  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.
