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.
Contributed by: Michael Trott with permission of Springer (March 2011)
From: The Mathematica GuideBook for Programming, second edition by Michael Trott (© Springer, 2008).
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