I'm wondering if there's a name that encapsulates the concept of a planet and the objects that orbit in its gravity. There's a solar system that encapsulates a star and its multiple planets and other objects, but I don't think that "solar system" describes the Earth and its moon, or Jupiter and it's many moons, for example.
This question has been asked before on the Space Exploration page.
In summary, the term used is system, e.g. the 'Jupiter system'.