Talk:Kirkwood gap

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[edit] Cause of the gaps

There is no doubt that the gaps are caused by orbital resonances with Jupiter. Hence, I have removed the parts of the article which implied that this was somehow disputed.

The abstract that was referenced in older versions of the article was about research that showed that the orbits of several asteroids which do exist in the gaps have orbits that are practically stable over timescales of 1000 Jupiter years (About 10000 Earth years). However, this is a very short time scale astronomically. The orbits of asteroids in the resonances change significantly only over times of many millions of years. Over the age of the solar system, there has been more than enough time to sweep the Kirkwood gaps clean many times over. Deuar 20:43, 21 December 2005 (UTC)

[edit] Rendering of the gaps

I've uploaded (but not installed into the article) the attached image of the gaps based on a diagram I found in Murray/Dermott's Solar System Dynamics. It seems to be a better image than the flat histogram shown in the article. Would it be useful? Or just misleading? It may also need some markup -- maybe some of the resonances given circles of different colours? mdf 20:13, 31 March 2006 (UTC)

Looks like a very good diagram. Overall I think it's more appealing than the present histogram because of the way it's instantly clear what is meant (well, I think so, but It's possible i've just been hanging around these asteroids for too long), and it's just cool-looking graphically. Ah, and it shows a wider range in semi-major axis as well. The histogram is still kind of nice in that it gives precise numbers, and labels the major gaps. Maybe it could be kept but moved down to second place.

I'm a bit puzzled that the trojans don't really cluster into two distinct groups, but maybe they're just more scattered around Jupiter's orbit than I thought. I suppose Jupiter is on the right somewhere, so that's why there aren't many trojans on the left? Deuar 18:04, 1 April 2006 (UTC)

The plot is just a rendering of the semi-major axis and longitude of perihelion for each object, not the actual position of the object. If one plots the actual positions of the asteroids, the Kirkwood gaps disappear in a blur ... but the Trojans stand out. See attached graphic. This is the kind of confusion that one probably wants to avoid in an encyclopedia, so I guess neither of these images should be used. mdf 19:15, 3 May 2006 (UTC)

Well, presumably the Kirkwood gaps are washed out in the bottom plot because eccentricity has been included, so maybe if you had this plot but ignoring eccentricity both the gaps and trojan clumps would be seen? I have to say I still like the top plot - it just shows the gaps so well. By the way - on the bottom plot, did yopu notice the fuzzy clump on the opposite side from Jupiter (probably a bit inside its orbit)? I wonder what that is! Deuar 10:04, 4 May 2006 (UTC)

Well, you can't plot an asteroid's position without considering it's eccentricity. The latter graphic is literally a snapshot of their "in space" positions, projected onto the ecliptic. Generally, the dynamical families (resonances, etc) are identified not from raw positions like this, but how their (suitably massaged) orbital parameters clump after being projected into some space. The trojans are an exception, in that they do obviously clump in "meat space". The 2:3 resonant hildas aren't as obvious in totality, but you spotted some of them opposite the un-plotted Jupiter. If you look between the Jovian Trojans and the main belt, there are other clumps of Hilda's, but it's not as clear. The remaining members of this family are strung out along the edges of this "triangle", and they are lost in the cloud of the main belt objects. Color-coding works better. I'm developing a small graphic-maker for this, so all these families can be given consistent looking plots. mdf 22:23, 4 May 2006 (UTC)

Duh. I think I now perceive what you had in mind by 'ignoring the eccentricity'. I'll have a new graphic in a few days. Pretty colours! mdf 21:13, 5 May 2006 (UTC)

Um, sorry, I should have made that clearer. Deuar 12:38, 6 May 2006 (UTC)

I've uploaded three new graphics. mdf 17:32, 9 May 2006 (UTC)

Cool! I think each of those plots is useful for showing its part of the whole story. The middle one can be a bit misleading, I agree, but with an appropriate brief caption like e.g. "schematic of asteroid positions showing the asteroid belt's structure (eccentricity has been artificially set to zero to bring out the fine structure)" it should be very informative.

If one selects only the low (<0.093412 (Mars's) or something) eccentricity asteroids in a plot of the real objects, shouldn't the gaps become visible? 84.230.190.177 05:03, 26 January 2007 (UTC)

In principle yes, however you have to choose really low eccentricity. E.g. the widest gap over at 2.5 AU is about ± 0.04 AU wide, meaning you have to have eccentricities no more than about 0.04/2.5 ≈ 0.016. A problem is that asteroids become really thin on the ground at such low eccentricities (Why is that, by the way? Anyone know?) Deuar 14:20, 1 February 2007 (UTC)

I keep seeing new thought-provoking things in your plots every time. e.g

• Why do the Hildas hang out in three clumps? Is this some influence of Jupiter? (by the way, their dark blue color is a bit hard to see)

The Hilda's are in a "triangle" because of (a) the non-zero eccentricity of their orbits, (b) the 2:3 resonance and (c) that it's in an asteroid's "favour" to be a perihelion when Jupiter is near (the natural tendency of the resonance is to 'rotate' the orbit into such a state over time; this is described in Solar System Dynamics). mdf 16:09, 16 May 2006 (UTC)

• The density of the outer band of the main belt also seems to have some non-random modulation (middle plot). Jupiter again?

There is also a noticable clumping even in meat-space. As an experiment -- I'm wondering if there may be a bug somewhere in my code or data selection -- I've uploaded an animated GIF of the whole shebang. Can you see any patterns that persist over a full Jovian revolution? Irritating: I can't reproduce the exact plot because the program's method of sampling has changed. mdf 16:09, 16 May 2006 (UTC)

• The bottom (density vs. a) plot showing the Kirkwood gaps looks very nice. I wonder why the old plot (with less asteroids) that is in the article shows some different structure which has now disappeared. E.g. the peak at 3 AU has completely disappeared, as has the trough at 2.3 AU. Were these caused by prominent asteroid families? Why have they disappeared now?

Good question. The plot doesn't change significantly if you select only "numbered" asteroids from the MPCORB data, or use all of them. It is also unchanged if you plot mean elements at http://hamilton.dm.unipi.it/cgi-bin/astdys/astibo?proper_elements:0;main. Even changing the resolution of the binning to 0.005au doesn't do much. Where did NASA get that data? mdf 16:09, 16 May 2006 (UTC)

Anyway, I think the new plots are great. Deuar 15:58, 13 May 2006 (UTC)

I've interspersed some responses above; apologies for any confusion. More recent versions of the plots have fixed the "blue" problem. And here is the animation. The "raw position" animation is rather striking at high resolution (but it chews space). Unless the animation has some value with some article, I'm going to ask it to be "speedy deleted" in a week or so. mdf 16:09, 16 May 2006 (UTC)

Very interesting to watch. Some of the behaviour caused by setting e=1 is funny. E.g. check out the white asteroid just interior of the Hildas that lags behind a lot, then suddenly zooms around about half a revolution. I wonder how big an eccentricity you need to get the effect that strong. The orphaned trojan opposite Jupiter also does this but a little less spectacularly. It's so fun to watch, it's a shame to delete it :-) Now, indeed, I can't seem to find any stable features in the outer main belt, but the ones in the still figure do look more significant than random. Puzzilng. Well, it's not a problem, anyway. Deuar 19:12, 17 May 2006 (UTC)

I seem to have found out what the deal with the NASA plot is. It's real old. If you take just the first 10 thousand numbered asteroids (i.e. discoveries up to about the mid 80s) the funny distribution appears again. See plots on the right. You also get a similar behaviour if you consider only the larger asteroids (H>13, diameter ~ 6 to 15 km, second new plot on right). That plot clearly shows the observational bias towards inner main belt asteroids as well. The reason for the difference between newer and the old NASA plot appears to be due to asteroid families. The Vesta family has zillions of small asteroids, but not many large ones, so its lack was largely responsible for the hole around 2.3 AU, while another big family (I think it's Eos) out at 3 AU appears to be lacking in small members (not sure which one that is). Deuar 20:48, 17 May 2006 (UTC)

[edit] weak gaps

There are a bunch of weak gaps mentioned in the article. They're not visible in the histogram. Are they real gaps in the distribution (narrow, perhaps?), or just calculated locations of resonances which do not lead to any significant depletion of asteroids? Deuar 16:22, 26 February 2007 (UTC)