Exoplanet Libration Phase Diagram

A tidally locked exoplanet is often described as having one face permanently frozen toward its star — true only for a perfectly circular orbit. This 2D companion strips away the orbital picture and plots the physics directly as angles: a dual-hand dial where the spin angle M advances at the constant mean-motion rate a tidal torque actually locks onto, next to the true anomaly ν, which speeds up at periapsis and slows down at apoapsis under Kepler's second law. Their difference, the libration angle ψ = ν − M, is traced live as a scrolling strip chart and as a closed polar loop whose size grows to roughly 2e radians as the orbit's eccentricity increases — the same forced libration that rocks a real tidally locked world's substellar point back and forth once per orbit.