Secular evolution of debris in highly eccentric and inclined orbits

The study of the secular motion of a test particle around an oblate Earth with external perturbations induced by the Moon, Sun, and other non-gravitational forces is a very timely subject. Most of the existing studies approximate the evolution of the system through expansions, considering small eccentricities and inclinations, which is not always the case. In our work, we use the second-order averaged Kaula expansion for the geopotential, and we consider the Kaufman-Dasenbrock expansion for the Lunar and Solar disturbing functions, extending the study of the secular evolution in the full domain of initial eccentricities and inclinations. We produce time-efficient codes for the simulation of the long-term dynamics. We use this method to investigate secular dynamical phenomena for arbitrary initial eccentricity and inclination, including the computation of proper elements. Furthermore, we investigate non-gravitational dissipative phenomena, namely the effects induced by atmospheric drag. Highly eccentric orbits cross multiple regions in the space around the Earth, causing a variety of dynamical phenomena, like dissipation due to atmospheric drag and secular resonances, to coexist. We choose initial conditions that trigger these interactions and we discuss their effect on the long-term evolution of the system. An innovative part of our work is the use of a closed-form Hamiltonian for modelling the gravitational, conservative, effects and the perturbed planetary equations for the non-gravitational, dissipative, forces. As a consequence, the derived equations globally describe the system, under the condition that Moon, Sun, and atmospheric drag are perturbations compared with the Earth’s Keplerian terms, and therefore the evolution of the orbital elements takes place on a secular timescale. The impact of our results extends to satellites in Molniya and Tundra orbits, which are highly eccentric and inclined. Furthermore, our study can be applied for purposes of post-mission disposal, namely in analysing possible re-enter strategies for satellites on eccentric orbits at the end of their life, in order to reduce the number of space debris around the Earth.