This might be worthwhile if you wish to continue this research. The reason is that the periodicity of the Earth’s change in orbital parameters are recorded geologically. Milankovitch cycles are climactic cycles caused by the Earth’s axial tilt, precession, and eccentricity. They have been investigated at least as far back as 2e8 years, so if you want to “ground-truth” your models of eccentricity evolution, this would be one way to do so.

If you’re interested, a place to start is:
Olsen, P.E., and Whiteside, J.H., 2007, Pre-Quaternary Milankovitch cycles and climate variability, in Gonitz, V. (ed.), Encyclopedia of Paleoclimatology and Ancient Environments, Earth Science Series, Kluwer Academic Publishers, Dordrecht, the Netherlands (in press).

Of course, since precession and axial tilt are dominated by lunar effects, you’d need to include a moon in future runs to compare them…

It is indeed intriguing to think about the fate of these objects, once they have escaped. Dave Stevenson (Nature, 1998) wrote a paper about the possibility of life being sustained on interstellar planets due to geothermal processes.

As far as detection goes, I have no idea ultra-precise gravitational lensing perhaps?

I think in order to get a rough estimate of the number of rogue planets, it would pay to study the dynamics of the earlier stages of planetary systems’ evolution in general, since the dynamics are more violent.

Right, wasn’t thinking of that.

Sorry if I insist, but… In your opinion, what order of magnitude can we expect for the average number of planets that are ejected from a star system?

Let me spam a bit my estimates… Your 1% estimate for the ejection of the inner planets of the solar system in its lifetime is pretty high. If, even taking into account early stages of planet formation the average is much less (say 0.1-0.001%), it means that in the Galaxy there is something like 10^7-10^8 planetary bodies not bound to any particular star. Which sounds impressive, but is a pretty small number, because there could be much less of these objects than stars – our chances to encountering one close in our solar system are far less than meeting an actual star. However they would be not exactly rare. Is there any chance to detect such objects? They look incredibly tricky to find to me (much more than bound exoplanets), but…

Much more titillating would be to find that a substantial percentage of stars, in their early formation, eject planetary bodies. What you say -and the little I know- about the “violence” of early planet formation seems to point towards that. This would mean that the Galaxy is teeming with such objects -say, 10-100 billion rogue planets. Seems fascinating.

I am also thinking that such objects would tend to accumulate, since they are basically cold objects that do not undergo a significant evolution.

Sorry for my trivial late-night babble…

Interesting idea – I think in order to get a rough estimate of the number of rogue planets, it would pay to study the dynamics of the earlier stages of planetary systems’ evolution in general, since the dynamics are more violent. Given that the process of planetary formation can be well modeled, with a large amount of computer power, one could get a probabilistic estimate.

I believe that the perturbative effect of rogue planets to the Solar System is rather negligible, and is probably lost in the soup of extrasolar perturbations. Nevertheless, I think rogue planets are pretty cool.

Two naive questions from someone who works in an entirely different domain (protein folding):

Could it be possible to generalize the results and obtain a back-of-the-envelope estimate of the number of rogue planets in the Galaxy, for example?

Moreover: if the chances of such planets to cross our planetary system are probably small or negligible (given the little cross-section), maybe the odds of them perturbing comets or other objects in the Oort cloud are significant. Again, what could be those odds? Could these rogue planets have a significant role in the evolution of solar systems?

tidal dissipation would no doubt attempt to save the day. Both, the circulization of the orbit and the decrease of semi-major axis would affect Mercury’s precession rate, but of course the actual damage depends significantly on the Q. My instinct is that tidal dissipation is too slow in competition with linear secular resonance, and Mercury would have the chance of attaining e > 0.7 before the tidal forces would significantly alter the g1 eigenfrequency.

the instability observed here is entirely inherent to the orbits. The unstable solutions are simply possible scenarios for the Solar System’s future. In fact, there were no asteroids present in our numerical model, and all bodies were treated as point-masses.

The mechanism which drives Mercury’s eccentricity to high values is linear secular resonance, so one would look to the frequency of the difference of perihelion precession rates of Mercury and Jupiter for a warning. If this frequency goes to zero, we’re in trouble. However, a secular cycle takes place over million year time-scales, so we would have a pretty early warning. For instance, right now, d(Omega1-Omega5)/dt ~ 1arcsec/yr = 1 cycle/1.3Myr.

This would be a pretty cool novel indeed! :)

And what would be the first sign that a “haywire” event was about to happen? How much warning would there be of such an event–are we talking millions of years or just a few hundred?

Sounds like a fascinating subject for a science fiction novel!