I think there are no examples in our own Solar System. But suppose we imagine a Jupiter-like gas giant orbiting a faraway star. This has several moons, including an Earth-like ball. Could there be a Luna-like rock orbiting?
Is there any reason why it couldn’t happen? Maybe the gravity of the main planet would prevent a stable orbit forming, or something.
Others more orbitally mechanically inclined will soon chime in, but I believe the answer is yes, but the choice of orbits that work for this is somewhat limited so would be more rare.
Not exactly what you were probably thinking of, but: Pluto’s (not a planet anymore, I know) moon Charon orbits Pluto in such a way that their joint centre of gravity is outside Pluto. In other words, the two planets orbit each other as a double planet system, and Pluto is just as much a moon of Charon as Charon is Pluto’s.
Our moon orbits the Earth which orbits the sun. So obviously you can have a three body system with that configuration. A fourth body would complicate the problem, but theoretically our Solar System could be orbiting a large black hole so we may already be in a 4 body configuration.
Not really. We are going around it, but it is not its gravity that holds us in orbit. If you removed the central black hole of the Milky Way, very little would change.
Anyway, to the OP, a very qualified yes. You can have a setup where a very large planet orbits a star, and a large moon orbits that planet, and a small object orbits that moon. It’s all about Hill spheres.
But, it would be very unlikely to develop on its own, and it would be very unstable and unlikely to last long, cosmologically speaking.
Do we have satellites orbiting our own moon? If so is it difficult for them maintain an orbit? Like more difficult than the ones we have orbiting the earth.
A little. Most require some level of station keeping. There really are no “permanent” orbits.
A satellite in Earth’s geostationary orbit will orbit for millions of years easy. I don’t think that you could find an orbit around the moon that would persist for hundreds, much less thousands of years.