Giga-Year Dynamical Evolution of Particles Around Mars

Particles of various sizes can exist around Mars. The orbits of large particles are mainly governed by Martian gravity, while those of small particles could be significantly affected by non-gravitational forces. Many of the previous studies of particle dynamics around Mars have focused on relatively small particles (radius of $r_{\rm p} \lesssim 100 \, \mu m$) for $\lesssim 10^{4}$ years. In this paper, using direct numerical orbital integration and analytical approaches, we consider Martian gravity, Martian $J_{2}$, the solar radiation pressure (SRP) and the Poynting-Robertson (PR) force to study the giga-year dynamical evolution of particles orbiting near the Martian equatorial plane with radius ranging from micrometer to meter. We also newly study the effect of the planetary shadow upon the particle dynamics. Our results show that small particles ($r_{\rm p} \lesssim 10 \, \mu m$) initially at $\lesssim 8$ Martian radii (below the orbit of today's Deimos) are quickly removed by the SRP due to eccentricity increase, resulting in a collision with Mars at the pericenter distnace. The orbits of larger particles ($r_{\rm p} > 10 \, \mu m$) slowly decay due to the PR forces (timescale of $> 10^{4}$ years). The planetary shadow reduces the sunlit area in the orbit and thus the efficiency of the PR drag force is reduced. However, we show that, even including the planetary shadow, particles up to $\sim 10$ cm in radius, initially at $\lesssim 8$ Martian radii, eventually spiral onto the Martian surface within $\sim 10^{9}$ years. Smaller particles require less time to reach Mars, and vice versa. Our results would be important to better understand and constrain the nature of the remaining particle around Mars in a context of giant impact hypothesis for the formation of Phobos and Deimos.