On the dynamics of a small body in a post Newtonian potential field created by a regular polygon formation of N bodies

Details On the dynamics of a small body in a post Newtonian potential field created by a regular polygon formation of N bodies On the dynamics of a small body in a post Newtonian potential field created by a regular polygon formation of N bodies

Jan 2012

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012hell.conf...23k&link_type=abstract

10th Hellenic Astronomical Conference, Proceedings of the conference held at Ioannina, Greece, 5-8 September 2011. Edited by Io

Astronomy and Astrophysics

Astronomy

Scientific paper

The N-body problem is one of the most important issues in Celestial Mechanics. In the relevant literature there are many particular cases one of which is based upon the so called restricted (N+1)-body regular polygon model where N=?+1 of the bodies-members of the system are spherical, homogeneous with equal masses m, and are located at the vertices of an imaginary regular ?-gon, while the ?th body has different mass m0 and is located at the center of mass of the system. This formation rotates around the center of mass with constant angular velocity so that all the primaries are in relative equilibrium. A small body, natural or artificial, moves in the neighborhood of the system under the action of all the primaries. The original version was based on the assumption that all big bodies create Newtonian force fields. Here we present a particular case where we assume that the central body creates a post-Newtonian Manev-type potential. The problem is characterized by three parameters, namely the number ? of the peripheral primaries, the mass parameter ?=m0/m and the coefficiente which measures the contribution of the non-Newtonian term of the potential of the central primary. Under these assumptions, we study some aspects of the dynamics of the small body and we expose some of the results obtained so far.

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