Analytic Approximation Solutions of Lyapunov Orbits around the Collinear Equilibrium Points for Binary α-Centuari System: The Planar Case
Jagadish Singh
Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria.
Jessica Mrumun Gyegwe *
Department of Mathematical Sciences, Federal University Lokoja, Lokoja, Kogi State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
A third order analytic approximation solution of Lyapunov orbits around the collinear equilibrium in the planar restricted three-body problem by utilizing the Lindstedt Poincaré method is presented. The primaries are oblate bodies and sources of radiation pressure. The theory has been applied to the binary α-Centuari system in six cases. Also, we have determined numerically the positions of the collinear equilibrium points and shown the effects of the parameters concerned with these equilibrium points.
Keywords: Approximate solutions, periodic orbit, RTBP.