Stability Analysis of Modified Circular Restricted Three Body Problem by Lyapunov Exponent Indicators

The circular restricted three body problem (CRTBP) is a well-known problem that has a very important contribution to understand the dynamics of celestial objects, including the binary stars and planetary system. In this study, we extend the classical version of CRTBP by assuming both primaries emit radiation and have oblate shape. We also consider the potential from a disk like structure that surrounds this three-body system. The stability of the infinitesimal body is investigated by using Lyapunov Exponent Indicators (LEI). First, we have done a numerical survey by testing several initial locations of the infinitesimal body that have chaotic or regular orbital behaviour. Second, we estimated the stability of triangular equilibrium points and show that the equilibrium points are conditionally stable with respect to the critical mass parameter ( μ c ). We found that the determined μ c from LEI method match μ c from linear stability analysis.