# Egg-Shaped Orbits of Non-Uniform Oscillators

Egg-Shaped Orbits of Non-Uniform Oscillators

A simple non-uniform oscillator follows the differential equation =1-acos(θ) (the blue curve). In an imaginary solar system where the planets follow this law of motion, but where angular momentum is conserved, planetary orbits would be egg-shaped (the red curve), with the parameter taking a role akin to the orbit eccentricity.

θ

a