Is there any known moon of a moon?
As far as I understand, a moon is an object in permanent orbit around a planet, dwarf-planet, asteroid, etc. If there was another object permanently orbiting this moon, would that be a moon-moon?
Is there any natural object of such kind that we know of?
If no, why are such objects so unlikely?
Edit: this is question is different from Do moons have moons? because I explicitly ask for a reason. Also, the terminology is included here.
Similar, not exactly the same question here: https://astronomy.stackexchange.com/questions/856/do-moons-have-moons
@userLTK thanks for this hint, the answer given there is very comprehensive.
I reckon the most likely candidates for moons to be orbited by a sub-moon would be Titan, Luna, and Triton. Perhaps also Callisto, but despite the high mass not Ganymede, because of its quite close orbit around the massive Jupiter and strong gravitational interaction with Europa.
No. One explanation for the equatorial ridge on Iapetus involves a now-lost subsatellite, so perhaps such objects existed in our Solar System's past.
Subsatellites tend to get rapidly removed by tidal forces causing changes to the orbit. Depending on the parameters of the system, the orbit may decay until the subsatellite collides with the moon or breaks up at its Roche limit. Alternatively it may migrate outwards until the subsatellite becomes unbound: at this point it would become a moon of the planet, though likely on an unstable orbit that would lead to scattering or a collision. The orbital evolution tends to be faster for more massive subsatellites. See Kollmeier & Raymond (2018) for details, who note that any subsatellites orbiting the candidate Neptune-sized exomoon in the Kepler-1625 system would need to be smaller than Ceres to survive.
It is ironic that the larger bodies (the ones you'd expect to have stronger structural integrity) are more susceptible to such forces than smaller ones. But then, astrophysics has known to be non-intuitive on more than one occasion.
Why is it the case that these 'subsatellites' are less stable than the satellites of a planet? If a planet was as massive as the sun, and had a satellites the same size and distance as earth, would its equivalent moon be inherently less stable than our own? because it's a 'subsatellite'?
@JeffUK No. I think it's a scale effect. The answer to https://astronomy.stackexchange.com/questions/856/do-moons-have-moons (linked by userLTK) explains it pretty well.