The semi analytical analysis of orbital evolution around an asteroid under the effects of the C₂₀ term, the solar radiation pressure and the asteroid's orbital eccentricity

This paper aims to develop a semi-analytical method of propagating orbital motion near the equatorial plane of an asteroid, considering the combined effects of the asteroid’s oblateness (the C₂₀ term), the solar radiation pressure (SRP) and the asteroid’s orbital eccentricity around the Sun (e_s). In the asteroid-centered frame, the Hamiltonian of the orbital motion is derived with Poincaré variables. It is firstly averaged over the orbital motion around the asteroid and then averaged over the asteroid's eccentric orbital motion around the Sun. Time-explicit analytical solutions of the orbital eccentricity and inclination are obtained. The Lie transformation is applied to recover the eliminated oscillating terms of the inclination during the second average for a complete solution. We analyze the validity of these solutions for different semi-major axes and different values of area-to-mass ratios (A/m). We demonstrate the importance of considering the asteroid's orbital eccentricity around the Sun and its role in enlarging the amplitude of orbital eccentricity for different A/m and orbital geometries. The solutions developed in this paper improve the knowledge of secular orbital evolution around asteroid. They can be applied to fast prediction of long-term orbital evolutions around near Earth asteroids (NEAs).