Resumen de Configuraciones de cuatro cuerpos en escenarios de exoplanetas

Pedro Pablo Campo Díaz , J. A. Docobo Durántez

• Lately, more and more exoplanets have been discovered and, thanks to the excellent programs dedicated to this task, the number is expected to increase considerably even with the detection of Earth-sized planets. Thus it is important to study the dynamical behavior of planetary systems. Among all the problems that may be considered, in this research we have focused on four-body planetary systems.

  First we examine all the possible situations that may be present in four-body planetary systems, including satellites, in both single and multiple stars. Step decomposition is a methodology explained by A. Abad and J. A. Docobo to deal with n-body problems with hierarchy. The use of this technique permits the reduction of the different cases to five configurations.

  Finally, we analytically integrate one of the cases established before. It is that in which a planet with a satellite orbits a component of a double star. Once the Hamiltonian of the problem is established, we formulate it in terms of three small parameters which can be reduced to two as is justified. After that, using Hori’s biparametric method, the angular variables are removed, thereby allowing the integration of the problem.