiting Newton at Cambridge and, without mentioning the bet, casually posed the question, "If the sun pulled the planets with a force inversely proportional to the square of their distances, in what paths ought they to go? " To Halley's utter and complete astonishment Newton replied without hesitation, "Why, in ellipses, of course. I have already calculated it and have the proof among my papers somewhere. Give me a few days and I shall find it for you." Newton was referring to the work he had done some 20 years earlier and only in this casual way was his greatest discovery made known to the world!

Halley, when he recovered from his shock, advised his reticent friend to develop completely and to publish his explanation of planetary motion. The result took 2 years in preparation and appeared in 1687 as The Mathematical Principles of Natural Philosophy, or, more simply, the Principia, undoubtedly one of the supreme achievements of the human mind.