Hi
I’m trying to follow the progress of corrections made to Kepler’s 3 Laws but haven’t found any websites that make the timeline of corrections (or even the details of the actual corrections) very clear. I hope someone can help me find a tidy analysis (but not quite dumbed down one either) regarding the matter of Kepler’s mistakes and corrections thereof. I look forward to your feedback.
Are you talking about the constant arising from putting law 3 into use ?? that constant ,may at some time have been determined only using the mass of the star, or larger object and not the sum of the two objects masses… But that is because the error is so tiny, it wasn’t noticed. However its the implied constant, which kepler didn’t explain, he just said that the system has a constant… change the orbit.
Where did you get any idea there is a history ? eg Mercator first said Kepler was wrong, but later said Kepler was correct.
The idea of transforming them to Newton’s laws doesn’t take you very far. I read that Carl Runge and Wilhelm Lenz identified a symmetry principle in the phase space of planetary motion (the orthogonal group O(4) acting) which accounts for the first and third laws … So you have to get quite involved to get from Newtons laws to Kepler’s deterministically ( not merely verifying keplers with the motion Newton predicts.)
The timeline is very simple, because it only contains three points:
Kepler came up with his Laws.
Newton came up with his own Laws, and used them to show how Kepler’s Laws could be derived (with some minor corrections).
Einstein came up with General Relativity, which gives a very slight correction to Newton’s law of gravity, and hence a corresponding correction to Kepler’s Laws.
Unless you want a timeline of Kepler’s own development of his Laws?
Could you give us an example of one of these “corrections?” I am a bit of a space and history geek, and I am not aware of any major (or minor) revisions to the three laws of planetary motion, as they really just describe what we would expect in a Newtonian universe.
Thank you all. Here is an interesting look at how his mistakes cancelled each other out. Whether there were any mistakes corrected by Newton or others, I’m not sure, but perhaps someone can point them out to me.
http://homepages.wmich.edu/~mcgrew/sleepwalk.htm
Now, at the very beginning of the hair-raising computations in chapter sixteen, Kepler absentmindedly put three erroneous figures for three vital longitudes of Mars, and happily went on from there, never noticing his error. The French historian of astronomy, Delambre, later repeated the whole computation, but, surprisingly, his correct results differ very little from Kepler’s faulty ones. The reason is, that toward the end of the chapter Kepler committed several mistakes in simple arithmetic — errors in division which would bring bad marks to a schoolboy — and these errors happen very nearly to cancel out his earlier mistakes. We shall see, in a moment, that, at the most crucial point of the process of discovering his Second Law, Kepler again committed mathematical sins which mutually cancelled out, and “as if by miracle” (in his own words), led to the correct result….
http://www.sparknotes.com/biography/kepler/section8.rhtml
"The book itself offers an interesting insight into Kepler’s mind, as he records the path he took to get to the two laws – mistakes and all. And Kepler made quite a few mistakes.
In emphasising particular mistakes, writers like Koestler both probably underestimate how frequently mathematicians and physicists make (usually minor) mistakes in calculations and also just how riddled with such mistakes the relevant chapters of Astronomia Nova are.
What make Kepler unusual is that he gave the terribly detailed account of the tangled path through his calculations. Much such research is a struggle with dead-ends, half-formed ideas, rough workings through, bits of calculation, etc. It no doubt varies from person to person, but simple mistakes are common along the way. If you’re lucky, you eventually hit what you’re trying to get to, at which point all that just largely falls away. The answer usually transforms your understanding of how to get to it.
Having found the two laws, anyone else would have stated them and then turned everything around by showing that they reproduced Tycho’s observations. That would have been demonstration enough. Indeed, since it’s the accuracy of his subsequent Rudolphine Tables in predicting future positions that seems to have convinced people, that’s pretty much like what eventually happened.
Instead, Kepler tried to reconstruct the discovery process in all its gory detail, missing many of the smaller mistakes along the way.
There’s no evidence that any of his contemporaries found this narrative particularly interesting, though of course historians of science do find it remarkable precisely because people tend not present research in this way. I’d actually wonder how many 17th century readers waded through it in enough detail to notice any such slips. Even in 1804, Richard Small could write his still useful very detailed paraphrase of Astronomia Nova, An Account of the Astronomical Discoveries of Kepler, and not mention errors. Delambre doesn’t, I think, discuss the matter until his Histoire de l’astronomie moderne in 1821. By that stage the issue was obviously already only of historical interest.
Donahue’s standard 1992 English translation basically gives up on noting all the mistakes in Chapter 16 and has a footnote (p258) directing the reader to Casper’s Johannes Kepler Gesammelte Werke for an incomplete list. And Caspar had (separately) translated it into German, so had been through the text thoroughly himself. Donahue found some new ones of his own. I very much doubt they’ve caught everything.
Thank you bonzer. Thank you all. That puts the matter to rest for me.