A semi-relativistic approach to the circular restricted three body problem and a numerical experiment around the 3:2 resonance

Details A semi-relativistic approach to the circular restricted three body problem and a numerical experiment around the 3:2 resonance A semi-relativistic approach to the circular restricted three body problem and a numerical experiment around the 3:2 resonance

2005-02-15

arxiv.org/abs/astro-ph/0502282v2

Class.Quant.Grav. 23 (2006) 673-682

Astronomy and Astrophysics

Astrophysics

6 eps figures, accepted to Class. Quant. Grav

Scientific paper

10.1088/0264-9381/23/3/008

A Hamiltonian that approaches the study of the three-body problem in general relativity is obtained. We use it to study the relativistic version of the circular restricted three-body problem in which the first body is the heaviest and the third body is a test-particle. We focus on the orbits around the 3:2 resonance. We show that, in spite of the notable difference between the relativistic and Newtonian orbits, most of the resonant region is preserved. Nevertheless, differently from the Newtonian case, the frequencies between the second and the third body are no longer commensurable.

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