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My dad commissioned me to design an orrery - a working model of the earth, moon and sun. Version 1 was completed just before Christmas, but it needed some tweaks for stability. So here's version 2, finally finished thanks to "working from home"

Here's a video of it in operation.

This is far from the first Lego orrery (see JKBrickworks, Ryu Yakimoto for examples) but I believe mine is unique in that the centre of rotation of the Earth-Moon system is offset by one stud. This because the Moon doesn't rotate around the Earth, in fact they rotate around each other (wikipedia: barycentre), but the centre of rotation just happens to be close to the centre of the Earth because the Earth has much greater mass.

You can see the barycentre offset in the next photo - there are two 8-tooth gears side by side under the black 1x7 liftarm; the one that's not directly beneath the Earth is the one around which the entire Earth-Moon system rotates:

The gear ratios are as follows (counting one model Earth rotation as one 'day'):
Moon completes one rotation around the Earth: 28 days (a synodic month*)
Earth completes one rotation around the Sun: 360 days (a year)
The sun rotates fully on its axis: 24 days **

The Americas and Greenland (I tried my best to recreate the all continents in a tiny scale):

Some of the internal gearing. It's surprisingly awkward to gear things down in multiples of 2, every second axle has to be offset by half a stud to link an 8-tooth to a 16-tooth.

There are loads more photos in the album on flickr.

* A synodic month should be about 29 days and a sidereel month should be about 27 days. A synodic month is one full lunar orbit with respect to the position of the sun, as viewed from Earth, whereas a sidereel month is one full lunar orbit with respect to the stars as viewed from Earth. There's a difference because the Earth is going round the sun and by the time the moon comes back around the Earth is not where it started. Comparing the moon to where the sun is is the equivalent of one full rotation of the small 28-tooth turntable that holds the Earth and Moon.

** The sun rotates, but not strictly every 24 days. Since the sun is a fluid, it doesn't rotate uniformly. The poles rotate roughly every 30 days and the equator rotates every 24 days. Since Lego can't be fluid I just chose 24.