How many planet-like celestial bodies of roughly the same mass (say within 50%) could orbit a star at roughly (say within 10%) the same distance from the star and be in stable orbits. By stable I mean they would not require tethers or significant energy to stay there.
I feel sure the answer is at least 2, Earth plus another body at Lagrangian Point L3. I have heard it's not 3 -- that putting Earth-size bodies at Earth's L4 and L5 would destabilize. Is that true? Please explain concisely and cite reputably. I'm asking in the interests of Earthling living space within the solar system, in the far future of course. (Or other stellar systems in the uber far future.)
Thanks to @dgh for steering the terminology away from "planet" which is defined by the IAU as having cleared its neighborhood (i.e. orbital radius) of other bodies.
- Klemerer Rosette (theoretically unlimited, but practically no more stable than a ball on a hill)
- Iridium Satellites (66 are active in stable, Low Earth Orbit, in six planes)
EDIT - Here's an excellent tool for playing around with this idea. (Though more visually than mathematically - Kids don't try this on your home planet.) Stefano Meschiari's Super Planet Crash game:
Note the untimely and unfortunate exit stage left of Planet 1, at what appears to be chillingly in excess of solar escape velocity. In the above simulation, 5 planets of varying sizes started out in the habitable zone, and stayed quite orderly for almost 25 years: they varied in distance from each other but stayed remarkably equidistant from the sun. The rerun seems to play out differently each run, due to butterfly effects I suppose.
On the other hand, the following is an 11-planet simulation that was stable for over 500 years:
I just clicked out the planets at the same distance to the sun, and they stayed there. This apparently defies the quote above, that the Klemerer Rosette is "no more stable than a ball on a hill". It may not sustain forever, but some dynamic could be observed keeping these 11 bodies apart.