Orrery. An orrery is a model of the Solar System used to show the order of the planetary orbits around the Sun. Here, there are nine 'planets' (including Pluto, now classed as a dwarf planet), and the Earth has its Moon. Here, only a vague attempt at showing the relative sizes of the planets has been made. In most orreries, a mechanism allows the planets and moons to rotate in the correct ratios of their orbital periods.