How many nested stable (1 Mio years) orbits are theoretically possible?

Question

If we look at our solar system we have the sun which has planet orbits and planets have moon orbits.

If we look at the possible size difference from hypergiants to small asteroids why shouldn't it be possible to nest orbits to an astounding degree: supergiant orbit a hypergiant, star orbits supergiant and so on ?

My first guess is that the size and distance must be so small in contrast to the primary that the gravitational gradient of the primary does not cause too much disturbance, but it should be possible.

Has anyone tried to find it out with celestial mechanics ? While it may be completely theoretical, it is IMHO a solid question and it would be nice to find out how deep celestial bodies can be nested and how it limits stability.

Some conditions:

• The orbits should be (very probably) stable for one million years. Hypergiants are burning fast, so I limit the stability for a relative short timeframe.

• The barycenter of both satellite and its primary are inside the primary. No double system.

• The first primary should be a star, not a black hole or a neutron star.

Answer 1

Yes, it's possible to have many nested levels, all stable. Each nested orbit needs to be inside the Hill sphere of its central body in order to be stable.

You can't nest any further when the Hill sphere gets too close to the Roche limit. Below the Roche limit the satellite disintegrates.

The exact number of nested levels depends very greatly on the characteristics of all bodies involved.

Answer 2

Tidal forces limit the stability.

Example: http://www.universetoday.com/109666/can-moons-have-moons/

It's easier if you set every orbiter far away from the orbited, but by setting large distances, that limits how many levels of nesting you can do. There are complicated star systems with like 6 or 7 suns, but they aren't nested in the way you suggest. Pluto is a 5 body system but it's also quite far from the sun and it stays far from all the outer planets, and it's got 2 inner bodies (Pluto and Charon) and 3 outer, smaller bodies. Pluto is also quite far from any large gravitational bodies. If Pluto orbited one of the planets, it's 5 body system wouldn't be stable.