Once Cassini was there, remember, he had already decided in Bologna that Astronomy had to be built from the ground up. That you couldn't trust even the obliquity of the ecliptic, and therefore you couldn't trust any latitude or longitude cuz it wasn't clear what the bloody obliquity even is.
And you knew that the parallax that was being used for corrections, the distance to the Sun, which if you recall is three- the angle was three minutes of arc by T CO had to be reduced to one minute of arc said it couldn't be larger than 15 minutes of art.
Of course, gets published in 1662 by after which almost everybody is using no more than, everybody but Newton and the first edition, is using no more than like 15 seconds of art. But Casini knew those things had to be done properly.so somebody, and I cant, we havent been able to figure out.
I talked to two followers at length about this and none of us can figure out be, by the way i should explain something, much more the royal society and its meetings kept minutes. And those minutes are available so you can get a reasonable idea of who said what at each meeting.
So-and-so complained about this in the experiment, type of thing and they are reasonably, carefully done minutes. Conversations held among these academicians, we have no record of at all. They're seeing one another every day all the time. They're talking to one another. Somewhere along the way, the group of them, and I assume it's Ozu, Piccard and Huygens and perhaps Cassini decide should not be an academician.
The leading French mathematical astronomer should not be included number one. Number two they decide the sensible thing to do with this point, and this is my phrase of course, is push Keplerian astronomy for all it's worth to see where it breaks down. So they essentially adopted the view of we're gonna start with Kepler.
Kepler's our prime system but we're gonna reconstruct astronomy from the ground up using the telescope. Do all new observations, get all new constants, get all new everything and we will prepare a table, a set tables that will tell us just how good Kepler is and Kepler isn't. Now that starts in the 1660s that tables are published in the 1740s, it's an 80 year effort.
And the only person who really knows much about where things stand during that time til he dies in 1712, is the elder Cassini cuz he's managing the whole thing. He's got assistants working under him but he doesn't seem to be the kind of person who hands everything to an assistant he seems to be a very dominant character.
How much of that is maybe his French is not great is perfectly good question but thanks to Cassini we get major expeditions. The first expedition is to send Picard off to Denmark to determine two things. First to get the exact location of so you can now correct the observations made and the second is to collect all those observations.
Write them all out. They're sitting out in Copenhagen. So Picard goes up there and obtains a copy of Tycho's observations. Now I hope everybody understands they didn't have copy machines, this is several volumes, okay. Page after page of observation with people sitting there writing them. That's why it's an expedition to say the least but John was asking before this is the first availability of all of Tycho's data outside of Kepler's hands, or people are sitting in Copenhagen themselves.
And they're brought back to the Royal Observatory where they're not published but the city has them. Two other nice things happens. Picard seems to have been a very nice guy, he, I'm doing the bottom of those four first. He finds this young astronomer working in Copenhagen, likes him a great deal, thinks he's very smart, decides he should bring him back to Paris, he's too good to leave in Denmark.
So Roemer comes back to Paris with Picard. The other thing Picard picks up on is an anomalous motion of the northern stars. Now, I wanna pause a moment. This whole second half I'm gonna go more slowly, cuz it's just some interesting stuff here. Think about course at annual stellar parallax this came up with Chip in the conversation the other day and I suddenly realized I'd never sat back and made you think what is it to observe annual stellar parallax?
All right, so the Earth is going around the sun, which stars are going to look like they do a circle once in the far north, because you are going to look at them from one side of the orbit, then from the other side of the orbit. So the natural place to look for Intestellar parallax was the northern stars and Picard picked up, in the roughly one year he was in Copenhagen, this is not a week visit to copy the things down, okay.
You go up there to do a lot of work, trying to recover all those observations as best he could. He picks up a motion in the northern stars. You'll see in a few moments, Hook picks it up independently of him and thinks he got an interstellar parallax. That doesn't get resolved until the 1720s, I guess it is.
It's not annual stellar parallax. We'll find out what it is after we finish the Principia, that's where James Bradley comes in. But at any rate, they're seeing some sort of motion in the northern stars. When I say it's not annual stellar parallax, it's going the wrong direction to be annual stellar parallax but that's neither here nor there.
The bottom expedition is much, much more ambitious. Cassini realizes that during the next roughly year, 1672, 73 period, Mars is going to be at opposition to the Earth. When the distance between the two orbits is least, that is Mars is going to be at opposition as near as it ever gets to the Earth.
This happened, I think, last year again nether time. At any rate, that gives you the maximum chance to pick up the parallax of Mars. If you know how far Mars is away from the Earth in Earth radii you already know how far Mars is away from the sun.
You've got all the dimensions. So the idea is we need to observe Mars from two very different locations. Let's send young Jean Richer off with a whole host of people for two or three years to the Island of Cayenne where they will setup an observatory. And start doing all these measurements and we will sort out what the parallax is, and with if we'll get atmospheric refraction corrections.
So here's where the thing Richer was charged to do. Cayenne's about five degrees as I recall. I can't remember, five or 15 but I think it's around five degrees from the Equator. It's very near equatory. So, determine the precise of liquidity of the ecliptic. The best place to do that is obviously near the equator, because there you can really get the angle of the motion and the Sun, relative to the Equator.
Precise times of equinoxes determine parallax of Mars, Venus, and the Sun. He wanted to do all of them, but, as I've already indicated, the real hope was to get Mars, because Mars was going to be so near. Venus and Mars are the two planets that give you the best chance, because they're nearest to Earth.
And the nearer you are, the greater the possibility of picking up a parallax angle from two very different locations and Paris and Cayenne are reasonably far apart. Paris is a little over, between 45 and 50 degrees latitude, assuming it's five degrees you're talking about a 40 degree latitude difference, that's a fairly substantial angle the most you can get is 90 but you're getting close to half of that.
Then record position motions in parallax of the moon, record motions of Mercury, record the positions of Southern hemisphere stars. There were no star catalogs for the Southern, Southern hemisphere because there just hadn't been much Astronomy done in the Southern hemisphere of this country. So it was starting to be done significantly at the Cape of Good Hope, but that was one of the things where Richer was required to do and notice, determine the precise longitude and latitude that's geographical.
Longitude and latitude is. He went and spent the better part of two years doing this. He had reasonably good equipment. I'll come to the last two items in just a moment. Reasonably good equipment. He returned, he issued his own report and around 1678, I could have brought it tonight, I have a copy of his full report.
Cassini doesn't finally publish his report from this expedition to Cayenne until 1684, just at the time Newton is starting into the writing of the Principia, it's important because one of the conclusions Cassini reaches is parallax could not be significantly above nine seconds work. Okay, he allows it as much as 9.5, as I remember.
The correct number is around 8.9. So we finally have almost the right number for the parallax. And Cassini determines that Tycho's refraction corrections all have to be thrown out and he gets very, very good refraction corrections. But he takes him 12 years to publish the results from this because he's working over them, doing double checks, doing all sorts of complicated things.
Okay, now the other part of this is interesting for a different reasons gonna become extremely important when we get to the Principia. Huygens has supplied Cassini excuse me Richer with a clock, carefully tuned in Paris. There had been a prior episode between Richer and Huygens that's worth mentioning cuz it will come up later.
Richer had been charged by Huygens to go out with one of his maritime clocks and do observations to get some longitudes and verify the clocks and Richer had really screwed the project up. And Huygens had lost all confidence in him. Okay? But Cassini thought very highly of him, and he was basically reporting to Cassini.
The reason this is important is when Richer comes back and says the gravity is slower at the Equator, less at the Equator than it is at Paris, Huygens doesn't believe him. He doesn't trust anything Richer has to say. It was an unfortunate mistake of Huygens it took him until 1684 before he concludes that Richer is probably right, but what happens is that Richer simply notices that against the stars that his clock is falling behind by two and a half minutes per day.
I've actually gone through the data to see the number. I'll say why. Newton in the second edition quotes it as two minutes and 28 seconds per day. When you look at the data, it ranges from about two minutes and 45 seconds, to about two minutes and ten seconds.
So I wondered where the two minutes and 28 seconds came from, so I averaged them over a year and got two minutes and 28 second which tells me Newton did the same thing. He simply went through it but, it was clear this was happening, so Richer then decides maybe gravity is different here.
He starts doing second pendulum measurements and discovers the second pendulum needs to be reduced one and a quarter lines. It's 2.8 mm and that gravity is definitely slower and that is the most famous single result to come out of Richer's expedition. Because it plays such a huge role in Newton's Principia.
In fact, all these other things were monumental for astronomy because they then supplied Cassini with the basis to start doing the project of really careful observations of the planets, night after night, with proper corrections, et cetera, to start getting them, in effect, to rebuild astronomy and do a real test of Kepler.
Fair enough? So these are major expeditions. Think of the money that's required to send maybe a boat load of people supplies and a bunch of scientists in their assistants down to Cayenne for a couple of years to do this and bring them back. Okay. This is big time effort in those days.
Louie the 14th was very productive for Science. By the way, what Louie 14th wanted most of all was really accurate map making of France and this was all sold to him constantly on this, to do maps, we really have to have the stars exactly right because we're gonna use this.