Philosophy 167: Class 12 - Part 11 - Two Proposed Accounts of the Purpose of the Moon Test: to Establish Universal Gravity, and to Establish Copernicanism over Tychonism.

Smith, George E. (George Edwin), 1938-

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Synopsis: Continues discussing the Moon Test and Newton's calculations for the force of gravity.

Philosophy and science.
Celestial mechanics.
Newton, Isaac, 1642-1727.
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ID: tufts:gc.phil167.142
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Now, what's he doing here? He's already figured out, three halves power rule, inverse square, given his solution for the circle. So, years later, this passage the original moon test gets cited as his in 1667, 68', 69', already proposing universal gravity holding the Moon up. This is after Hook and Ether's say that he stole from them.
He's comes to make a claim I had it all beforehand. The claim ultimately gets embellished to do him saying the Principia was written in the 1660's but because he used the wrong radius from Galileo and the test didn't work. He dropped the whole thing, what's the test? If the Earth's gravity is holding the moon in orbit and gravity varies in an inverse square ratio with distance from the center of the Earth and assuming the Moon is 60 earth radii from the earth, the force of gravity should be 3600 times greater than the endeavor to the Moon that we see at just 60 squared.
The comparison thus gives reason to conclude that the moon is not held in orbit by inverse-squared terrestrial gravity. That becomes the later claim. He had the right idea, but Galileo's wrong radius convinced him that the Moon is not being held by terrestrial gravity, okay? Now that's the single most important step toward celestial gravity, the conclusion it's one in time, the terrestrial gravity.
And it's this test that ultimately establishes that. It's a very big deal. He does it in the 1660's he claims and get's the wrong number. The claim get's embellished all over the place, this one I'll read in english to you in a moment. The one on the left of Rupert Halls biography, the Universally Familiar Tale of Newton and the Falling Apple.
Was told un-dramatically by Conduitt who had it from his wife, that's Catherine of course. In the year 1665 when he retired to his own estate, on account of the plague in Cambridge, he first thought of his system of gravity which he hit upon by observing the fall of an apple from a tree.
Some have thought that gravity hit upon Newton while he was voluntarily exiled in England. Voltaire had the entre to a group of men who gathered round the Princess of Wales, Princess Caroline, later queen of England. He met Newton's friend Samuel Clarke, Newton's half-niece Catherine Conduitt and her husband, and Newton's physician.
From the last Voltaire obtained the assurance he gave to readers of his letters of Newton's nation that Newton was certainly a virgin. Biographies do not repeat biographers. From Mrs. Conduit, Voltaire heard the story of Newton and the apple, which he told at some length in letter 15. Being retired in 1666 on account of the plague, to a solitude near Cambridge.
As he was walking one day in the garden, and saw some fruits fall from a tree. He fell into a profound meditation on that gravity. The cause of which had so long been sought but in vain by all philosophers. Why may not this power which causes heavy bodies to descend and is the same without any sensible diminutions.
At the remotest distance from the center of the Earth, or on the summits of the highest mountains, why, said Sir Isaac, may not the power extend as high as the Moon? These are all passages from 18th century embellishing this idea that Newton saw an apple fall and got the idea that the moon is held in orbit by gravity.
I pass this around it's a hilarious picture to that effect from a Japanese painting. Obviously late 19th century or early 20th century. There are three accounts here. To save time I'm going to let you read them on your own. Then Wistin was his follower. Replaced him as Lucasin lecturer.
And was somebody quite close to him. Wistin says an inclination came into Sir Isaac's mind to try. Whether some power did not keep the moon in our orbit. Notwithstanding her projectile velocity, which he knew always tended to go along a straight line. The tangent of that orbit would make stones and all heavy bodies with us fall downward, which we call gravity.
Taking this postulatum, which had been thought of before, that such power might decrease. Might decrease, in a duplicate proportion of the distances etc. He did a trial which he took a degree of a great circle of the earth's surface etc. and he ends up concluding that its the wrong number.
Pemberton gives a very similar account, though it includes references to the apple. Well to the garden. Newton's own account. I found the motion of fluctions. This is in a letter. By degrees in the year 1665 1666. In the beginning of the year 1665 I found the method of approximating series and the rule for reducing any dignity of any binomial.
Into such a series. The same year, in May, I found the method of tangents of Gregory and in November, had the direct method of fluxions, and the next year, in January, had the theory of colors, and in May following, I had entrance into the inverse method of fluxions.
In the same year I began to think of gravity extending to the orb of the moon and having found out how to estimate the force with which a globe resolving within a sphere presses the surface of the sphere. From Keplers rule of the periodical times of the planets being sesquialterate proportion of their distances from the center of the earth, I deduce that the forces which keep the planets in their orbs must be reciprocally is the square of the distances from the centers on which they revolve, and thereby compare the force requisite to keep the moon in her orb with the force of gravity at the surface of the Earth, and found them answer very near.
I think that's right. All this was in the two plague years of 1665, 66', for in those days, I was in the prime of my age of invention, and minded mathematics and philosophy more than at any time since. So, that's all the sources of the origin of the apple story and the bright idea.
Sam Whiteside, in his biography, totally dismisses this remarking that the idea that the theory of gravity was a single bright idea totally, I forget the exact phrase, you can see it in the notes, in predicting that phrase you can see it in the note. But it's silly to even think that's possible.
Almost all of this does appear to be Newton defending himself of having the all this in tow way before he had any contact with. I mean let's look at the problem now. First of all we know something from last week and I'm now just repeating it typed out in my handwriting, rather than a scan of the book.
From Street's Astronomia Nova, we know that he had already proposed that the magnetic tendency, toward the Earth, kept the clouds and everything else towards the Earth, and suggested it extend to the Moon. That's why the Moon moves with the Earth and Jupiter satellites move with it. So, the idea of terrestrial gravity extending to the Moon, Newton, this is the book he learned astronomy from, while he was an undergraduate.
Now, fair enough three halves power rule shows you inverse square. How does the three halves power rule apply around the Earth? We don't know that it does. Why not? Because there's only one body for sure and in fact if you take the Sun to be going around it too, it violates the three has Power Rule quite seriously.
Now one of the nice things is, three has Power Rule if and only if inverse square, given the solution for circles. So my claim is what Newton was doing was trying, this whole document, this two page, is all about Copernicanism versus ticanism. And what he was doing was trying to show that gravity diminishes in an inverse square ratio from the earth to the moon.
If you show that, then the three house power rule has to hold around the Earth too, if the Earth is holding the Sun in its orbit as in Tycanism. But we know it doesn't, therefore we can show Tycanism is false. So my picture of what he was originally doing was trying to show that there's an inverse square relation of terrestrial gravity extending all the way to the moon.
The test failed. He got 4375 instead of 3600, and he drops the issue until 1684. Late 1684. You'll see it week after next when he redoes this with new numbers. Now, why do I think that's the right answer? Well, I looked at the whole document. It is all about comparing econism.
He had read Galileo's Two World Systems. In roughly the time he was home, how else are you going to show that inverse square works around the Earth, that terrestrial gravity? Further than that, when we get to the first version of the Principia, he uses the moon test what for what to establish terrestrial gravity diminishes in an inverse square ratio to the moon.
So the first place he actually uses this at the time when he has the successful moon test is to establish the inverse square. So, my picture is he was doing something perfectly natural at the time, and years later, after Hooke challenged whether Newton had stolen the whole idea of inverse square gravity extending from the earth from Hooke.
He claims, I had all that back in the 1660s. We know he showed that two-page manuscript to David Gregory in an attempt to prove that he had it, because Gregory remarked, he showed me the manuscript that clearly shows he had it before Hooke etc. That doesn't make it any less important.
But the moon tests is you're gonna be hearing about it from now on, it's very celebrated because it's crucial to the idea terrestrial gravity extends into space. Which he then turns into the tendency towards the sun is the same as terrestrial gravity. It's all the same thing. It's all inverse squared.
And I think it's a great moment. It fails because Galileo's having a bad number for the radius of the Earth. It succeeds in 1685 because Picard's giving him a good number for the radius of the Earth and everything falls into place at that point. But it's a very, very celebrated moment here.
I've given you enough I hope. That you understand where the legend of the apple came from. The legend of the garden and the legend that Newton had the key ideas for the Pricipia in the 1660's but Galileo's wrong number stopped him.