This alternate introduces a different type of orrery based on the ancient geocentric model, where the Earth is at the center. The most known version of the model is the so-called “Ptolemy” model. This model can be built with parts of the #42179 set only for a manual version, but it can easily be motorised with a few additional parts.
The orrery features the Earth, the Moon, and the Sun, but also Venus and Mercury (so actually more celestial objects than the original model!).
In this model, the positions of the celestial objects are relative to the Earth, as they all rotate around it. The two simplest ones are the Moon and Sun, which show simple rotations. Mercury and Venus’ movements are more complex, as from the Earth’s perspective, they seem to sometimes move backward. To account for this observation, the ancients modeled their movement using so-called Epicycles; that is, they turn around a point that itself turns around the Earth, an orbit called the “deferent”.
The center of Venus’ and Mercury’s deferents are aligned on a Earth-Sun axis, which is why I chose to use this axis as the main part of the orrery, as a kind of bench, with the Earth turning on itself instead of the axis revolving around the Earth, for better stability. Note that in the Ptolemy model, Venus is closer to the Sun, and Mercury is closer to the Earth.
I tried to keep the rotation speeds and epicycle radii as close to their “true” values, which I took from this source: https://github.com/skyfielders/astronomy-notebooks/tree/master/Medieval.
Here are the periods (in days) for each object:
- Moon: 27.32163085309721
- Sun = Mercury’s deferent = Venus’ deferent : 365.2584871884172
- Mercury’s epicycle : 87.97141388757626
- Venus’ epicycle : 224.70096268375522
We then need to compute the relative rotation rates. As the axis Earth-Sun is fixed, the Sun’s rotation is our reference rate from which the others are derived:
- Sun: 1.0
- Moon: (1 / 27.32163085309721) / (1 / 365.2584871884172) = 13.369
- Mercury’s epicycle: (1 / 87.97141388757626) / (1 / 365.2584871884172) = 4.152
- Venus’ epicycle: (1 / 224.70096268375522) / (1 / 365.2584871884172) = 1.626
As for the radii, we have (in units of the Earth’s radius):
- Moon: 59.7
- Mercury: deferent = 104.0407, epicycle = 39.40877
- Venus: deferent = 226.0463, epicycle = 163.3619
Since the Earth and Sun Lego models are anyway not to scale, I built everything related to the Moon’s orbit radius, which gives
- Mercury: deferent = 1.743, epicycle = 0.660
- Venus: deferent = 3.786, epicycle = 2.736
In the model, the Moon is mounted on a 7-beam, so that the radius is equal to 6. Similarly, the radii of Mercury and Venus are 4 and 11, respectively. Relative to the Moon, this gives ratios of 4/6 = 0.6666 and 11/4 = 2.75, so not too far from the true values.
The rotation rates are more challenging to obtain, based on the gears available in the original model. Here are the values I could get:
Moon
We have the following chain: Turntable (60 teeth) / 20t -> 24t / 8t -> 20t / 12t -> 20t / 24t / mini-turntable (28t). The resulting speed is: 60/20 * 24/8 * 20/12 * 20/24 * 24/28 = 10.71429. This is a bit slower than the true speed (13.369).
For Mercury we have: turntable (60t) / 20t / 12t -> 24t / 8t -> 16t / 16t -> 8t / mini-turntable (28t).
This gives 60/20 * 20/12 * 24/8 * 16/16 * 8/28 = 4.285714, for a true relative speed equal to 4.152. Not bad, uh?
And for Venus: turntable (60t) / 20t -> 36t / 12t -> 12t / 12t -> 12t / 60t, which then gives 60/20 * 36/12 * 12/12 * 12/60 = 1.8 for a true value of 1.626.
All epicycles turn in the same direction, as they should. You can see the model in action in the trailer video:
Presentation on TechLUG.fr (in French): https://www.techlug.fr/Forum/viewtopic.php?f=5&t=13060
Building instructions available at Rebrickable: https://rebrickable.com/mocs/MOC-186679/alter-lego/42179-alternate-geocentric-orrery/