A study on the positions and velocity sensitivities in the restricted three-body problem with radiating and oblate primaries

Abstract

This paper investigates triangular points' positions and velocity sensitivities in the circular restricted three-body problem framework for Luyten 726–8 and Achird systems. We observe that the possible boundary regions for both systems depend on the value of the Jacobian constant C and the oblateness coefficients (A1&A2). As the oblateness coefficients increase with other fixed parameters, the Jacobian constant value increases, making it possible to connect the primary regions. The Poincare's Surface of Section of the two binary systems has been utilized to display their sensitivity to change positions and velocities. With certain initial conditions, the systems possess regular orbits, however, the orbits become irregular when these initial conditions are changed. An increase in oblateness coefficients results in the singularities and stiffness of the non-linear system. Considering the range of stability and instability given as 0<μ<μc for stable triangular points and μc≤μ≤12 for unstable triangular points, we have established that the triangular points are unstable for the binary systems: Luyten 726–8 and Achird. In our analysis, for each set of values, there exists at least one complex root with a positive real part. Hence in the sense of Lyapunov, the triangular points are unstable for the systems as mentioned earlier.