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Specifically, how with Newton's Laws was the location of Neptune pinned down with such accuracy? I think this is what FFT (and I as well!) are most interested in
Indeed this is what I was thinking about. I like the historical explanation PropulsionDisk but to make a more in-depth discussion we should talk about the actual calculations.
Propulsion Disk wrote:
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And that's about it! Hope this answered your question FFT, and sorry if I missed some things, I was mainly trying to just get your question answered!
These are not just questions. They are proposed topics for a debate here. The story around the discovery of Neptune is quite interesting but I would like to have the "Solar System Dynamics" part of it also. I don't know if we can redo the calculations here (I would love to see that, if anyone is willing to attempt) but at least explain how Newton's laws gave rise to such an accurate prediction. We need in-depth comprehension, not just a resume, but this is a good start
And no, stating the universal law of gravitation is not actually what we are asking either. That is just part of the premise not the actual calculations.
By the way I would like to point out some statements that I belief are erroneous here
, in your historical summary. Just for any future reader to take these into account (don't hate me please).
Propulsion Disk wrote:
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THE FIRST THEORY OF NEPTUNE'S EXISTENSE WAS MADE BY GALILEO GALILEI, ON DECEMBER 28, 1612, PROBABLY ONE OF THE MOST WELL KNOWN ASTRONOMERS, WAS ONCE LOOKING AT THE NIGHT SKY, SEARCHING FOR NEW PLANETS. THAT NIGHT, HE FOUND SOMETHING VERY INTERESTING, IT WAS WHAT SEEMED TO BE A STAR THAT DIDN'T TWINKLE, AND THEREFORE GALLIEO THOUGHT HE HAD FOUND A PLANET! HE LOOKED AT AGAIN A YEAR LATER TO FIGURE OUT THAT IT WAS STARTING TO GO RETROGRADE AND THEN PROVED THAT IT WAS INDEED A PLANET, HE WROTE IT IN HIS DRAWINGS OF THE SOLAR SYSTEM WITH NO NAME AND SHOWED IT TO THE PUBLIC, ASTRONOMERS KEPT LOOKING FOR NEPTUNE AND EVENTUALLY FOUND OUT THAT IT WAS JUST A STAR THAT WAS IN CONJUCTION WITH JUPITER WITCH IS WHAT MADE IT LOOK LIKE IT WAS MOVING TO GALLIEO, AND HIS SMALL TELESCOPE, AND WAS NEVER FOUGHT OF AGAIN INTILL 1821.
Galileo's notes never mention any "theory of a new planet". Galileo observed Neptune in two documented occasions and confused it with a star. He never mentioned this apparent star as possible planet. And that presumed star indeed turned out to be Neptune (so Galileo skipped Uranus, which was undiscovered, and saw the farthest known planet in the Solar System). The fact that Galileo noticed its movement is true but not as you explained. He named the "star" "fixa", as a fixed point of reference to understand Jupiter's motion, he never thought that this "fixa" could have moved just because the relative separation with Jupiter increased (this was expected and no confusion at all for Galileo). What he observed is that another star (HD 105374
) was moving relative to this "fixa" and that was what in turn confused him since any two stars should have been at the same relative positions.
This discovery (of Galileo's observations) was published in Nature by Charles T. Kowal & Stillman Drake in 1980. The article
is interesting on its own if anyone wants to research on the history of "the precovery of Neptune". It seems that Galileo pointed his telescope to Jupiter in a very appropriate moment; our current high-accuracy ephemerids show that Neptune was been occulted by Jupiter in January 1613 (a one in a century event at best). That means that the months before and after that event Neptune was close to Jupiter in the sky and any curious eye trying to learn something about Jupiter would have been able to possibly spot Neptune.
The diagram above shows Jupiter and the relative postion of Neptune from 12/28 (December 28th) to 1/30 (January 30th). The second lucky thing is that Jupiter started in January 1613 it's retrogade motion (apparent from Earth). This is why in the diagram (where Jupiter is fixed) Neptune appears to return. The fact Neptune was slowing down and returning close to Jupiter's position is also good since that incremented the chances of Galileo to spot it.
Galileo is known to have been able to spot even magnitude 9 stars. Since Neptune never gets above magnitude 8 that means that Galileo indeed should have been able to see Neptune in some observation that moth. The field in the sky where the first observation was made is depleted of bright stars so this "fixa" must have been Neptune indeed.
Let's look at the actual notes done by Galileo.
Lets zoom in to the upper part of the second page of his notebook:
In the upper part he writes the time when the observation was made. It is December 27th, 1612, 15 hours and 46 minutes after noon. Galileo's way of formating time seems strange to us now. 15 hours and 46 minutes after noon is just 03:46 am of the next day. So the observation was made at 03:46 local time in December 28th of 1612. The first drawing shows Jupiter and 3 moons aligned in the same plane, he also puts "distance" measurements between Jupiter and each moon; the one in the left was at 9 jupiter radii, and the two on the right where at 9 and 10,3 jupiter radii respectively. He wrote "fixa" for a star in the upper left part of the image which he would take as a fixed point during this set of Jupiter observations.
The lower drawing shows the situation a few hours after that. The moons have moved a little (one of the four moons has just started to emerge from the glare of Jupiter's disk) and "fixa" still remains more or less fixed in place.
Now compare the first drawing with the actual positions calculated using modern ephemerids:
As you can see "fixa" must be the planet Neptune and not a star. The moons marked by Galileo in the first drawing are (from left to right) Ganymede, Europa and Callisto.
Now let's jump one month to these notes:
Here again we see Jupiter and three moons (from left to right: Ganymede, Europa and Callisto at 5,10 , 8,40 and 20,40 Jupiter radii away from Jupiter according to Galileo). This observation was made the 28th of January 1613, 6 hours after sunset. A star labeled with an "a" can be seen 29 Jupiter radii away in the far left of the image. This new fixed point he used was indeed a star. The star is SAO 119234 (or HD 105374). He used these fixed points as references to understand the motion of Jupiter in the sky. Little he knew that the fixed point used a month before, "fixa", was Neptune and therefore not fixed at all. He wanted to use a secondary fixed point for this new observation so he took another star, "b" which was a little farther away than "a" but basically in the same direction. Since "b" couldn't fit in the space left in that page he splitted the drawing and continued the Jupiter-a-b line in the lower right part of the image. Well, it turns out that "b" was "fixa" again that had displaced in the sky (look at the first image of this post). "b" was Neptune. You can see how well it agrees with our ephemerids of that observation here:
The interesting thing here is that in this observation Galileo wrote that "b", which was also observed in the preceeding night, and "a" seemed to be more remote from each other (inter se) than the previous night. This means Galileo was able to correctly detect the motion of Neptune, even if he dismissed the idea and never thought of it again. I want to emphasize "correctly detected" because he was aware that Jupiter and "b" would be moving relative to one another but the fact that "b" separated from "a" (both supposedly fixed celestial marks) was really unexpected.
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and he used what he knew about gravity to figure out how big Neptune should be, but the problem was, Neptune could be very big and far away from Uranus, or small but close to Uranus, to be honest, he didn't even know that himself because these equations were imperfect
This is not entirely correct either. Le Verrier predicted the mass and orbital parameters of the planet (aswell as the current position) so he had a very good estimate as to how massive and far away Neptune was. That said it is true that semi-major axis and mass were educated guesstimates.
By the way it is also worth noting that Adams is currently disregarded as a contributing force for the discovery of Neptune. Nearly all the credit goes to Urbain Le Verrier. Chauvinism and english nationalism ended in an embarrassing situation where the brits just evaded to show any calculations and even traveled with Adams documents across the world just to make sure no-one ever read them and maintain their prestige