## Difficult Relationships

In April 1667 Newton returned to Cambridge and, against stiff odds, was elected a minor fellow at Trinity. In the next year, upon receiving his master of arts degree, he became a senior fellow, and in 1669, before he'd reached his twenty-seventh birthday, he succeeded his old tutor, Isaac Barrow, in the coveted position of Lucasian Professor of Mathematics.

There's a temptation to think of Newton as the first of the modern scientists. The phrase Newtonian mechanics is often used to describe the science that, once and for all, swept away the old Aristotelian dogma. Yet Newton himself was really the last of the old guard. He still practiced astrology and believed in the power of alchemy. In 1678 he suffered a serious emotional breakdown, and in the following year his mother died. His response was to cut off contact with others and immerse himself in alchemical research. Hiding behind the pseudonym Jeova Sanctus Unus (God's Holy One), he wrote in his notebooks of ethereal spirits and a secret fire pervading matter. In quicksilver—mercury—he saw "the masculine and feminine semens . . . fixed and volatile, the Serpents around the Caduceus, the Dragons of Flammel."

What part such esoteric musings played in shaping his scientific worldview isn't easy to fathom. But there's no doubt that Newton's alchemical studies opened theoretical avenues not found in the mechanical philosophy—the worldview that sustained his early work. While the mechanical philosophy, which he shared with many great thinkers going back to the Greeks, reduced all phenomena to the impact of matter in motion, the alchemical tradition upheld the possibility of attraction and repulsion at the particulate level. It may be that Newton's later insights in celestial mechanics are traceable in part to his alchemical interests.

In any event, his excursions into the realm of the Philosopher's Stone were interrupted in November 1679 by a letter he received from Robert Hooke. An extraordinarily fertile inventor and source of new ideas—and perhaps the greatest English experimentalist before Michael Faraday in the nineteenth century—Hooke lacked the technical gifts of Newton and some of his other contemporaries; otherwise he might have crafted more comprehensive theories. This weakness often led him into bitter disputes because he would claim that his original concepts had been stolen and elaborated on by his rivals. He had already come into conflict with Newton in 1672, for example, following the publication of Newton's theories of color and light. Hooke insisted that what was correct in Newton's thesis was plundered from his own ideas about light, arrived at seven years earlier, and what was original was wrong. Now Hooke wrote to Newton asking his opinion "of compounding the celestiall motions of the planetts of a direct motion by the tangent and an attractive motion towards the centrall body. . . . [M]y supposition is that the Attraction always is in a duplicate proportion to the Distance from the Center Reciprocall."

The second of these statements refers to an inverse square relationship—exactly the kind of law that Newton had derived in the plague years and then set aside because the moon test data he used didn't quite bear it out. The first statement of Hooke's, however, hints at something new, and in ensuing correspondence, Hooke specified more clearly what he had in mind. There's a central attractingforce, he believed, that falls off with the square of the distance. This was the vital conceptual leap Newton needed to be able to crack the problem of planetary orbits. When he had analyzed the orbital motion earlier, his attention had been on centrifugal tendencies. But now he realized that the key lay in central attraction—the pull of a central force that continuously diverted the orbiting body from what would otherwise have been a straight-line path. The written exchanges with Hooke in 1679 mark the start of a new phase in Newton's gravitational studies. Having seen the way ahead, Newton abruptly broke off the correspondence, and, sometime in early 1680, he began quietly and alone to push toward the brink of an all-embracing gravitational synthesis. First he proved that Kepler's second law followed directly from the assumption that what holds a body in orbit is a central gravitating mass. Then he showed that if the orbital curve is an ellipse under the action of central forces, the radial dependence of the force is inverse square with the distance from the center.

In June 1682 at a meeting of the Royal Society, Newton heard about the work ofJean Picard, who was mapping France with sophisticated instruments and had found the length of a degree to be 69.1 miles. Repeating his former moon test calculations using Picard's value, Newton found that the rate of the moon's fall to Earth exactly corresponded with that predicted by the inverse square law. All the pieces of the puzzle of planetary motion were beginning to fall into place.

No one as yet had an inkling of the tremendous progress Newton had made in bringing gravity to heel. He rarely published anything promptly, and he wasn't about to announce a discovery that might leave him open to criticism. In the coffee houses of London, Robert Hooke and two other leading intellects of the day, the astronomer Edmund Halley and the architect Christopher Wren, met and wrestled with the very problem that Newton had already solved. Finally, in August 1684, Halley paid a visit to the great man in Cambridge, hoping for an answer to his riddle: what type of curve does a planet follow in its orbit around the sun, assuming an inverse square law of attraction? To Halley's joy and amazement, Newton replied, without hesitation, an ellipse. When asked how he knew, Newton said that he'd already calculated it.

In private and without telling anyone, Newton had solved one of the great conundrums of the age. He alone possessed the mathematical tools to have done so because the solution rested on his own brilliantly conceived method of fluxions. The key was to be able to study an orbit not as something frozen and predetermined but as an entity that varied continuously, like a flowing river. Newton considered the motion along an orbit from one point to another during an infinitesimally small interval of time and worked out the deflection from the tangent (a line just touching the curve) during that interval, assuming the deflection to vary as the inverse square of the distance from the center of motion. In this way, he proved, mathematically, beyond any possibility of doubt, that the curve a planet follows under the sun's attraction, or that the moon follows around the Earth, is an ellipse.

Unfortunately, and again this was characteristic of the man, he had misplaced the calculation. Halley, however, was not to be put off so easily. Dynamic, ebullient, charming, and diplomatic, he was the very antithesis of Newton, who at forty-one was fourteen years his senior. Before the young man left, Newton had promised to track down the errant papers and send them to Halley in London. His search proved unsuccessful, and he had to do the calculations again. When Halley eventually received them a few months later, he immediately grasped their importance and again traveled to Cambridge. This time he was given what Halley called "a curious treatise," De motu corporum in gyrum (On the motion of bodies in an orbit). Halley was so excited by what he read that he urged Newton to set down all his main mathematical arguments, proofs and conclusions to do with motion and gravity, together with their implications for astronomy, in the form of a book. Initially, Newton refused, but Halley persisted, bringing his outstanding powers of persuasion to bear.

Just as Rheticus had urged Copernicus to publish De Revolutionibus, so Halley pressed Newton, using just the right blend of tact, urgency, and discreet flattery, and promising to take care of all the practical arrangements. In the end, Newton agreed, and Halley, true to his word, personally financed Newton's magnum opus and guided it safely through a minefield of potential hazards. Not the least of these took the form of Robert Hooke's claim, with some justification, that his letters of 1679 to 1680 had earned him the right to a bit of recognition in Newton's discoveries. Newton was so furious with Hooke for trying to muscle in on what he considered his personal accomplishments that he threatened to suppress the final part of the book altogether, denouncing science as "an impertinently litigious lady." Although Newton finally calmed down under Halley's soothing influence, he wouldn't acknowledge Hooke's contribution; on the contrary, he systematically deleted every possible mention of Hooke's name from his work.

## Telescopes Mastery

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