All right, here's Flamsteed's answer, which will indeed answer Corey's question. First remark in here. I believe you are endeavoring to define the curve of that comet described in the ether from your theory of motion. And if my assistance is so useful, a design might help. I would lend it most willingly.

Two comments about that, and of course, first of all. Flamsteed doesn't gloat. Remember, Newton wrote Flamsteed is not one comet. Now Newton's back looking at that comet, and Flamsteed doesn't say didn't I tell you so? is that what you're looking at? Not at all, second thing though, the nice willingness I'll do whatever you need to help, Newton totally turns on Flamsteed in about 1712, even to the extent that Mrs. Flamsteed was petrified, when her husband died, that they would come in and destroy all his papers.

So she sneaked them out of Greenwich, so they could be published independently of Newton and Halley. This is one of the least attractive aspects of Newton. He could turn on people, and when he did, he was not a nice person. But it's striking here because Flamsteed is really being as cooperative as possible, so it makes Newton look all the worse when next term we see him doing this.

And down at the bottom I found this question. I have not been strict enough to affirm that there is no such ex-orbitation as you suggest of Saturn, but after the next term if not sooner, I will inquire diligently so we. Though to confess my thoughts freely to you, I can scarce think there should be any such influence since the distance of the planets from each other in those positions is near four radii of the Earth's orbit.

So that in such yielding matter as our ether I cannot conceive that any impression made by the one planet upon it can disturb the motion of the other. But if you think that when they approach so near each other, they're attractive powers exert themselves more vigorously and either draw them nearer or thrust them further from each other than they would do, were the planets at a greater distance.

I can openly say that it seems unlikely such small bodies as they are compared to the Sun. So that's the answer to Cory. Namely, Flamsteed can't conceive of this. But he goes on to say, I've gotta look, okay. Newton's response, I'm giving you the footnotes to these as well.

So you can read them on your own. In my last, I made an allowance for the distance of Jupiter and Saturn, one from another, diminishing their virtue in a duplicate proportion of the distance. But yet I spake there but at random, not knowing their virtues till I had your numbers for Jupiter.

By which I understand his virtue is less than I suppose. But I am still at a loss for Saturn. I have not at all minded astronomy for some years, till on this occasion which makes me more to seek. I cannot with Huygens' book of Saturn. Mercator and another or two, which I have consulted leave me as wise as I was.

Not very. I find Saturn's ring to his body, now he starts going into details, and then makes a remarkable statement that you should remember a we read next term. Now I am upon this subject. I would gladly know the bottom of it before I publish my papers. Okay.

He would gladly figure out everything that's going on before he publishes his papers, okay. This is early 1685, He sends book one of the Principia to Halley in April 1686 and books two and three a year later. So he's got some work to do. Finally, I was apt to suspect there might be some cause or ether unknown to me, which might disturb the sequi alter proportion.

What's he worried about? Some other force disturbing it. Because if some other force is disturbing it, he's gotta be able to take account of that force. That's his big hope, the only force is the gravity toward all the bodies. If that's the only thing going on, and he can calculate the magnitudes of all those forces, he can do something.

If there are other forces out there that he can't determine and calculate, that's not a happy situation, so he's worried about that. For the influences of the planets upon one another seem not great enough, though I imagine Jupiter's influence greater than if your numbers determine it. It would add to my satisfaction if you would be pleased to let me know the long diameters of the orbits of Jupiter and Saturn assigned by yourself and Mr. Halley and your new tables.

That I may see how the proportion, the three has power proportion, fills the heavens together with another small proportion which must be allowed for. Well that's a very interesting remark, another small proportion that must be allowed for. What it tells you is that he's now got a full rigorous solution to the two body problem.

Two bodies with an inverse square attraction toward one another, different in magnitude, going around their center of gravity. Whenever that happens, the correction to the three body problem has a term in the denominator, one plus the ratio of the tendency toward the planet divided by the tendency toward the Sun.

Which I've already told you in the case of Jupiter, that's a number about one in 1,000. So that whole thing is a very, very small correction. One plus one over 1,000. Or 1.001 in that case. Now what's nice about that? There are two nice things about it. Number one, it tells you that if this shows up, this small proportion, Jupiter and the Sun are interacting.

If it doesn't show up, they're not interacting. So we actually have an empirical way to determine whether they're interacting and moving around the common center of gravity. Second, if Jupiter is not the largest, and it's 1 over 1,000, so it actually gives you a chance of detecting it maybe, that's why he wants the exact orbits to see whether he can detect this.

Then all the rest, if they're less than that, you can't detect this correction in them. You can be sure that the tendencies toward them are less than the tendencies towards Jupiter. So you're gonna able to get a cross check on planets for which you don't have satellites what tendency there is toward them and how strong it is, by seeing whether they interact with the Sun with this correction.

So this is quite correct. I'll just summarize. The first two Kepler laws remain in tact in the two body solution. It's a pair ellipses satisfying the area around the center of gravity. That's great. The third law changes for the two body versus the one body case. But that's a good thing because it gives away of detecting interaction versus no interaction.

The problem is detecting it is not easy. Because it's so damn small. All right. This is Flamsteed's last letter in this sequence. I received your papers from Mr. Paget before your last without date, so he's now got a copy of De Motu Corporum. And he gives the distances for Saturn and for Jupiter, so that Newton could do these calculations.

I've already told you there's a slight problem with Saturn and Jupiter. If it's got a 900 year period inequality and it's large, it's called the great inequality. It's huge compared to anything else in our planetary system. Jupiter and Saturn are gonna remain a problem until you figure that out.

And they will and it's a mystery what's going on with Jupiter and Saturn up to 1780 after which Laplace solves it. In that letter I have considered what would be the change of the visible place of Saturn in emitting him thrust, out of his orbit. It would scarce be sensible, though observed in the quadrature's, but it would be something sensible in Jupiter if he be so thrust out of his path.

Now the problem he's doing here is Saturn's very far away, and it's gonna be hard to detect just what Jupiter's action is on Saturn. Okay. That's what he's saying. And I included this last underline because it's now, that's the end of the correspondence with Flamsteed. We have a month of intense correspondence.

It's clear Newton wants more data, it's clear Newton is worried about comet, the comet of 1680-81. He's working on that. It's equally clear he wants to verify planets are interacting with the Sun and interacting with one another, and he wants very precise values of centripetal tendencies. So he's going empirical at this point.

And it's because he has the two body correction, that I feel so sure that the augmented version of De Motu, precedes this communication, the set of communication. The line at the bottom I throw out and we'll take a break at this point. And now on I'm to go to Lincolnshire for a month or six weeks.

When I showed you the chronology of Newton's life two weeks ago, Rupert Hale said in it, that in the 1679 visit after his mother died was the last time he was ever at. I said at the time I thought he had been there at a subsequent time, namely this.

Five or six weeks at this point, maybe he didn't go. Maybe he decided not to go, if he went it's all the more remarkable what he accomplished in 1685. If he spent a month to six weeks at home in his mothers house and then came back, because presumably he didn't do a lot of work there.

And that's what we're gonna be doing after break we're gonna pick up from this correspondence and look what happens after the correspondence in Newton himself.