# History of Newtons law of gravitation

I have some questions about the history of Newtons law of universal gravitation.

1. Did Newton discover his three laws of motion before he discovered the universal law of gravitation?

2. I know two versions of how he discovered it. The first one is that he applied Keplers laws to derive it. The second one is that he considered the motion of the moon compared to an imaginary cannon ball going around the earth. More precisely he compared the centripetal accelerations of the two (assuming that the orbit of the moon is circular). Knowing the radius $r_E$ of the earth and that the distance of moon earth is roughly $60 \cdot r_E$ he derived that the centripetal acceleration of the moon is $3600 = 60^2$ times smaller than that of the cannon ball ($g = 9,81\,\mathrm{\frac{m}{s}}$). Thus he guessed the $\frac{1}{r^2}$ dependency. With his second and third law he also established the proportionality to the masses of moon and earth. I think he already tried this 15 years but didn't succeed because the radius of the earth was not known precisely enough. A third version I know is that at first he did the second derivation and after that he also did it using Keplers laws.

It would be great if someone could bring all this into the correct history order and give more details and dates about the history of the discovery of the universal law of gravitation. I am also looking for good references about this.

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– Ben Crowell Jun 13 '13 at 21:39
This is only related to what you ask, in case you do not already know. Thomas Kuhn's dissertation on the Copernician Revolution is a classic and reads like some SciFi novels, – babou Jun 13 '13 at 22:33

The first law and some aspects of the second predate Newton. I believe there's a story about how he did the moon calculation but got the wrong answer, only finding out years later that it was because the number he had access to had been in the wrong units. (I think he may have had to rely on his memory because of the plague, which prevented him from visiting a big-city library.) Inverse-square laws were already known before Newton, and people had already speculated that gravity might be inverse square.

Newton's really original accomplishments weren't the three laws of motion or the law of gravity. What was really original was: (1) conceiving of these as universal laws that would apply both on earth and in the heavens; and (2) developing the mathematical techniques that would allow these laws to be used to prove and explain Kepler's laws.

Like some other great scientists, Newton wrote up his work in a way that didn't reveal how he came to his conclusions. The Principia is written in the style of Euclid's elements, which was the model of mathematical reasoning at the time. Like Euclid, he wrote laws (postulates) as if they'd been received directly from God on a stone tablet. Newton also invented the calculus, and most likely used it to work out a lot of his physics, but when he presented his work to other people, he couldn't present it using calculus, or even algebra, which educated people of the time didn't know. He was a secretive, private, and asocial person, and he was especially secretive about his work in alchemy and his Arianism (which he wrote a vast amount about, and which would have gotten him in trouble if he'd revealed it). One of the reasons for the Newton-Leibniz controversy over credit for the calculus was that Newton didn't disseminate his results for decades.

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