The science
What you see. Planet arms are turned by tooth gears. Cyan ghost markers show where Kepler's laws put the planets; the brass arms follow uniform circular motion set only by tooth counts.
Kepler. 1) orbits are ellipses with the Sun at a focus; 2) the radius vector sweeps equal areas in equal times, areal speed dA/dt = πab/P; 3) P² = a³ (years, AU).
M = L − ϖ mean anomaly
M = E − e sin E Kepler's equation (Newton)
ν = 2 atan2(√(1+e) sin E/2, √(1−e) cos E/2)
r = a(1 − e cos E), λ = ν + ϖ
C(M) ≈ 2e sin M + 1.25e² sin 2M equation of centre
gear train: θ_planet / θ_Earth = (a/b)(c/d)
drift = 360°·[(a/b)(c/d)/P_E − 1/P_planet] per year
brass error = drift·t − C(M(t))
Assumptions. Mean J2000 elements (typical values after the JPL approximate-positions table; spot-check against the source); elements held constant (no perihelion precession), orbits coplanar, Earth's gear is the 1:1 reference (zero drift by construction), tooth meshing drawn with different modules per stage (cosmetic), orbit radii compressed for display. The real 18th-century orreries are also a crude approximation: this lab shows exactly how crude, and why.
Checks. running…
Virtual model for education. Not an instrument for real astronomical prediction.