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Newton notebook page (1685): motion in resisting medium, notes on Continental currencies, and theological views of Church Fathers (in Greek)
According to the classic tale by Abraham De Moivre, a friend of Halley and Newton,
“In 1684, Dr. Halley came to visit [Newton] at Cambridge, after they had been some time together, the Dr asked him what he thought the Curve would be that would be described by the Planets supposing the force of attraction toward the Sun to be reciprocal to the square of their distance form it. Sr Isaac replied immediately that it would be an Ellipsis, the Doctor struck with joy & amazement asked him how he knew it, why saith he I have calculated it, whereupon Dr Halley asked him for his calculations without any further delay, Sr Issac looked among his papers but could not find it, but he promised him to renew it, & then sent it him.”
Newton first responded with the short De Motu Corporum in Gyrum (On the Motion of Bodies in Orbits). In 9 pages, he laid out how the elliptical orbit arises from an inverse square force directed toward one focus of the ellipse. The orbit thus describes a conic section, which generalized the problem from the moon to any object moving under an attractive force. Halley saw the power of the work, and encouraged Newton through the months of writing the Principia.
Initially, Newton had followed typical Cartesian fashion by trying to describe orbits as a balance of forces — the centrifugal from the planet’s motion around the center and the centripetal from attraction to the center. By 1672 he was allowing himself to treat the motions purely mathematically, and moved toward the mathematical description seen later in the Principia — straightline motion (inertia), affected by attraction.
This was the central idea challenged by Hooke, who claimed priority for such a treatment. In an exchange of letters with Hooke in 1679, Hooke had asked for Newton’s opinion on his theory of orbital motion (published in 1674, Attempt to Prove the Motion of the Earth). Hooke wrote that he could explain Kepler’s laws as arising from the single attractive force of attraction to the sun, acting on the inherent tangential motion of the moon. In the short 28-page treatise, he argued for the new philosophy, that
“We see therefore the necessity of the conjunction of Physical and Philosophical with Mechanical and Experimental Knowledge, how lame and imperfect the study of Art doth often prove without the conjunction of the study of Nature. . . .”
He provided new arguments for the Copernican system, including that naked-eye observation cannot resolve parallax, so no definitive proof and no argument for or against heliocentric systems. That implies a “vastly bigger” universe than usually imagined. Playing to his strengths, and reputation, in optics, he described flaws in telescope and problems of measurement, provided new design and set-up of telescopes, and measured “a sensible parallax of the Earths Orb . . . confirmation of the Copernican System”.
More to the point for Newton’s interests, Hooke on the last page suggested that the planets have an attractive “power towards their own Centers”, and thus their linear motion is deflected into “compounded Curve”, and “these attractive powers” decrease with distance, although the quantity is unknown by experiment. He promised that “the precise solution will be the key to the universal principle for astronomy.”
But Hooke, despite his claims to the Royal Society that he had undertaken the derivation, did not and could not work out the mathematics. This Newton took to be crucial. He did have the precise solution, and the mathematical construction of deriving it from geometrical principles. Hooke was offended that his conceptual priority received insufficient credit. In Newton’s view, several philosophers (including Huygens, Wren, and Halley) had also come to the same conclusion that Kepler’s rules required a force that receded as an inverse square of distance. The trick was to derive it as a law of motion. Although he himself had adjusted his view from a balancing tendency to a deflected motion — perhaps prodded by Hooke? — Newton was irritated enough to remove whatever credit he had given Hooke. In a letter to Halley, Newton complained that Hooke
“has done nothing and yet written in such a way as if he knew and had sufficiently hinted all but what remained to be determined by the drudgery of calculations and observations, excusing himself from that labour by reason of his other business, whereas he should rather have excused himself by reason of his inability. For tis plain by his words he knew not how to go about it. Now is not this very fine? Mathematicians, that find out, settle, and do all the business, must content themselves with being nothing but dry calculators and drudges; and another that does nothing but pretend and grasp at all things, must carry away all the invention, as well of those that were to follow him, as of those that went before. Much after the same manner were his letters writ to me, telling me that gravity, in descent from hence to the centre of the earth, was reciprocally in a duplicate ratio of the altitude, that the figure described by projectiles in this region would be an ellipsis, and that all the motions of the heavens were thus to be accounted for; and this he did in such a way, as if he had found out all, and knew it most certainly. And, upon this information, I must now acknowledge, in print, I had all from him, and so did nothing myself but drudge in calculating, demonstrating, and writing, upon the inventions of this great man. And yet, after all, the first of those three things he told me of is false, and very unphilosophical; the second is as false; and the third was more than he knew, or could affirm me ignorant of by any thing that past between us in our letters.”
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