The Eccentric Frame Method and the Hernquist-Newton Potential

Details The Eccentric Frame Method and the Hernquist-Newton Potential The Eccentric Frame Method and the Hernquist-Newton Potential

Jul 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007dda....38.1404m&link_type=abstract

American Astronomical Society, DDA meeting #38, #14.04

Astronomy and Astrophysics

Astrophysics

Scientific paper

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, which can similarly be defined for an arbitrary central force field 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 orbit or libration. The motion with respect to inertial space is then given by integrating the argument of periapsis of the eccentricty vector with respect to time. A central force field potential that has received some attention recently in the astrophysics community is the Hernquist potential, that describes the potential energy field due to spherically symmetric dark matter distributions in galaxy halos. For galaxies with central black holes, we can couple the hernquist potential to a central Newtonian point mass. We will look at sample orbits in the Newton-Hernquist potential, a potential no harder to deal with using the Eccentric Frame method, and discuss its implications.

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