A working model of the solar system is called an orrery. This apparatus contains the sun, planets and often their satellites in their correct positions and phases. According to Reference.com, the first such model was made for Charles Boyle, the Earl of Orrery for whom it was named.
An orrery is a mechanical model that is used to portray the movements of the planets and their satellites at appropriate relative speeds, although most orreries are not sized according to scale. George Graham invented this type of planetarium around 1713. Such an apparatus that focuses only on the sun, Earth and its moon without the other planets is called a tellurion.