<p>This is actually a very subtle question, much more so than the answers to the similar questions provided in the comments give it credit for.  When I was in graduate school at Ohio State I routinely asked this question to visiting dynamicists and invariably got different answers.</p>

<p>The very basic answer is that if you have two sufficiently strong resonances sufficiently close together, then the resonance will be unstable.  Otherwise, the resonance will be stable.  But what determines "sufficiently strong" and "sufficiently close" is where things get very complicated quickly.  A basic criterion is the <a href="https://en.wikipedia.org/wiki/Chirikov_criterion" rel="noreferrer">Chirikov criterion</a>.  (The <a href="http://www.scholarpedia.org/article/Chirikov_criterion" rel="noreferrer">Scholarpedia article</a> is somewhat more detailed.)  However, the Chirikov criterion is not universally valid.</p>

<p>If you have overlapping resonances, then an object gets bounced back and forth between these two resonances chaotically.  These different resonances perturb the orbit in different ways, and eventually they will perturb the orbit into an unstable orbit, thus leading to depletion of the resonance.  If a resonance is "distant" from other resonances, then the resonance tends to keep objects locked in place, leading to an excess of objects in the resonance.</p>

<p>Most of the resonances in the asteroid belt are fairly close together, which leads to them being unstable.  The Kirkwood Gaps are the most prominent manifestation of these instabilities.  For example, the <a href="https://en.wikipedia.org/wiki/Alinda_family" rel="noreferrer">Alinda family</a> of asteroids are in a 1:3 resonance with Jupiter, and are very close to a 4:1 resonance with the Earth.  This leads to instability, and hence very few asteroids in this family.  However, in the outer Solar System, the resonances are generally far apart, and so are mostly stable.  The <a href="https://en.wikipedia.org/wiki/Plutino" rel="noreferrer">plutinos</a> are one example of such a stable resonance, being in a 3:2 resonance with Neptune.</p>

CC BY-SA 3.0
2017-05-24T19:52:44.090Z
Upon further investigation the answer to my question may even be simpler than this. It may be that the resonance is an "attractor" when objects are of the same order of magnitude of size (even Neptune and Pluto) and an "ejector" when one of the objects is much bigger (such as Jupiter and the Kirkwood gaps and Mimas and some of Saturn's ring gaps. It would seem that Plutinos are more about the 1:1 resonance with Pluto than the 3:2 resonance with Neptune.
Jack R. Woods
CC BY-SA 3.0
2017-05-24T22:00:31.930Z
I don't think the relative masses of the objects really matters.  The Hilda asteroids, for instance are in a relatively stable dynamical state of a 3:2 resonance with Jupiter despite being much less massive.
J. O'Brien Antognini
CC BY-SA 3.0
2017-05-30T02:06:41.300Z
Here's an interesting older review article: http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1976ARA%26A..14..215P&amp;data_type=PDF_HIGH&amp;whole_paper=YES&amp;type=PRINTER&amp;filetype=.pdf                It doesn't seem to me that there is a consensus yet on resonances and it's way too complicated for me, but the gap explanation may be that although there is stability at the resonances, the objects also librate (oscillate about the resonance) and so tend to have more collisions than non-resonant objects. The Hilda and Alinda groups would be the "survivors".
Jack R. Woods
CC BY-SA 3.0
2017-05-30T02:07:49.603Z
Maybe about the relative sizes of the objects in resonance?
Jack R. Woods
CC BY-SA 3.0
2016-05-24T19:43:49.413Z
2016-05-24T19:43:49.413Z
J. O'Brien Antognini
<p>The <a href="https://en.wikipedia.org/wiki/Kirkwood_gap" rel="nofollow noreferrer">Kirkwood gaps</a> in the asteroid belt are associated with orbital resonances with Jupiter yet planets seem to prefer resonant locations. Why don't asteroids accumulate near the &quot;Kirkwood locations&quot; rather than avoid them??</p>

CC BY-SA 3.0
2016-05-23T22:32:13.257Z
[Very similar question on Physics.](https://physics.stackexchange.com/questions/90517/stable-and-unstable-orbital-resonance)
HDE 226868
CC BY-SA 3.0
2016-05-24T00:10:28.113Z
See also https://astronomy.stackexchange.com/questions/13204/stability-of-orbital-resonance.
HDE 226868
CC BY-SA 3.0
2016-11-20T20:06:18.553Z
[Duplicate of this earlier question](http://astronomy.stackexchange.com/q/13204/7142), which is also answered.
JDługosz
<asteroid-belt><orbital-resonance>
Planetary orbital resonances
Jack R. Woods
# Planetary orbital resonances

(Asked by: username_0 on 2016-05-23)

The [Kirkwood gaps](https://en.wikipedia.org/wiki/Kirkwood_gap) in the asteroid belt are associated with orbital resonances with Jupiter yet planets seem to prefer resonant locations. Why don't asteroids accumulate near the "Kirkwood locations" rather than avoid them??

**Tags:** asteroid-belt, orbital-resonance

> **Comments:**
> **username_1**: [Very similar question on Physics.](https://physics.stackexchange.com/questions/90517/stable-and-unstable-orbital-resonance)  
> **username_1**: See also https://astronomy.stackexchange.com/questions/13204/stability-of-orbital-resonance.  
> **username_2**: [Duplicate of this earlier question](http://astronomy.stackexchange.com/q/13204/7142), which is also answered.  

---

## 1 answers

### Answer by username_3 on 2016-05-24. Score: 9 | Accepted answer

This is actually a very subtle question, much more so than the answers to the similar questions provided in the comments give it credit for. When I was in graduate school at Ohio State I routinely asked this question to visiting dynamicists and invariably got different answers.

The very basic answer is that if you have two sufficiently strong resonances sufficiently close together, then the resonance will be unstable. Otherwise, the resonance will be stable. But what determines "sufficiently strong" and "sufficiently close" is where things get very complicated quickly. A basic criterion is the [Chirikov criterion](https://en.wikipedia.org/wiki/Chirikov_criterion). (The [Scholarpedia article](http://www.scholarpedia.org/article/Chirikov_criterion) is somewhat more detailed.) However, the Chirikov criterion is not universally valid.

If you have overlapping resonances, then an object gets bounced back and forth between these two resonances chaotically. These different resonances perturb the orbit in different ways, and eventually they will perturb the orbit into an unstable orbit, thus leading to depletion of the resonance. If a resonance is "distant" from other resonances, then the resonance tends to keep objects locked in place, leading to an excess of objects in the resonance.

Most of the resonances in the asteroid belt are fairly close together, which leads to them being unstable. The Kirkwood Gaps are the most prominent manifestation of these instabilities. For example, the [Alinda family](https://en.wikipedia.org/wiki/Alinda_family) of asteroids are in a 1:3 resonance with Jupiter, and are very close to a 4:1 resonance with the Earth. This leads to instability, and hence very few asteroids in this family. However, in the outer Solar System, the resonances are generally far apart, and so are mostly stable. The [plutinos](https://en.wikipedia.org/wiki/Plutino) are one example of such a stable resonance, being in a 3:2 resonance with Neptune.

> **Comments:**
> **username_0**: Upon further investigation the answer to my question may even be simpler than this. It may be that the resonance is an "attractor" when objects are of the same order of magnitude of size (even Neptune and Pluto) and an "ejector" when one of the objects is much bigger (such as Jupiter and the Kirkwood gaps and Mimas and some of Saturn's ring gaps. It would seem that Plutinos are more about the 1:1 resonance with Pluto than the 3:2 resonance with Neptune.  
> **username_3**: I don't think the relative masses of the objects really matters.  The Hilda asteroids, for instance are in a relatively stable dynamical state of a 3:2 resonance with Jupiter despite being much less massive.  
> **username_0**: Here's an interesting older review article: http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1976ARA%26A..14..215P&amp;data_type=PDF_HIGH&amp;whole_paper=YES&amp;type=PRINTER&amp;filetype=.pdf                It doesn't seem to me that there is a consensus yet on resonances and it's way too complicated for me, but the gap explanation may be that although there is stability at the resonances, the objects also librate (oscillate about the resonance) and so tend to have more collisions than non-resonant objects. The Hilda and Alinda groups would be the "survivors".  
> **username_0**: Maybe about the relative sizes of the objects in resonance?  

---

