Moon Orbit Angle

The Moon orbit is implemented by a turntable set at an angle to the ecliptic.  The real angle is about 5º, the orrery uses an exaggerated angle of almost 21º.

For 3D work we need to know α and β

We know
AC=5×8.0=40.0
BC=4×8.0=32.0
AD=6×8.0=48.0
BD=9.6+3.2+32.=16.0

From that follows:  $$AB=\sqrt{A{D}^2+B{D}^2}=\text{50.596443}$$

$$\theta =\arctan (\frac{BD}{AD})=\text{18.434949º}$$

In the general triangle ABC of which we know the three sides we apply the sine rule:

$$2s=AB+BC+CA=\text{122.5964}$$

$$\sin \frac{(\theta +\alpha )}{2}=\sqrt{\frac{(s-AC)(s-AB)}{AB.AC}}$$

$$\theta +\alpha =\text{39.2169}º$$

$$\alpha =\mathrm{39.2169º}-\mathrm{18.434949º}=\mathrm{20.78195º}$$

Likewise

$$\sin \frac{\beta }{2}=\sqrt{\frac{(s-CA)(s-CB)}{CB.CA}}$$

$$\beta =\mathrm{88.5675º}$$

Bracing of main Arm

Bending and sagging of the main arm is prevented by a strut on either side, to brace the slender assemblies of long bearing bricks.

The only way to achieve right angles is to use Pythagorean triples (the best known triple is 3-4-5, since $3^2+4^2=5^2$ ).

We use 6-8-10 (twice the 3-4-5 triple) on the counterweight side, and 7-24-25 on the Moon orbit side.

Further pages

Here is a sequence of pages on how to build it:

• Basic Mechanism