In 1679, Newton returned to his work on (celestial) mechanics by considering gravitation and its effect on the orbits of planets with reference to Keplers laws of planetary motion. This followed stimulation by a brief exchange of letters in 1679–80 with Hooke, who had been appointed to manage the Royal Societys correspondence, and who opened a correspondence intended to elicit contributions from Newton to Royal Society transactions.Newtons reawakening interest in astronomical matters received further stimulus by the appearance of a comet in the winter of 1680–1681, on which he corresponded with John Flamsteed.After the exchanges with Hooke, Newton worked out proof that the elliptical form of planetary orbits would result from a centripetal force inversely proportional to the square of the radius vector (see Newtons law of universal gravitation – History and De motu corporum in gyrum). Newton communicated his results to Edmond Halley and to the Royal Society in De motu corporum in gyrum, a tract written on about 9 sheets which was copied into the Royal Societys Register Book in December 1684.[56] This tract contained the nucleus that Newton developed and expanded to form the Principia. The Principia was published on 5 July 1687 with encouragement and financial help from Edmond Halley. In this work, Newton stated the three universal laws of motion that contributed to many advances during the Industrial Revolution which soon followed and were not to be improved upon for more than 200 years. Many of these advancements continue to be the underpinnings of non-relativistic technologies in the modern world. He used the Latin word gravitas (weight) for the effect that would become known as gravity, and defined the law of universal gravitation. In the same work, Newton presented a calculus-like method of geometrical analysis using first and last ratios, gave the first analytical determination (based on Boyles law) of the speed of sound in air, inferred the oblateness of the spheroidal figure of the Earth, accounted for the precession of the equinoxes as a result of the Moons gravitational attraction on the Earths oblateness, initiated the gravitational study of the irregularities in the motion of the moon, provided a theory for the determination of the orbits of comets, and much more. Newton made clear his heliocentric view of the solar system – developed in a somewhat modern way, because already in the mid-1680s he recognised the deviation of the Sun from the centre of gravity of the solar system.For Newton, it was not precisely the centre of the Sun or any other body that could be considered at rest, but rather the common centre of gravity of the Earth, the Sun and all the Planets is to be esteemd the Centre of the World, and this centre of gravity either is at rest or moves uniformly forward in a right line (Newton adopted the at rest alternative in view of common consent that the centre, wherever it was, was at rest). Newtons postulate of an invisible force able to act over vast distances led to him being criticised for introducing occult agencies into science.Later, in the second edition of the Principia (1713), Newton firmly rejected such criticisms in a concluding General Scholium, writing that it was enough that the phenomena implied a gravitational attraction, as they did; but they did not so far indicate its cause, and it was both unnecessary and improper to frame hypotheses of things that were not implied by the phenomena. (Here Newton used what became his famous expression hypotheses non fingo). With the Principia, Newton became internationally recognised.He acquired a circle of admirers, including the Swiss-born mathematician Nicolas Fatio de Duillier, with whom he formed an intense relationship. This abruptly ended in 1693, and at the same time Newton suffered a nervous breakdown. Classification of cubics and beyond Descartes was the most important early influence on Newton the mathematician. Descartes freed plane curves from the Greek and Macedonian limitation to conic sections, and Newton followed his lead by classifying the cubic curves in the plane. He found 72 of the 78 species of cubics. He also divided them into four types, satisfying different equations, and in 1717 Stirling, probably with Newtons help, proved that every cubic was one of these four types. Newton also claimed that the four types could be obtained by plane projection from one of them, and this was proved in 1731. According to Tom Whiteside (1932-2008), who published 8 volumes of Newtons mathematical papers, it is no exaggeration to say that Newton mapped out the development of mathematics for the next 200 years, and that Euler and others largely carried out his plan.
Posted on: Sun, 05 Oct 2014 07:16:56 +0000
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