DEDUCTIONS from the previous observations concerning the And, in the first place, since they are sometimes behind, sometimes before Jupiter, at like distances, and withdraw from this planet towards the east and towards the west only within very narrow limits of divergence, and since they accompany this planet alike when its motion is retrograde and direct, it can be a matter of doubt to no one that they perform their revolutions about this planet, while at the same time they all accomplish together orbits of twelve years' length about the centre of the world. Moreover, they revolve in unequal circles, which is evidently the conclusion to be drawn from the fact that I have never been permitted to see two satellites in conjunction when their distance from Jupiter was great, whereas near Jupiter two, three, and sometimes all four, have been found closely packed together. Moreover, it may be detected that the revolutions of the satellites which describe the smallest circles round Jupiter are the most rapid, for the satellites nearest to Jupiter are often to be seen in the east, when the day before they have appeared in the west, and contrariwise. Also the satellite moving in the greatest orbit seems to me, after carefully weighing the occasions of its returning to positions previously noticed, to have a periodic time of half a month. Besides, we have a notable and splendid argument to remove the scruples of those who can tolerate the revolution of the planets round the Sun in the Copernican system, yet are so disturbed by the motion of one Moon about the Earth, while both accomplish an orbit of a year's length about the Sun, that they consider that this theory of the universe must be upset as impossible: for now we have not one planet only revolving about another, while both traverse a vast orbit about the Sun, but our sense of sight presents to us four satellites circling about Jupiter, like the Moon about the Earth, while the whole system travels over a mighty orbit about the Sun in the space of twelve years. 31 NEWTON In the year 1642 Galileo died and Newton was born. Galileo had prepared the way by demonstrating the properties of moving bodies, and by inventing the telescope, which made possible accurate astronomical measurement. The possession of one of Galileo's instruments enabled his contemporary John Kepler to extend the observations of his master Tycho Brahe, and finally to summarize all the varied movements of the planets by simple laws. Of these the most important was that the planets moved in elliptical orbits round the sun at one of the two foci. By Galileo's principle of inertia it was clear that a planet would continue in motion if unobstructed, but the reason for its deflection from a straight path into a closed orbit round the sun was yet to seek. The idea of an attracting force was perhaps in the air, and Newton, turning his unrivalled mathematical genius to the problem, proved that, if the force were inversely proportional to the square of the distance, the path would be an ellipse round the attracting body in one of the foci, in conformity with Kepler's observed law for the planets. Moreover, the familiar phenomenon of weight suggested an attraction by the earth, measured by the rate at which bodies fell to the ground. Why should not this be the same force which kept the moon in her orbit? Reduced by the inverse square law, its magnitude at the distance of the moon could be calculated. Misled by a false estimate of the moon's distance, at first Newton found a discrepancy, and put away his calculations. But hearing of a newer estimate, he took them up again, and in excitement, it is said, so great he could scarce see his figures, he found conformity between his theory and the facts. The moon was but a stone ever falling towards the earth, and so kept in its orbit. The terrestrial and familiar force of gravity controlled the path of a heavenly body. THE MATHEMATICAL PRINCIPLES OF NATURAL PHILOSOPHY By SIR ISAAC NEWTON. Translated into English by ANDRew Motte. From the AUTHOR'S PREFACE SINCE the antients (as we are told by Pappus) made great account of the science of mechanics in the investigation of natural things; and the moderns, laying aside substantial forms and occult qualities, have endeavoured to subject the phænomena of nature to the laws of mathematics, I have in this treatise cultivated mathematics so far as it regards philosophy....Our design not respecting arts, but philosophy, and our subject not manual but natural powers, we consider chiefly those things which relate to gravity, levity, elastic force, the resistance of fluids, and the like forces, whether attractive or impulsive; and therefore we offer this work as mathematical principles of philosophy; for all the difficulty of philosophy seems to consist in this from the phænomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phænomena; and to this end the general propositions in the first and second book are directed. In the third book we give an example of this in the explication of the System of the World; for by the propositions mathematically demonstrated in the first book, we there derive from the celestial phænomena the forces of gravity with which bodies tend to the sun and the several planets. Then from these forces, by other propositions which are also mathematical, we deduce the motions of the planets, the comets, the moon, and the sea. I wish we could derive the rest of the phænomena of nature by the same kind of reasoning from mechanical principles; for I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards each other, and cohere in regular figures, or are repelled and recede from each other; which forces being unknown, philosophers have hitherto attempted the search of nature in vain; but I hope the principles here laid down will afford some light either to that or some truer method of philosophy. In the publication of this work the most acute and universally learned Mr Edmund Halley not only assisted me with his pains in correcting the press and taking care of the schemes; but it was owing to his solicitations that its becoming public is owing; for when he had obtained of me my demonstrations of the figure of the celestial orbits, he continually pressed me to communicate the same to the Royal Society, who afterwards, by their kind encouragement and entreaties, engaged me to think of publishing them. But after I had begun to consider the inequalities of the lunar motions, and had entered upon some other things relating to the laws and measures of gravity, and other forces; and the figures that would be described by bodies attracted according to given laws; and the motion of several bodies moving among themselves; the motion of bodies in resisting mediums; the forces, densities, and motions, of mediums; the orbits of the comets, and such like; I put off that publication till I had made a search into those matters, and could put out the whole together. What relates to the lunar motions (being imperfect) I have put all together in the corollaries of prop. 66, to avoid being obliged to propose and distinctly demonstrate the several things there contained in a method more prolix than the subject deserved, and interrupt the series of the several propositions. Some things, found out after the rest, I chose to insert in places less suitable, rather than change the number of the propositions and the citations. I heartily beg that what I have here done may be read with candour; and that the defects I have been guilty of upon this difficult subject may be not so much reprehended as kindly supplied, and investigated by new endeavours of my readers. CAMBRIDGE, TRINITY COLLEGE, May 8, 1686. ISAAC NEWTON. From THE SYSTEM OF THE WORLD of It was the antient opinion of not a few, in the earliest ages philosophy, that the fixed stars stood immoveable in the highest parts of the world; that under the fixed stars the planets were carried about the sun; that the earth, as one of the planets, described an annual course about the sun, while by a diurnal motion it was in the mean time revolved about its own axis; and that the sun, as the common fire which served to warm the whole, was fixed in the centre of the universe.... It is not to be denied but that Anaxagoras, Democritus, and others, did now and then start up, who would have it that the earth possessed the centre of the world, and that the stars of all sorts were revolved towards the west about the earth quiescent in the centre, some at a swifter, others at a slower rate. However, it was agreed on both sides that the motions of the celestial bodies were performed in spaces altogether free and void of resistance. The whim of solid orbs was of a later date, introduced by Eudoxus, Calippus and Aristotle; when the antient philosophy began to decline, and to give place to the new prevailing fictions of the Greeks.... Whence it was that the planets came to be retained within any certain bounds in these free spaces, and to be drawn off from the rectilinear courses, which, left to themselves, they should have pursued, into regular revolutions in curvilinear orbits, are questions which we do not know how the antients explained; and probably it was to give some sort of satisfaction to this difficulty that solid orbs were introduced. The later philosophers pretend to account for it either by the action of certain vortices, as Kepler and Des Cartes; or by some other principle of impulse or attraction, as Borelli, Hooke, and others of our nation; for, from the laws of motion, it is most certain that these effects must proceed from the action of some force or other. But our purpose is only to trace out the quantity and properties of this force from the phænomena, and to apply what we discover in some simple cases as principles, by which, in a mathematical way, we may estimate the effects thereof in more involved cases; for it would be endless and impossible to bring every particular to direct and immediate observation. We said, in a mathematical way, to avoid all questions about the nature or quality of this force, which we would not be understood to determine by any hypothesis; and therefore call it by the general name of a centripetal force, as it is a force which is directed towards some centre; and as it regards more particularly a body in that centre, we call it circum-solar, circumterrestrial, circum-jovial; and in like manner in respect of other central bodies.... That there are centripetal forces actually directed to the bodies of the sun, of the earth, and other planets, I thus infer. The moon revolves about our earth, and by radii drawn to its centre describes areas nearly proportional to the times in which they are described, as is evident from its velocity compared with its apparent diameter; for its motion is slower when its diameter |