Physics / Astronomy
Retrograde motion
Ptolemy vs Copernicus: the same planets, two frames. Pin the Earth and epicycles appear by themselves - Mars walks backwards once per synodic period.
What happens
Nothing here is staged: six planets run on their real J2000 Kepler elements, and the frame button only changes which point is subtracted before drawing. In the pinned-Earth frame the heliocentric ellipses become looping epicycles, and Mars visibly reverses along the sky for seventy-odd days around every opposition - the rate chart dips below zero exactly then, once per 779.9-day synodic period, a number the model never stores. Outer radii are compressed (r^0.62) so Saturn shares the stage with Mercury; angles are untouched, so every station is where the sky put it.
Equations used in the module
Equations M = E−e sin E; r = a(1−e cos E) λ = atan2(y_p−y_E, x_p−x_E) 1/S = |1/T_E − 1/T_p| dλ/dt < 0: λ(t+Δt) < λ(t)
