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The following is an archived discussion of a featured article nomination. Please do not modify it. Subsequent comments should be made on the article's talk page or in Misplaced Pages talk:Featured article review. No further edits should be made to this page.

The article was promoted.

Laplace-Runge-Lenz vector

Self-nomination. The LRL vector is important in celestial mechanics as a convenient method for describing the shape of an orbit, and was historically important in the first derivation of the hydrogen-atom spectrum using modern quantum mechanics. It also reveals a subtle but beautiful symmetry of the Kepler problem, which is the problem of calculating the motion of two particles interacting by gravity or electrostatics. This article is stable, thoroughly referenced and has undergone scientific and non-scientific peer reviews. A translation of this article was voted recently to Good Article status without opposition on the Russian Misplaced Pages. Although technical, the article has been written as accessibly as possible for the lay-reader. Willow 10:30, 31 December 2006 (UTC)

• Comment: As presently constructed this fails the grandmother test, namely there is no sentence in the introduction that I believe my grandmother would be capable of understanding. Sure it is a technical topic but there should be at least some statement of what the concept is that will encompass its importance and still be accessible to someone with no training in physics or math. Further, as this is a general encyclopedia and not a physics/math text, I would encourage you to collect some of the various derivations, descriptions and proofs and place them in a mathematical appendix at the end of the article. Knowing how some of those results and descriptions are derived is not directly significant to understanding the key applications, significance, etc. Dragons flight 12:14, 31 December 2006 (UTC)

Umm, none of my sisters are mathematicians or physicists, but they all understand roughly what a vector is and followed the gist of the lead. However, I'm willing to believe that the lead could be further re-worded for clarity, especially the first sentence. I could also imagine putting the Conservation and Parabolic coordinates sections into two appendices, but that would interrupt the flow slightly; also, that seems not to be customary at WP. Willow 14:09, 31 December 2006 (UTC)

My friend with a BS in biology, who took a year of undergrad physics, read the introduction and came away with:

"I can tell that it's (1) a constant that (2) has something to do with gravity and other things that vary by the inverse square of the distance between them. But its actual effect is completely opaque, at least in the introduction. The bit about 'subtle symmetry of the Kepler problem' might as well be written in Greek. The correspondence principle sounds like sympathetic magic, and I don't know why the introduction to this thing is talking about some other, similar thing. If it's actually talking about the same thing, that's not at all clear. And the picture is frankly scary."

Given that the lead of featured articles will be read by people with no physics/math training at all, at least some part of this needs to be more accessible than this. Dragons flight 22:23, 31 December 2006 (UTC)

I would oppose moving things into a separate "mathematical appendix". It would turn what is now a very nice article into Emmenthaler. The topic of the article is more technical than any present FA on a subject in mathematics or physics, and I feel the treatment (including the lead section) is entirely commensurate. At least the first sentence tells you that if you don't know what classical mechanics is, or a constant of motion, you'd better read up on those first. The reader who does know these concepts should also see the potential importance. I'm not saying no further improvement is possible, but I feel the assumed reader for who the lead is optimized should have at least some understanding of the most essential concepts of physics.  --Lambiam 17:21, 31 December 2006 (UTC)

I think you misunderstood what I meant about appendix. I didn't mean that every equation should be placed at the end, or anything like that, but rather that the sections that exist solely for the sake of proving things shouldn't be dumped in the middle when it is the conclusions (rather than the proof itself) that is important to understanding the rest of the article. I have now rearranged these to my liking to show what I intended. Dragons flight 22:00, 31 December 2006 (UTC)

One shouldn't need to read up on classical mechanics or constant of motion in order to learn that the LRL vector is a constant that can be used to define the shape and orientation of an elliptical orbit. Dragons flight 22:23, 31 December 2006 (UTC)

Your re-arrangement seems good, Dragons flight! I only fear that such "ghettoization" of the math may tempt some people to delete those sections altogether, which I think would be a loss for the article. I also tinkered with the lead — does it read better now? Willow 19:24, 1 January 2007 (UTC)

I do think that lead is a considerably improvement, thank you. Dragons flight 01:23, 7 January 2007 (UTC)

• Comment - The Derivation of the Kepler orbits, Circular momentum hodographs, and Poisson brackets sections appear to contain no references. This needs to be rectified to demonstrate that the derivations are not original research. (I presume that the nominator can reference books that show these derivations.) Dr. Submillimeter 12:31, 31 December 2006 (UTC)

I've added the references, which were cited in the lead for the same conclusions but did not get copied to the main body of the text — sorry! I've also alerted the astronomical and mathematical WikiProjects per your request. Is everything else OK? Willow 14:09, 31 December 2006 (UTC)

The references are satisfactory. I do not see anything else that I want to comment on. The derivations do look sound (although they appear to skip a few algebraic steps in some places). However, I also do not feel like trying to validate all of the vector analysis at this time. Dr. Submillimeter 21:56, 31 December 2006 (UTC)

• A few Comments:

• Should the abbreviation "LRL vector" be used throughout the article after the first couple of occurrences of the full title? "Laplace-Runge-Lenz vector" is a bit of a mouthful. That is an abbreviation that has been used in the literature (see ).

I totally agree, and I like that abbreviation as well. Replaced throughout, except for a few instances where it seemed good to stress the full name.

• We don't seem to have an article on "Kepler's problem" (the closest we have is a disambig link at Kepler's problem). It would probably be an idea to create that article, especially given the prominent mention of it at the top of this article. Or is this "Kepler's problem" that discussed at Keplerian problem?

Added fuller explanations of the various Kepler problems under the disambig page; do you think it merits its own page?

I'll give more detailed comments when I have more time. Mike Peel 14:34, 31 December 2006 (UTC)

Thanks muchly, Mike! :) Willow 19:24, 1 January 2007 (UTC)

• Additional comments, as promised above. Starting from the top:
  • Is there not a simple, illustrative image that can be placed at the top of the page? I agree with the moving of the complex one that was there before, but it still needs something there. As it stands, there is no image in the first three sections of the article, and the first one readers encounter (in the fourth section) looks very complex.

I'll work on this, but I don't have access to Xfig at the moment. :( Can you wait a few more days until I get back home? Thanks!

• • "This higher symmetry results from two lucky coincidences" -- are they actually coincidences? I'd reconsider this phrasing.

You're very right; "coincidences" was a cute and (from one perspective) valid wording, but could be misconstrued. Changed to "properties".

• • I dislike the wikilinking to other sections of the article where this wikilinking is not made obvious by the surrounding text. I've just changed one instance of this to illustrate what I mean; I'm sure there are others amongst the article text too.

I'm honestly not sure which ones would be bothersome; could you make a list or ("Mike is nice! He'll do it.") fix them yourself?

• • Try to make clear the main points of each section at the start of it, rather than the end. At the end of "Evolution under perturbed potentials", you state "This agreement with experiment is considered to be strong evidence for general relativity." That is a statement that is easier for the lay reader to pick up on, however odds are they will loose interest in the section when they get to the big equation in it. Consider starting off the section by saying something like "The LRL vector can be used to illustrate one of the key pieces of evidence for the validity of general relativity."

I'll try to do that, but everyone seems to have a different idea of what should be emphasized. For example, for me, the Mercury-GR story is a nice illustrative example that people may have heard about; but it's not the main point of the section, which for me was "What happens to the LR vector when the interaction is not quite an inverse square force?"

• • I'm generally worried about the complexity of the article. To understand what some of it is talking about, I would have to go away and do a fair bit of reading. I will support the nomination to FA status, but would recommend against featuring the article on the home page. It makes a fine reference article, but I don't think it's for everyone. Mike Peel 21:42, 1 January 2007 (UTC)

If you would be so good as to identify the passages that aren't as clear as they should be, or where you would have to do outside reading, that'd be very helpful, so that we could work on improving them. Thanks, Mike! :) Willow 02:47, 7 January 2007 (UTC)

• Support an excellent and very thorough presentation of a specialized subject. I'm surprised I didn't think of putting all of the proofs as subsections when I read this article before. I don't think the article will be plagued with many math-deleters, or many other editors at all :)

My only comment, which is tangentially related to this article, is the disambig for Kepler's problem - there is also a separate article Keplerian problem which, grammatically at least, ought to refer to the same thing as Kepler's problem. I see that Keplerian problem has a proposed merge; maybe the merge ought to be performed and Keplerian problem redirected instead to the disambig at Kepler's problem. Considering the importance of the subject to the LRL vector explanation, it seems these should be sorted out somehow. (In particular, I'm very familiar with the general n-body problem but was unaware, when I first read the article, that any special case of it was called "Kepler's problem".) Opabinia regalis 01:08, 2 January 2007 (UTC)

• Support. This article covers its subject in a fashion clear and comprehensible to a reader who would actually be concerned with the topic, i.e., someone with at least a good chunk of an undergraduate physics education. I would like to see the Kepler problem disambig thing sorted out, and a picture for the lead might be nice. The absence of punctuation in equations which terminate sentences irritated me a bit, and it should be fixed to conform with the style manual. The only technical matter I could think of which might merit inclusion is the connection between LRL-vector conservation, supersymmetric quantum mechanics and BPS states (M. Faux and D. Spector, J. Phys A 34 (2004): 10397–407). It relates to the Pauli solution of the hydrogen atom, I believe, and the SUSY method for finding the hydrogen atom's eigenstates. That is, however, perhaps too peripheral a matter to mention. Anville 20:41, 2 January 2007 (UTC)

Thanks very much for the support, both of you! I've written up a short summary of the Kepler problem that should suffice for readers to understand the context of the Laplace-Runge-Lenz vector. The term "Kepler problem" is indeed an accepted term for the special case of the two-body problem, although perhaps only among physicists? The related Keplerian problem could be merged neatly with the new article as well, or perhaps summarized as a subsection within it; it should probably be discussed first on the Talk pages of the two articles. The BPS article is indeed cool and thought-provoking, but I agree that it seems somewhat peripheral here. Thanks for the careful reviews and thoughtful comments! :) Willow 01:07, 7 January 2007 (UTC)

"Kepler problem" is the usage in Caltech's The Mechanical Universe TV series, so I imagine it was widespread or standard usage in the early 1980s (and, AFAIK, today). Anville 14:29, 8 January 2007 (UTC)

• Comment This could be a bit more accessible to a reader of a general encyclopedia. I didn't notice a link to Kepler's laws of planetary motion, but they are perhaps vaguely familiar to more readers and could help provide some context for LRL. Also, some of the notation (esp in the "Perturbed Potentials" section, the < > operator) doesn't seem to be explained on first use. Gimmetrow 19:54, 3 January 2007 (UTC)

Kepler's laws aren't really necessary to introduce here, are they? They're a consequence of the equations of motion for this potential, just as the LRL vector is. But the latter does not follow from the former. I'll try to fix the notation; thanks for catching that! :) Willow 01:07, 7 January 2007 (UTC)

• Support. Especially after the more recent improvements this well-written and thorough treatment of such a technical subject is a good example of the best on Misplaced Pages.  --Lambiam 14:47, 7 January 2007 (UTC)

• Support. I made quite some suggestions on Misplaced Pages:Scientific peer review/Laplace-Runge-Lenz vector and Talk:Laplace-Runge-Lenz vector, and I don't know how the article could be improved further. It is a topic with a lot of appeal (at least to people studying physics), but in my experience, it is hard to find information about it. Nevertheless, an excellent article has been written. The only drawback is that I'm not sure whether everybody will be able to get something from the article; I think the reader may need to know high school physics. But that's the nature of the subject, and in my opinion, it's okay for a featured article to require high school knowledge. -- Jitse Niesen (talk) 21:45, 7 January 2007 (UTC)

• Comment I don't oppose featuring this article, because the most important criteria are met and surpassed. On the other hand, some of them could use work. Rearrangments aside, the article is still long and detailed, to the point where it would benefit from summary style. The table of contents is also a bit overwhelming. The issue I'm most conflicted on is whether the article stays close enough to its main topic; I think it probably does, but I'm a little uncomfortable with it. I could ramble on that issue for pages... Melchoir 04:43, 8 January 2007 (UTC)

The above discussion is preserved as an archive. Please do not modify it. Subsequent comments should be made on the article's talk page or in Misplaced Pages talk:Featured article review. No further edits should be made to this page.