Orbits around and through a Sphere

This Demonstration shows the orbit of a probe mass in the gravitational field of a homogeneous sphere. Assume that the particle can penetrate the sphere without frictional forces being exerted. Inside the sphere, the gravitational force forms a harmonic oscillator (potential ) and outside the sphere the potential is a pure Coulomb potential (potential ). In both cases, the orbits are ellipses. In case the orbit has segments inside and outside the sphere, rosette orbits are obtained.