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I keep thinking of various planetary system configurations, and would like to know:

  • What are the fundamental references based on Monte Carlo long-term simulation of planetary systems' evolution that put testable restrictions on the distribution of stable configurations around Sol-like stars (books, papers, software packages)?

  • How rare is the configuration wherein a dwarf planet (Ceres, I'm looking at you) is located in the inner system?

The main question is the first one, in the vein of "teach a man to fish...".

Related Q&A's here that do not answer my question:

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    $\begingroup$ The orbit of a dwarf planet in the inner planetary system is almost certainly chaotic and hence unstable, unless it is in orbital resonance with a major planet. $\endgroup$
    – Walter
    Commented Dec 1, 2014 at 15:32
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    $\begingroup$ Our solar system is odd in that our innermost gas giant, Jupiter, is quite far out. In systems with hot Jupiter's, the dwarf planet would have to be much closer in that Ceres. $\endgroup$
    – HDE 226868 ♦
    Commented Dec 1, 2014 at 21:20
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    $\begingroup$ @HDE226868 It is too soon to say the solar system is odd. Lots of 10 year orbit gas giants are starting to be found. It is the hot Jupiters that are odd, occurring in only ~1% of stars. $\endgroup$
    – ProfRob
    Commented Dec 19, 2014 at 7:55
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    $\begingroup$ @HDE226868: That could be observational bias. Hot Jupiters are easy to find; since they're both massive and close to the parent star, they cause the star to move and are more likely to block some of its light. $\endgroup$
    – Keith Thompson
    Commented Dec 20, 2014 at 2:59
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    $\begingroup$ Ceres is a dwarf planet that sits quite happily inside Jupiter's orbit. There's no reason to assume similar orbits are unstable. On a much smaller scale, Io and Europa have stable orbits inside Ganymede's. The key to stability is resonance. 4:1 and 2:1 for Io and Europa relative to Ganymede, and 5:2 for Ceres relative to Jupiter. $\endgroup$
    – ganbustein
    Commented Dec 31, 2014 at 10:32

2 Answers 2

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This is just a repository of useful links to software and papers along the way.

  • NEMO

  • On Toolboxes and Telescopes , by Hut and Sussman, (1986) in: The Use of Supercomputers in Stellar Dynamics, Springer Verlag, p 193-198.

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I have an answer for the first part of your question, because I looked it up in answering https://physics.stackexchange.com/questions/8827/question-on-the-stability-of-the-solar-system/161973#161973 on Physics SE.

If you want to see what the current state of the art on solar system simulations is you could do worse than watch Sean Raymond's presentation at "Protostars and Planets VI" from 2013. You can find the actual write up here. Or from the same conference there is Melvyn Davies' review of the long-term dynamics of planetary systems. The talk can be seen here. This review does contain the sort of information you are looking for. It discusses the past and future evolution of our solar system, as well as planetary systems in general. It presents and reviews simulations and discusses the relevant issues. Both of these guys are excellent speakers.

A brief summary would be that the solar system is probably stable for the remaining lifetime of the Sun. However, there is the intriguing possibility that Mercury could fall into the Sun or collide with Venus in the next billion years or that Mars could be ejected from the solar system on a similar timescale (e.g. from the N-body simulations of Battygin & Laughlin 2008).

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