pp 1–27 | Cite as

Networks of periodic orbits in the circular restricted three-body problem with first order post-Newtonian terms

  • Euaggelos E. ZotosEmail author
  • K. E. Papadakis
  • Md Sanam Suraj
  • Amit Mittal
  • Rajiv Aggarwal


The motivation of this article is to numerically investigate the orbital dynamics of the planar post-Newtonian circular restricted problem of three bodies. By numerically integrating several large sets of initial conditions of orbits we obtain the basins of escape. Additionally, we determine the influence of the transition parameter on the orbital structure of the system, as well as on the families of simple symmetric periodic orbits. The networks and the stability of the symmetric periodic orbits are revealed, while the corresponding critical periodic solutions are also identified. The parametric evolution of the horizontal and the vertical stability of the periodic orbits are also monitored, as a function of the transition parameter.


Circular restricted three-body problem Post-Newtonian approximations Periodic orbits Stability 



The authors would like to thank the two anonymous referees for all the apt suggestions and comments which improved both the quality and the clarity of the paper.


The authors state that they have not received any research Grants.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Physics, School of ScienceAristotle University of ThessalonikiThessaloníkiGreece
  2. 2.Department of Civil Engineering, Division of Structural EngineeringUniversity of PatrasPatrasGreece
  3. 3.Department of Mathematics, Sri Aurobindo CollegeUniversity of DelhiNew DelhiIndia
  4. 4.Department of Mathematics, ARSD CollegeUniversity of DelhiNew DelhiIndia
  5. 5.Department of Mathematics, Deshbandhu CollegeUniversity of DelhiNew DelhiIndia

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