The mechanics of the Principia was an exact quantitative description of the motions of visible bodies. It rested on Newton's three laws of motion: (1) that a body remains in its state of rest unless it is compelled to change that state by a force impressed on it; (2) that the change of motion (the change of velocity times the mass of the body) is proportional to the force impressed; (3) that to every action there is an equal and opposite reaction. The analysis of circular motion in terms of these laws yielded a recipe of the quantitative measure, in terms of a body's velocity and mass, of the centripetal force necessary to divert a body from its rectilinear path into a given circle.

When Newton substituted this formula into Kepler's third law, he found that the centripetal force holding the planets in their given orbits about the Sun must decrease with the square of the planets' distance from the Sun.

Because the moons of Jupiter have to also obey Kepler's third law, an inverse square centripetal force must attract them to the centre of their orbits. Newton was able to show that a similar relation holds between the Earth and its Moon.

The distance of the Moon is approximately 60 times the radius of the Earth. Newton compared the distance by which the Moon, in its orbit of known size, is diverted from a tangential path in one second with the distance that a body at the surface of the Earth falls from rest in one second.

When the latter distance proved to be 3,600 (60 60) times as great as the former, he concluded that one and the same force, governed by a single quantitative law, is operative in all three cases, and from the correlation of the Moon's orbit with the measured acceleration of gravity on the surface of the Earth, he applied the ancient Latin word gravitas literally, "heaviness" or "weight" to it.

The law of universal gravitation, which he also confirmed from such further phenomena as the tides and the orbits of comets, states that every particle of matter in the universe attracts all other material with a force which is equivalent to the product of their masses and inversely proportional to the square of the distance between their centres.

When the Royal Society received Newton's finished manuscript of Book I in 1686, Hooke raised the cry of plagiarism, a charge which cannot be backed-up in any credible sense. On the other hand, Newton's response to it reveals much about him. Robert Hooke would have been satisfied with a generous credit; it would have been a decent gesture to a dying man well into his decline, and it would have cost Newton nothing. Newton, instead, went through his manuscript and eliminated nearly every reference to Hooke. Such was his fury that he refused either to publish his Optics or to accept the presidency of London's Royal Society until Hooke was dead.

Newton's Principia was immediately raised to global prominence. In their continuing loyalty to the mechanical ideal, Continental scientists rejected the idea of action at a distance for a generation, but even in their rejection they could not withhold their admiration for the technical expertise revealed by the work. Young British scientists spontaneously recognized him as their model. Within a generation the limited number of salaried positions for scientists in England, such as the chairs at Oxford, Cambridge, and Gresham College, were monopolized by the young Newtonians of the next generation. Newton, whose only close contacts with women were his unfulfilled relationship with his mother, who had seemed to abandon him, and his later guardianship of a niece, found satisfaction in the role of patron to the circle of young scientists. His friendship with Fatio de Duillier, a S wiss-born mathematician resident in London who shared Newton's interests, was the most profound experience of his adult life.

Immediately after the Principia's publication, Isaac Newton, a fervent if unorthodox Protestant, helped to lead the resistance of Cambridge to James II's attempt to Catholicize it.   Continued

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