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Have we discovered any natural satellites of natural satellites of planets or dwarf planets? Even very small, or relatively short-lived - e.g. ringlets around Saturn's moons, some meteorites orbiting Jupiter moons, or something to orbit Charon? Or is the Star-Planets-Moons the deepest naturally ocurring orbital recursion level?

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I don't have any hard evidence but I think a moon is defined partly by orbiting a planet and might otherwise just be a natural satellite. That's assuming the object isn't pulled into the planets orbit by it's much stronger pull. – RhysW Nov 4 '13 at 13:14
I tend to use titles that are more descriptive than factually accurate; I tend to explain more and stick to proper nomenclature in the actual question body. As for "assuming", well, that's what this question is asking about! – SF. Nov 4 '13 at 13:34
Hmmm at what level do you want us to stop? Because I don't think there's any proper size limit or a limit of how many iterations of smaller objects orbiting slightly bigger one there can be. Case in point, Rhea might have its own ring system, which, if true, would mean it has tiny moonlets then. I also remember that antenna cover floating around the ISS, although that's already a dual artificial satellite system LOL. There are also some wacky orbits possible, like the horseshoe orbits that can trap asteroids between two bodies. ;) – TildalWave Nov 4 '13 at 15:47
@TildalWave: If there is any level for natural satellites, I'd like to know it. (artificial satellites like that antenna cover don't count). If Rhea has a ring, that would be what I seek. Any periodic orbit would work, but please no cheats like two overlapping minimally elliptical orbits that make the bodies move in circular path relative to each other despite not really interacting gravitationally with each other, just following independent path around their planet.) – SF. Nov 4 '13 at 16:44
Well frankly I don't know where to start answering it. It's a bit like asking how many cogs can be in a clockwork and still make it show true time. Planetary systems can be as complex in theory as we are capable of imagining, and as complex in reality as we're able to observe. – TildalWave Nov 4 '13 at 18:59
up vote 8 down vote accepted

I don't think there are any in the Solar system. We do have around 250 asteroids with moons. Rhea's ring seems to be the only exception.

Edit: originally I said "a moon with a moon would be an unstable system, due to the gravitational influence of the planet". @Florian disagrees with this. However, the answer is more complex than the Hill sphere alone.

At first approximation, the Hill sphere gives a radius in which orbits around a moon could be stable. Our Moon's Hill radius is 64000 km.
For our own Moon, we know that most low orbits are unstable due to mascons: mass concentrations below the surface which make the Moon's gravitational field noticeably uneven. There are only four inclinations where an object orbiting the Moon avoids all mascons and would be stable: 27º, 50º, 76º, and 86º.
High orbits above the Moon aren't all safe either: above 1200 km and inclinations of more than 39.6º, Earth's gravity disrupts the satellite's orbit. Note that these orbits are comfortably within the Moon's Hill sphere.
There are stable orbits at high inclinations and high eccentricity:
Stable moon orbit
As for other moons in the solar system: most of them are smaller and orbit around larger planets, so their Hill spheres are small, and the planet's gravity will disrupt much of the volume inside the Hill sphere too.
Moons below the limit where their gravity is strong enough to make them spherical, will have problems with uneven gravitational fields. Mascons may also be present.

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"a moon with a moon would be an unstable system" - this is incorrect. Orbits are stable within the Hill sphere. BTW, please don't use articles as "supporting evidence". – Florin Andrei May 1 '14 at 16:51
Feel free to write a better answer. – Hobbes May 1 '14 at 16:56
Anyway, the article doesn't mention "unstable systems" :) – Py-ser May 2 '14 at 1:33
Well, 'boulders up to several decimeters in size' within Rhea's ring aren't exactly 'moons' but I wouldn't hesitate to call them 'natural satellites', so, yes, this is clearly a case of a planet's satellite with own natural satellites. – SF. May 4 '14 at 15:52

There is a prior answer here claiming that "a moon with a moon would be an unstable system". That is incorrect.

Intuitively: Of course satellites can have satellites with long-term stable orbits. Think of the Earth orbiting the Sun, and the Moon orbiting the Earth. The orbit of the Moon (a satellite's satellite) is long-term stable.

More rigorously:

The orbit of a satellite's satellite will be stable if it's deep enough inside the Hill sphere, within the so-called true region of stability. The limits are a bit fuzzy, but the true region of stability is typically the lower 1/3 to 1/2 of the Hill sphere.

If you look at the gravitational potential, the Hill sphere is the area where contours become circular. Deep into that zone, orbits are long-term stable:

enter image description here

Bottom line is: A moon can have its own moons if it's big enough, and far enough from the planet, and if the secondary moons are close enough to the primary moon.

One way to calculate the Hill sphere is given on the wiki page linked above. Some more math can be found here:

A few extra articles about the issue of long-term stability of satellite orbits:

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-1, this is answer is incorrect. The Hill sphere is just an approximation, and for a moon, it is not a good approximation of the region of stability. The Hill sphere ignores perturbations such as non-spherical gravity, other gravitating bodies (e.g., the Sun in the case of the Hill sphere of a Moon), effects such as the Kozai mechanism, and non-gravitational forces. – David Hammen Feb 28 '15 at 16:38

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