Newton bluntly refused to correspond but, nevertheless, went on to mention an experiment to demonstrate the rotation of the Earth: let a body be dropped from a tower; because the tangential velocity at the top of the tower is greater than that at the base, the body should fall slightly to the east.

He sketched the path of fall as part of a spiral ending at the centre of the Earth. This was a mistake, as Hooke pointed out; according to Hooke's theory of planetary motion, the path should be elliptical, so that if the Earth were split and separated to allow the body to fall, it would rise again to its original location.

Newton did not like being corrected, least of all by Hooke, but Newton had to accept the basic point; he corrected Hooke's figure, used the assumption that gravity is constant.

Robert Hooke countered by replying that, although Isaac Newton's figure was correct for constant gravity, his own assumption was that gravity decreases as the square of the distance. Several years later, this letter became the basis for Hooke's charge of plagiarism. He was mistaken in the charge.

His knowledge of the inverse square relation rested only on intuitive grounds; he did not derive it properly from the quantitative statement of centripetal force and Kepler's third law, which relates the periods of planets to the radii of their orbits.

Moreover, unknown to him, Newton had so derived the relation more than ten years earlier. Nevertheless, Newton later confessed that the correspondence with Hooke led him to demonstrate that an elliptical orbit entails an inverse square attraction to one focus--one of the two crucial propositions on which the law of all gravitation would ultimately depend.

What is more, Robert Hooke's description of orbiting motion--in which the constant action of an attracting body continuously pulls an object away from its inertial path--suggested a cosmic application for Newton's concept of force and an explanation of planetary paths employing it.

In 1679 and 1680, Newton dealt only with orbital dynamics; he had not yet arrived at the concept of universal gravitation. Universal gravitation

Almost five years later, in August 1684, Newton was visited by the English scientific astronomer Edmond Halley, who was also troubled by the problem of orbital dynamics. Upon learning that Newton had solved the problem, he extracted Newton's promise to send the demonstration. Three months later he received a short tract entitled De Motu ("On Motion"). Already Newton was at work improving and expanding it. In two and a half years, the tract De Motu grew into Philosophiae Naturalis Principia Mathematica, which is not only Isaac Newton's masterpiece but also the basis book for the whole of modern science.

Significantly, De Motu did not state the law of universal gravitation. For that matter, even though it was a treatise on planetary dynamics, it did not contain any of the three laws of motion. Only when revising De Motu did Isaac Newton embrace the principle of inertia his first law and arrive at the second law of motion. The second law, the force law, proved to be an accurate statement of the action of the forces between bodies which had become the central members of his system of nature. When quantifying the idea of force, the second law completed the exact fundamental of mechanics which has been the model of natural science ever since.

The precise mechanics of the Principia are not to be mistaken with the mechanical philosophy. The latter is a philosophy of nature which endeavours to show natural events by means of imagined mechanisms among unobserverable particles.   Continued

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