Script for Geartrain Module
This shows a design for a way to use multiple stacked turntables. The premise of this method is that each level is turned by the level beneath it, and each level contains all of the gearing to drive the level above it.
A single central shaft provides the power to drive all of the levels. A large number of gears of different sizes takes the speed of that central shaft and converts it to a slower speed to run the level above. The final gear runs a chain that goes to the turntable above.
This type of design needs to have very low friction to work well and it does, as you can see here I can run it backwards by turning the slowest part.
There is also a bevel gear and a radial axle that goes out to where the planet would be. This allows us to have one or more moons that move around the planet.
The Wikipedia Orrery article is a great place to start.
Here are some other Lego orrerys, ranging from very serious to totally whimsical:
 George Moody (and son), Lego Orrery (web page). This model of the Sun-Earth-Moon system duplicates the rotational period of all three objects and the orbital periods of Earth and Moon to within ±1%, at a scale of 3.5 seconds = 1 day.
 Michael Whiting, "Orrery Developments: The Use of Meccano in Constructing Planetaria", Bulletin of the Scientific Society (94), 2007.
 Alex Allmont, Portfolio (website), 2011-2012. Has a list of recent installations and projects, and relevant videos. "Music of the Gears" is particularly relevant to orreries.
 Guy Himber ("V&A Steamworks" on Flickr), inspired by "a giant fantasy orrery in the movie Dark Crystal", made this somewhat whimsical Lego Orrery, 2011. There is also a video at Makezine: Lego Orrery, also at YouTube: Lego Orrery.
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The graph paper in my newer photos is ruled at a specing of 1 LSS, which is about 7.99 mm.
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