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WOLFRAM|DEMONSTRATIONS PROJECT

Orbits around and through a Sphere

​
solution time
initial conditions:
r
0
v
0
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
V∼
2
r
) and outside the sphere the potential is a pure Coulomb potential (potential
V∼1/r
). In both cases, the orbits are ellipses. In case the orbit has segments inside and outside the sphere, rosette orbits are obtained.
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