Orbital dynamics of Earth-orbiting particles under perturbing forces

The work presented in this paper aims to further the research done on evaluating the effects of various perturbing forces on Earth-orbiting particles by using numerical tools and techniques. Colombo et. al.^{1, 2} studied the orbital dynamics of "smart-dust particles" in orbits lying on the ecliptic plane under the effects of solar radiation pressure (SRP) and drag. The numerical model developed here will expand on that work, but will use Hamiltonian equations of motion instead of Gauss equations. It incorporates perturbations due to SRP, drag, J₂ and Moon's gravity, while also accounting for the ecliptic angle. None of the effects are averaged, thus this model can provide optimal initial orbits where the effects of the forces will negate each other to cause minimal changes in orbital elements. Sample Monte-Carlo simulation results are presented. By running the simulation for a large number of points, a set of initial orbital elements conducive to a long lifespan can be determined, not only for Earth-orbiting bodies, but also for lunar satellites.