The Eccentric Frame Decomposition of Central Force Fields

Details The Eccentric Frame Decomposition of Central Force Fields The Eccentric Frame Decomposition of Central Force Fields

2007-12-20

arxiv.org/abs/0712.3511v1

Astronomy and Astrophysics

Astrophysics

27 pages, 15 figures, to appear in the Journal of Celestial Mechanics and Dynamical Astronomy, January 2008

Scientific paper

10.1007/s10569-007-9105-6

The rosette-shaped motion of a particle in a central force field is known to be classically solvable by quadratures. We present a new approach of describing and characterizing such motion based on the eccentricity vector of the two body problem. In general, this vector is not an integral of motion. However, the orbital motion, when viewed from the nonuniformly rotating frame defined by the orientation of the eccentricity vector, can be solved analytically and will either be a closed periodic circulation or libration. The motion with respect to inertial space is then given by integrating the argument of periapsis with respect to time. Finally we will apply the decomposition to a modern central potential, the spherical Hernquist-Newton potential, which models dark matter halos of galaxies with central black holes.

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