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Does the moons have moons?
the moon has 12 moons of its own, and they rotate at the speed of Jupiter
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Does the moon have a moon?
No. Mainly becuase the moon's gravity is not large enough to attract other satellites (other moons) around it
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Can a moon have moons?
Yes. Think of it like this, and object, orbiting an object, orbiting an object, orbiting an object. If Earth can orbit the sun with the moon still orbiting the Earth, then what keeps a moon from...
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Can a moon have a moon?
It is possible but unlikely due to gravitational perturbations with the host planet which would pull the secondary moon out of it's orbit around the primary moon.
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Can the moon have moons?
Yes it can. If an object small enough to get caught in its gravity and orbit the moon does get caught then yes it can have a moon.