The eccentric frame decomposition of central force fields
Abstract
The rosetteshaped 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.
 Publication:

Celestial Mechanics and Dynamical Astronomy
 Pub Date:
 January 2008
 DOI:
 10.1007/s1056900791056
 arXiv:
 arXiv:0712.3511
 Bibcode:
 2008CeMDA.100...43M
 Keywords:

 Central force fields;
 Dark matter halos;
 HernquistNewton potential;
 Central black hole;
 Axisymmetric potentials;
 Astrophysics
 EPrint:
 27 pages, 15 figures, to appear in the Journal of Celestial Mechanics and Dynamical Astronomy, January 2008