How did the heliocentric model explain the existence of Jupiter's moons more economically than the geocentric model?

Answer

By allowing other centers of motion to exist

The heliocentric view allowed for Jupiter to act as its own small center for its satellites, just as Earth centers the Moon, making the observation naturally fit the structure.

How did the heliocentric model explain the existence of Jupiter's moons more economically than the geocentric model?
Galileoastronomyobservationsheliocentric modelJupiter's moons