Distance between stable orbits

[ajtribick]

Any way of working out how far apart two planets must be so that they won't disrupt each others orbits too much?

[selden]

Well, you could always use a variant of Bode's Law

See http://astrosun2.astro.cornell.edu/academics/courses//astro201/bodes_law.htm

I dunno if anyone has tried to figure out if something like that might be valid in other systems.

[Evil Dr Ganymede]

Well, you could always use a variant of Bode's Law

See http://astrosun2.astro.cornell.edu/academics/courses//astro201/bodes_law.htm

I dunno if anyone has tried to figure out if something like that might be valid in other systems.

I thought Bode's "Law" broke down for Neptune?

But yeah, the other world design systems I've seen usually assume some variant of Bode's Law.

[tony873004]

You could run a simulation. Based on your question, I tried this in Gravity Simulator. I placed a planet inbetween Earth and Venus in a circular orbit, and another planet at 2 AUs from the Sun, just exterior to Mars' orbit, also in a circular orbit. After letting the simulation run for about 280,000 years (1 day actual time), I observed that the planet inbetween Earth and Venus quickly departed from a circular orbit. Its orbit kept changing shape, and sometimes intersected Earth's orbit, and at other times intersected Venus' orbit, but never both at the same time. A collision with one of those two planets is probably the new planet's destiny. The planet at 2 AUs had its orbit get more and more elliptical. Right now its at .2 eccentricity, but I suspect that this will increase if I let the simulation run longer. It will probably reach some maximum level and then begin getting more circular with time, and then repeat the process over and over again. I believe this explains Mars' high eccentricity. I think Jupiter just tugs it into and out of round. Maybe later I'll remove Jupiter and try it again just to see if Jupiter is the cause.

[granthutchison]

I've never understood how Titius-Bode has retained popularity for so long - with a smallish random dataset you can come up with a similar numerical relationship more often than not.
Solar System Dynamics manages to dispose of it by page 8. After a statistical examination of the supposed regularity in spacing of the major Uranians, they conclude: "There is no compelling evidence that the uranian satellite system is obeying any relation similar to the Titius-Bode 'law' beyond what would be expected by chance. This leads us to suggest that the 'law' as applied to other systems, including the planets themselves, is also without significance."

Grant