I think in theory it is possible for a star to have a planet which has a moon that has a moon…. but I don’t think we’ve found one. In fact I don’t think we have a name for them so lets call it a moon2 for now. From what I remember from the physics I did at university, a moon2 is possible provided the moon had it’s own rotational axis. Our moon keeps the same face pointing towards the earth at all times, so the interaction between the earth an the moon (the tides) causes the orbit of any satellite (natural or man made) to decay, and the object would crash after a few years. One of the others might know more.
The way that gravity works is that if there is a small object close enough to the moon and that it isn’t affected by the gravity of a bigger object then it will orbit the smaller object. So yes in theory it’s possible, although we’ve never found a moon orbiting a moon. I think this is a great question, well done!
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