# Question on the stability of the solar system

One of the pertinent questions about many body systems that causes me much wonder is why the solar system is so stable for billions of years. I came across the idea of "resonance" and albeit an useful concept, it hardly explains the long stability of the solar system. Normally an N body problem with inverse square mutual interaction is an example of a chaotic system. Is there any real progress about this stability issue?

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It is important to note that chaotic systems can still have bounded orbits; chaos does not preclude stability. –  Chris White May 15 at 20:11

Jack Wisdom at MIT has extensively studied the question of the stability of the solar system. He has a list of papers with links to freely-readable PDF files on his website:

http://groups.csail.mit.edu/mac/users/wisdom/

A good starting point might be "Is the Solar System Stable? and Can We Use Chaos to Make Measurements?" (PDF) (in Chaos, proceedings of the ''Joint Soviet-American Chaos Conference'' held at Woods Hole, June, 1989).

The abstract begins:

This talk addresses two separate questions: "Is the solar system stable?" and "Can we use chaos to make better measurements?" In the first part, a review is presented of the numerical experiments which indicate that the motion of Pluto, and indeed the whole solar system, is chaotic.

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A more recent analysis, extending through $5\cdot10^9$, years can be found at Existence of collisional trajectories of Mercury, Mars and Venus with the Earth. –  mmc Apr 21 '11 at 1:10

The classical work on the stability of the solar system was of course done by Laplace, see e.g. http://en.wikipedia.org/wiki/Pierre-Simon_Laplace#Stability_of_the_solar_system

Using perturbation theory he found an argument why the system Sun-Jupiter-Saturn is stable. However, nowadays people doubt the assumptions he made about the behavior of higher order terms; Instead high precision numerical simulations are used to predict the future of the solar system (links to this research have been posted in answers already).

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The sun contains about 99.9% of the mass of the solar system, so the motion of a planet is approximately that of a two body problem with $m<<M$, which is quite stable.

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Perturbations of one planet's orbit due to the others are small, but it's not at all clear that they wouldn't add up to produce instability over long time scales. As I recall, the long-time stability of the solar system was an active research question not all that long ago (the 80s and 90s?), but I don't know how or if it was eventually resolved. –  Ted Bunn Apr 18 '11 at 15:41
Experimentally it's stable for around 5Bn yr - the future is less certain! –  Martin Beckett Apr 19 '11 at 20:09
What exactly is meant by stable here anyways? And what is a long-time scale? Long compared to what? –  user1708 Apr 19 '11 at 20:21
@Martin: the experiment is skewed by the boundary condition that we are here to observe it. Maybe the stability scale is only 100mn years, and we got lucky. –  Ron Maimon Oct 8 '11 at 21:57
@Ron well presumably it's been stable enough for 5Bn years to have the earth remain intact. And stable enough for life for 3.5Bn –  Martin Beckett Oct 8 '11 at 22:24