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Wobbling

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@BlueMoonlet: If you'd care to read my edit summary, you'd see I never said orbital planes were stationary. I said that there is an unchanging plane in the absence of perturbations. And, of course, that is not a realistic situation, there are always perturbations. Then, if you'd care to look at the actual changes I made, you'd see that I tried to clarify what this wobbling of the orbital planes is, to clearly differentiate it from other things. This wobbling is a change of their inclination, which can hardly be described as a 'rotation around an axis'. --JorisvS (talk) 07:17, 9 April 2015 (UTC)[reply]

@JorisvS: Hi. I apologize if I was a bit short. Your edit summary said that, "except for the effect of perturbations orbital planes are stationary." I frankly don't understand this; it seems like saying, "except for all the water lying about, the ocean was dry." The whole point of this article is that orbital planes do not remain stationary due to the effects of perturbations, which cause them to move about a mean plane called the invariable plane.
Your edit itself was factually incorrect. It says, "The planets orbit their primary while their inclinations with respect to the invariable plane vary." The planet's motion around the primary is not the point; that motion takes place within a plane, and that plane itself rotates on much longer timescales. Most importantly, the inclination of the orbital plane with respect to the invariable plane does not vary, at least in the case of simple perturbations. Rather, the inclination remains constant while the line of the ascending node (the intersection between the two planes) circulates from 0° through 360°. To put it another way, the orbit normal (the vector that is perpendicular to the orbit plane) precesses around the invariable plane normal in the same way that the axis of a top precesses around the vertical direction.
These are tricky concepts, and if what I'm saying isn't clear to you I am happy to blame my attempt to speak clearly. Please let me know if you have further questions or concerns. --BlueMoonlet (t/c) 15:36, 9 April 2015 (UTC)[reply]
The original appears to talk about a body orbiting a primary ("they rotate around its axis while their inclinations to it vary"), rather than a circulation of the orbit's orientation, although it is somewhat ambiguous, while supposedly explaining wobbling around the invariable plane. In my edit summary ("except for the effect of perturbations orbital planes are stationary and only the planets' positions would change"), I was really just trying to explain that a body orbiting a primary and a wobbling of the inclination of its orbit are two different things.
"Most importantly, the inclination of the orbital plane with respect to the invariable plane does not vary, at least in the case of simple perturbations. Rather, the inclination remains constant while the line of the ascending node": Yes, but that is not close to what this section is currently saying: it talks about planets' inclinations wobbling, but not about the ascending nodes of their orbits circulating. So far, I've only tried to patch it up (my typical first approach to seeing something that does not make sense), but it has become quite clear to me that that whole section is woefully crappy at explaining what is actually happening, with my patching up never going to be enough, and that it basically has to be rewritten from scratch. The numbers could likely stay by integrating them into the new text, though. You've already done a far better job at explaining it here than any of the past versions of that section, so I'd like to invite you to rewrite it, telling there what you've said here. Your analogy with the precessing orientation of tilted bodies is particularly catchy. --JorisvS (talk) 16:22, 9 April 2015 (UTC)[reply]
I just looked over the article a bit more carefully, and I've concluded that the section that was troubling you is vestigial. It predates any improvements I've made to the article, and it's not even entirely correct (as mentioned in the Intro, orbital planes precess about the Laplace plane, not the invariable plane; the two are equivalent only when all perturbers and resonances are distant). So I've deleted it.
Perhaps this satisfies your concern? Please don't hesitate to identify other aspects of this article that might be improved. Thanks, --BlueMoonlet (t/c) 10:00, 20 April 2015 (UTC)[reply]

Invariable plane vs. the ecliptic plane

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I have a question. Maybe this is obvious to an expert, but for a casual reader, it seems like for a given planet the difference between these two planes should be the same.

For example, Mercury's two angles are 7.01 and 6.34, a difference of .67, while for Venus it's 3.39 and 2.19, a difference of 1.20.

Why isn't the difference a constant for all planets? (With value 1.57, I would think.)

I guess it's because one plane passes through the center of the sun, while the other plane passes through the barycenter, which is some (small?) distance from the center of the sun?

Maybe you could add some text to the article explaining this?

Of course, a drawing showing the geometry of the two planes would be really fantastic. — Preceding unsigned comment added by GregHolmberg (talk • contribs) 01:14, 30 January 2016 (UTC)[reply]

The line of nodes is the line along which two planes intersect.
The answer to your question has to do with different orientations of the line of nodes. I've taken the image from that article and put it here. Consider a plane that is just like the yellow plane in its inclination to the gray plane, except that its line of nodes (the line along which the planes intersect) is 90 degrees different. The plane I've just described will have the same inclination to the gray plane that the yellow plane has, but it will also be inclined to the yellow plane.
In expecting the difference between the two inclinations to work out to a constant value, you are imagining that all three planes have the same line of nodes. This is an easy mistake to make, and I have certainly made it several times as I have worked to understand this complex topic. --BlueMoonlet (t/c) 15:27, 30 January 2016 (UTC)[reply]


Thanks, BlueMoonlet. I can visualize what you're describing. There are two lines of nodes (one from each plane of reference), and they aren't co-incident. (Although they are of course both in the plane of the orbit, right?)

What I'm wondering is, why is this the case here? Is it because the centers of the two planes (i.e. the center of the sun and the barycenter) are not co-incident? Where are the two centers located, exactly? Except for case of the Earth and the Ecliptic, neither center is on the plane of the orbit of any given planet, right?

I'm having troubles visualizing the whole thing for our solar system specifically.

For example, the drawing in this blog claims to show the invariable plane and the ecliptic, but from what you've said, this is not the right picture. I googled for other images showing the two reference planes, but couldn't find any.

And, of course, I'm not just asking for myself. It would be nice if you could enhance the article for everyone, and not just the Talk page.

GregHolmberg (talk) 04:06, 1 February 2016 (UTC)[reply]

The distance between the barycenter and the center of the Sun is not an issue here. Every angle we are talking about here is the angle between two planes (the planet's orbital plane on one hand and either the ecliptic or the invariable plane on the other hand), and that angle does not change if you offset one of the planes by any distance, much less a distance as small as that between the barycenter and the Sun's center.
There are three nodal lines we can consider here: 1) that between the planet's orbital plane and the ecliptic plane, 2) that between the planet's orbital plane and the invariable plane, and 3) that between the ecliptic plane and the invariable plane. Of course #1 and #2 must be in the planet's orbital plane. On the other hand, #3 is generally not in the planet's orbital plane, but it could be. In fact, if line #3 is in the planet's orbital plane, that is the case in which you would expect the two angles you have described to have a constant difference.
The article you linked seems fine, but it doesn't really address the question of Neptune's orbital plane. The way the figure is drawn might make you think that Neptune's orbital plane is right in between the ecliptic plane and the invariable plane and shares the same line of nodes with them, but that is probably not actually true. Instead, because all of the inclinations are quite low, the orientation of Neptune's orbital plane doesn't much matter for the article's stated business of calculating Neptune's orbital longitude.
This whole business is actually quite hard to visualize, because it can't easily be reduced to a two-dimensional representation. This is one reason this Wikipedia article doesn't go into it in much detail; such a discussion seems more likely to provoke confusion than to relieve it. But if you have specific suggestions for improving the article, please articulate them. --BlueMoonlet (t/c) 05:45, 3 February 2016 (UTC)[reply]

An illustration would be helpful here

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The "angular momentum vector" with regard to the Sun or any other body is not easily discoverable to the lay person. Kortoso (talk) 18:07, 20 October 2016 (UTC)[reply]

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