The Post-Newtonian Hill Problem

2nd International Conference on Mathematical Modeling in Physical Sciences 2013

物理学;数学

Lisbôa, A.F. Steklain^1 ; Letelier, P.S.^2,3

Departamento de Matemática, Universidade Tecnológica Federal do Paraná Curitiba, Paraná 80230-901, Brazil^1

Institute de Física Gleb Wataghin, Universidade Estadual de Campinas, Campinas, 13083-970, São Paulo, Brazil^2

Departamento de Matemática Aplicada, Instituto de Matematica, Estatistica e Computacao Cientifica, Universidade Estadual de Campinas, 13083-970, Campinas, São Paulo, Brazil^3

关键词: Binary systems;    Classical problems;    Different mass;    Lyapunov exponent;    Newtonian dynamics;    Newtonians;    Poincare;    Totally stable;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/490/1/012156/pdf
DOI  :  10.1088/1742-6596/490/1/012156

来源: IOP

【 摘 要 】

A relativistic approach of the Hill Problem is presented by using an approximate binary system metric obtained from the first post-Newtonian expansion (1PN). We employ Poincare´ maps and Lyapunov exponents to study the stability of bounded orbits of the system for different mass arrangements, and compare with the classical problem based on Newtonian dynamics. We find that for larger masses the system become totally stable, a striking behaviour that is not predicted by the Newtonian dynamics.