Analysis of Third-Order Resonant Periodic Orbits in Perturbed Circular Restricted Three-Body Problem

Abstract

The inner resonant 3rd-order periodic orbits are studied in the environment of perturbed circular restricted three-body problem (PCR3BP). This analysis is derived by choosing Saturn as an oblate sphere while Titan has a regular spherical shape. Starting location of periodic orbits and their path around primaries and Lagrangian points are examined for various values of oblateness and Jacobi constant C. Nonlinear regression models are constructed by taking Jacobi constant (C) as an independent variable while starting location of periodic orbits as a dependent variable for three, five and seven loops of inner resonant periodic orbits. The regression model can able to obtain the starting location of periodic orbit without constructing PSS. By examining the error values of the model, it can be concluded that the regression model provides the closest predicted values of starting location of orbits without creating the PSS.