# Orbits around and through a Sphere

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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).

Open content licensed under CC BY-NC-SA

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"Orbits around and through a Sphere"

http://demonstrations.wolfram.com/OrbitsAroundAndThroughASphere/

Wolfram Demonstrations Project

Published: March 7 2011