Time characterization of the coupled solar radiation pressure-planetary oblateness dynamics

Recent works demonstrated that the dynamics caused by the planetary oblateness coupled with the solar radiation pressure can be described by means of an analytical model based on singly-averaged equations of motion. The coupled perturbations affect the evolution of the eccentricity, inclination and orientation of the orbit with respect to the Sun-Earth line. The model can provide the location of the central and hyperbolic invariant manifolds which drive the phase space evolution, and the dynamical systems theory can be applied for performing a preliminary mission analysis for practical applications. In this work, we will continue the analysis by focusing on the timescale associated with a given dynamical behavior. First the bifurcation diagram for the phase space evolution is derived, then a possible exploitation for deorbiting from the LEO region is described. The characterization of the corresponding time-scales is given analytically on the basis of the linear theory, as a function of the semi-major axis, area-to-mass ratio, initial phase with respect to the Sun and the integral of motion associated with the dynamical system.