Earth’s Moon doesn’t have its own satellite (called a “sub-moon”) because Earth’s gravity would quickly destabilize the sub-moon’s orbit, either ejecting it from the system or sending it into orbit around Earth.
NASA /JPL / Northwestern University
If a sub-moon could form around (or be captured by) a satellite, the gravity from the parent planet would quickly destabilize the sub-moon’s orbit, either ejecting it from the satellite system or sending it into orbit around the planet.
