Luna’s Convex Orbit

Luna orbits Earth and Earth orbits Sol (where Luna is Earth’s moon and Sol is Earth’s star, the sun). As a kid, I thought Luna’s solar orbit formed a loopy spirograph pattern. Instead, Luna’s orbit is convex!

Neglecting the eccentricity and tilts of the orbits and the incommensurability of the periods, Luna’s counterclockwise path around Sol is roughly a dodecagon, as in the idealized animation, where the distance between Earth and Luna varies from cartoon large to proportionally correct. Colors code the path’s curvature, red for counterclockwise-rotating velocity vectors and cyan for clockwise-rotating velocity vectors, with magnitudes proportional to the saturation, so white is straight. Due to the convexity of both Earth and Luna’s orbits, some planetary scientists consider Earth and Luna to be a double planet.