%0 Journal Article
%T Periodic Orbits of the First Kind in the Autonomous Four-body Problem  with the Case of Collision
%A M. R. Hassan
%A Md. Aminul Hassan
%A Payal Singh
%A Vinay Kumar
%A R. R. Thapa
%J International Journal of Astronomy and Astrophysics
%P 91-111
%@ 2161-4725
%D 2017
%I Scientific Research Publishing
%R 10.4236/ijaa.2017.72008
%X In this manuscript, the existence of periodic orbits of collision of the first kind has been discussed on the model of Autonomous Four-body Problem by the method of analytic continuation given by Giacaglia [1] and Bhatnagar [2] [3]. For the existence of periodic orbits, DuboshinĄ¯s criterion [4] has been satisfied and it has been confirmed by analyzing the Poincare surfaces of section (PSS) [5]. Also it has been shown that the case of collision given by Levi-Civita [6] [7] is conserved by the method analytic continuation. In all sections of this manuscript, equilateral triangular configuration given by Ceccaroni and Biggs [8] has been considered. In this model, third primary of <em>L</em><sub><em>4</em></sub> inferior mass (in comparison of the other primaries) is placed at the equilibrium point   of the R3BP.
%K Autonomous Four-Body Problem
%K Regularization
%K Periodicity
%K Poincare Surfaces of Section
%K Collision Orbit
%K Zero Velocity Curves
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=76819