# What is orbital resonance

## Orbital resonance stability

Lately I've gotten more interested in the topic of the stability of planetary systems. I've read about it and it seems that orbital resonances play an important role in the stability of the solar system (as well as for the moons of Jupiter and other planets).

I thought at first that the orbital resonance is somehow more stable and therefore we have several cases in the solar system.

But as I read on, I found that there were some gaps in the asteroid belt, right where the resonances occur, so the resonances are actually unstable for asteroids.

I then thought that some resonances are stable while others are unstable, but some of the resonances that form gaps in the asteroid belt are actually present in the solar system between planets so I am completely lost.

Why are resonances sometimes stable and sometimes unstable? What am i missing Maybe I'm getting something wrong because it doesn't make sense to me. Any help is welcome.

I'm not very familiar with orbital dynamics (please correct me if I'm wrong). I was told that, for example, with the mean motion resonances that cause most of the Kirkwood gaps in the asteroid belt, not only the ratio of the periods but also the timing is important.

Take Pluto as an example, which is in 2: 3 resonance with Neptune. Although Pluto crosses the orbit of Neptune, the two bodies will never come closer than a certain threshold. That is, because the timing between their orbits primarily prevented close encounters, which is then amplified by the resonance.

If the timing were different, close encounters would be possible, thereby destabilizing the orbit of the smaller body. In the case of medium movement resonances, there is an algebraic expression with which the stability of a resonance can be examined (see e.g. here https://en.wikipedia.org/wiki/Resonant_trans-Neptunian_object [towards a formal definition]). .

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