WOLFRAM|DEMONSTRATIONS PROJECT

Egg-Shaped Orbits of Non-Uniform Oscillators

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a
0.9
A simple non-uniform oscillator follows the differential equation

θ
=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
a
taking a role akin to the orbit eccentricity.