Spirographic Orbit of a Star in Extended Mass Distribution

This Demonstration shows the orbit of a point mass through a Hernquist potential, which represents a star moving through a spherically symmetric extended mass distribution with a density profile of the form , where is the dimensionless radius and is the length scale of the potential. This type of mass density has been used to model physical systems such as dark matter halos, elliptical galaxies, and embedded young star clusters.



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is the dimensionless energy parameter.
is the dimensionless angular momentum parameter.
represents dimensionless time.
L. Hernquist, "An Analytical Model for Spherical Galaxies and Bulges," The Astrophysical Journal, 365, 1990 pp. 359–364.
F. C. Adams and A. M. Bloch, "Orbits in Extended Mass Distributions: General Results and the Spirographic Approximation," The Astrophysical Journal, 629, 2005 pp. 204–218.


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