And if it did, what would we call it?
While you probably haven't, a curious four-year-old did back in 2015 and on Tuesday, his astronomer mom and one of her colleague's published a paper that essentially says: Yes, a moon can have its own moon.
No known moons have a moonmoon, but Sean Raymond and Juna Kollmeier, the astronomers working on the paper titled "Can Moons Have Moons?" argue that the existence of such a moon is possible given the right conditions.
Moonmoons (or submoons) need to be close enough to the moon to be bound by its gravity - but not so close they're torn to bits by tidal forces.
Natasha Frost explains on Quartz that moonmoons could occur when all the proper pieces are in place "if, for instance, the large moon is quite large, the small moon is quite small, and both are sufficiently far away from the host planet".
Within the Solar System, four moons now meet that particular requirement: Earth's Moon, Jovian moon Callisto, and Titus and Iapetus in orbit around Saturn.
Could a moon actually have its own moon, orbiting around it, rather than around the planet?
And then that delicate gravitational balance would have to be maintained. Along with moonmoons, they could also be called submoons, moonitos, moonettes, or moooons.
One name being considered is "moonmoon, "according to New Scientist. He was the inspiration for the work and if he likes moonmoon or moonito or whatever, I have to back it!"
And, given the difficulty in detecting even a moon outside the Solar System, our chances of spotting an exomoonmoon are, for the time being, pretty much zero. That's a very intriguing notion that could have real-world applications for how we deploy satellites and understand the formation of planetary systems.
The mere possibility of them, and their absence from where we might expect to see them "provides important clues to the formation mechanisms and histories of" solar systems.