Wikipedia:Peer review/Newton's theorem of revolving orbits/archive1

Newton's theorem of revolving orbits

 * A script has been used to generate a semi-automated review of the article for issues relating to grammar and house style; it can be found on the automated peer review page for August 2008.
 * A script has been used to generate a semi-automated review of the article for issues relating to grammar and house style; it can be found on the automated peer review page for August 2008.

This peer review discussion has been closed.

I'd appreciate a peer review of this article before suggesting it as a Good Article (GA) nominee or Featured Article (FA) candidate. Is it understandable? Are the Figures enlightening? Does anything need a reference? Am I understanding everything correctly? Have I overlooked something?

Honestly, I'm not sure whether GA or FA would be appropriate; that might be another helpful question to address in the peer review? The present article is significantly shorter than a typical Featured Article, but very few people have ever discussed this topic; its entire scholarly literature seems to consist of a few papers/books. There's even a 1995 quote from expert physicist Subrahmanyan Chandrasekhar that the theorem is discussed in only one major book, that of E. T. Whittaker. I haven't mentioned that in the article, but I could.

I thought about adding a "History" section, but it'd be very short, e.g., "Newton discovered it in 1687 and applied it to lunar motion. Largely ignored for four centuries, with the exception of the 1937 dynamics book by Whittaker.  First generalized in 2000 by Mahomed and Vawda."

Thanks muchly for your help! :) Willow (talk) 20:08, 7 August 2008 (UTC)


 * Ozob's review

You always write such beautiful articles, Willow. And this one has beautiful animations, too. Here are my comments:


 * blush Thank you, Ozob; I'll try to live up to your beautiful words. :)  The article will be much better for all your insights! Willow (talk) 18:27, 14 August 2008 (UTC)


 * I don't think it should be excluded from GA or FA on the basis of its length. Some topics need long articles and others need short ones. This needs a short one.
 * That's reassuring, but perhaps it's better to take it to GA first? I've never actually succeeded in getting a Good Article, so it might be nice for that reason as well. Willow (talk) 18:27, 14 August 2008 (UTC)


 * In the "Overview" section, you comment that when we exclude time, we obtain the path of the particle (a minor comment: "particle" becomes "planet"). Then you juxtapose this with the statement, "If the path of the first particle is described in the form r = g(θ1)" (emphasis added). That's a big if, and unfortunately it's easy to misread as, "When we forget about time, the path of the first particle..." (That's how I read it the first time.) And of course that's not true, because then the orbit couldn't precess. (The same thing happens in the "Generalizations" section.) So while the article is literally correct, I think there must be a better wording for that sentence.
 * I tried to explain the unusual definition of θ being used, and in particular that θ need not be bounded between -180° and 180°. Is it better now? Willow (talk) 17:57, 15 August 2008 (UTC)


 * In the "Qualitative behavior and orbital precession" section, I am not so sure that the article is correct, and I have attempted to fix it. What got me thinking was that the statement "its orbit would resemble the first particle's orbit" is a little vague. How precisely does it resemble the first particle's orbit? When I tried to figure it out my conclusion was that the article was getting tangled up in different reference frames; while the statement and the algebra were correct, I don't think the text reflected the physics. But please read my change carefully, because you're an expert in this and I'm not.
 * I'm no expert, unfortunately! :P I did try to go through it, though, and make sure that everything read well. Willow (talk) 17:57, 15 August 2008 (UTC)


 * In the "Limit of nearly circular orbits" section, you mention that Valluri, Wilson and Harper explain why Newton felt justified in applying his method to large eccentricities. Could you include a one-sentence summary of their explanation? (Do you have access to the article? I could probably do this if you don't.) Or is the explanation in the following paragraphs?
 * I tried to sketch their argument in a sentence or two. The basic idea is that the precession rate shouldn't be identically zero for arbitrary forces   and arbitrary orbital eccentricities ε.  For a given force, it might well be zero for particular values of ε, but a randomly chosen ε (such as those of the planetary orbits of the solar system) is unlikely to yield a zero precession rate. Willow (talk) 17:57, 15 August 2008 (UTC)


 * Also in that section, the meaning of the displayed equation with dC/dr seems rather opaque to me. How does it cause the long axis "to rotate as Newton's theorem of revolving orbits"? What does that last sentence mean? Is this what is being explained in the following paragraphs?
 * The idea is that you can derive an effective k for an arbitrary central force, as long as you consider only orbits that are very close to being circular. The mean precession rate Ω of the orbit equals (k-1) ω, where ω is the mean angular speed of the particle revolving about the central point. Willow (talk) 17:57, 15 August 2008 (UTC)


 * By 2 4/243, I presume you mean the fraction 2 + 4/243; I think it doesn't show up well on the screen when the 4/243 is written horizontally, but I don't know how you could format it better without going into TeX: $$2\textstyle\frac{4}{243}$$. And while that's clear it doesn't look very good.
 * Yes, that's exactly what I was trying to convey. I took both of your suggestions, writing it in a TeX formula initially and as 2 + 4/243 later in the text. Willow (talk) 17:57, 15 August 2008 (UTC)


 * In the "Cotes' spirals" section, the diagram does not agree with the text: The diagram uses θ for the position of the particle while the text uses θ1. (The caption agrees with the diagram.)
 * Yes, I'd wanted to use θ instead of θ1 so that other people could re-use the image? But that seems unlikely, so I changed it to θ1. Willow (talk) 18:27, 14 August 2008 (UTC)


 * It would be nice to have pictures of at least one form of Cotes' spirals.
 * I managed to persuade Gnuplot to make the spirals in SVG. Thank you, KSmrq! :) Willow (talk) 18:27, 14 August 2008 (UTC)


 * Maybe there's a way to make the presentation of the different types of Cotes' spirals more uniform? If there's one particular kind that's especially important, then that should be first, of course, but otherwise the presentation suggests that the second form (which, oddly, is not named even though the other two are) is some sort of monstrous aberration of the first.
 * I've since learned that the cosh form is a type of Poinsot's spiral. :) The only difference between the cos and cosh spirals is the relative strength μ of the inverse-cube central force; if μ is less than a certain positive threshold, the cos spiral holds, whereas the cosh spiral holds if μ is greater than the threshold. Willow (talk) 18:27, 14 August 2008 (UTC)


 * The "Closed orbits and inverse-cube central forces" section has some very special formatting. Is this necessary? If the two images were on opposite sides, then the text would flow better on my screen; right now, their vertically adjacency makes them taller than the section's text.
 * I tried that, too, but that squeezed the text, making it far taller than the images. A good way of formatting this section isn't obvious to me, unfortunately. :( Willow (talk) 18:27, 14 August 2008 (UTC)


 * In "Newton's derivation", the notation is inconsistent: Sometimes it's r(t), other times it's r1(t) (later you comment on this, but it's not clear at the start); and sometimes it's theta(t) and other times θ1(t).
 * Thank you for catching all that! I think I've fixed the inconsistencies. Willow (talk) 18:27, 14 August 2008 (UTC)


 * Also in "Newton's derivation", what is the derivation intended to show? The article says it's his Proposition 43, but doesn't state Proposition 43.
 * I added more to the Newton section. That makes a lot of sense, since his Principia is the only book that discusses his theorem in any length! :) Willow (talk) 18:27, 14 August 2008 (UTC)


 * I think it would be nice to include the Chandrasekhar quote on how little work has been done here.
 * Yes, I put a blurb into the lead, although I didn't include it in the article, since there wasn't much more to say? Willow (talk) 18:27, 14 August 2008 (UTC)

I liked reading the article. It makes me want to go flying in a spaceship. :-) Ozob (talk) 22:24, 7 August 2008 (UTC)


 * Zoom, zoom — you rock. :) Willow (talk) 18:27, 14 August 2008 (UTC)

Comments from ''' This is my initial review. Article flows well, but FA is still pretty far. I would recommend that you nominate it at GAN following this peer review. Now for the real comments...
 * Meldshal42's review


 * There may be too much compliance with the animations/diagrams in this article. A little bit of it is alright, but a large amount of this article depends on the images.
 * I think the images are needed for the readers who don't want to grind through the math. Perhaps they're eye-candy, but they're instructive eye-candy, no? ;) Willow (talk) 23:22, 19 August 2008 (UTC)


 * The Closed orbits and inverse-cube central forces and generelization sections are a mess.
 * I tried to fix those sections up; are they any better now? Willow (talk) 23:22, 19 August 2008 (UTC)

i couldn't find any prose issues because honestly I don't know how a FA level theory article would go, but this article is very well done. Very interesting, it really sucked me in. Well done, WillowW. -- Meld    shal    42?   11:52, 16 August 2008 (UTC)
 * Yep. all finished. -- Lord    Sunday   20:21, 20 August 2008 (UTC)

Thanks for your review, Meldshal! :) I took your advice about GAN prematurely; I waited a few days, and I honestly didn't expect anyone else to review such a far-flung topic, when there are so many others more deserving. But thank you all for coming, and I'll try to incorporate your advice! :)  Willow (talk) 23:22, 19 August 2008 (UTC)

Sweet effect!
 * Mike Peel's review
 * Perhaps a definition of "radial motion" would be useful, e.g. "the distance from the central object as a function of time". My brain also got confused about "angular motion"; it read it as "angular momentum". I shouldn't try to proof-read things over breakfast...
 * I always need to wait until I've had my coffee, too; there's no telling what I might say, otherwise! ;)
 * Your idea of defining the radial motion is excellent and I'll do that right away. Thanks! :) Willow (talk) 23:22, 19 August 2008 (UTC)


 * I think you need an animation right at the top, showing what happens in the case of a circular orbit, rather than jumping straight to movies of elliptical orbits. That way you can show just the speed increase before the particles start behaving oddly in radius. Another possibility would be to do a diagram in 1D (or an inset into the current diagrams in 1D), that is, just showing the radial position of the particles over time to reinforce that they are the same. Also, a trace of the path that the green planet takes might be useful (unless that would complicate the diagrams too much...)
 * We think alike! :) The path of the green planet in Figures 2 and 3 is shown in Figures 8 and 9, respectively.  The red planet was meant to show the radial motion without the angular motion, although it does that pretty indirectly, I concede. :P  Your idea of a purely circular orbit is excellent, but given the previous review, I'm concerned about adding too many similar animations.


 * Could the movies be saved as animated GIFs, rather than Ogg movies? They would then be viewable by more people (Ogg isn't too well supported yet), and would also start playing automatically and loop.
 * Alas, you weren't around when I had this discussion with some mathematicians. The Figures were all originally looping, animated GIFs, but I changed them.  The OGG videos are definitely of worse quality, but they don't incur the same memory penalty when loading the article.  Perhaps I should include a link to the GIFs?  That would keep the download memory load small, but offer a way to see the better images.  Willow (talk) 23:22, 19 August 2008 (UTC)

I wrote the above comments a few days ago, meaning to continue, but I haven't had the time yet. More comments will be coming when I get the time to give the article my full attention. Mike Peel (talk) 08:44, 19 August 2008 (UTC)


 * Next review!

Comments from
 * You said you wanted to know what to work on before taking to FAC, so I looked at the sourcing and referencing with that in mind. I reviewed the article's sources as I would at FAC.
 * current ref 5 (http://arxiv.org/abs/0807.2708v1) is lacking a publisher
 * Hope this helps. Please note that I don't watchlist Peer Reviews I've done. If you have a question about something, you'll have to drop a note on my talk page to get my attention. (My watchlist is already WAY too long, adding peer reviews would make things much worse.) 13:55, 24 August 2008 (UTC)