ABSTRACT The (153591) 2001 SN263 asteroid system, a target of the first Brazilian interplanetary space mission, is one of the known three triple systems within the population of near-Earth asteroids. One of the mission objectives is to collect data about the formation of this system. The analysis of these data will help in the investigation of the physical and dynamical structures of the components (Alpha, Beta, and Gamma) of this system, in order to find vestiges related to its origin. In this work, we assume the irregular shape of the 2001 SN263 system components as uniform-density polyhedra and computationally investigate the gravitational field generated by these bodies. The goal is to explore the dynamical characteristics of the surface and environment around each component. Then, taking into account the rotational speed, we analyse their topographic features through the quantities geometric altitude, tilt, geopotential, slope, and surface accelerations among others. Additionally, the investigation of the environment around the bodies made it possible to construct zero-velocity curves, which delimit the location of equilibrium points. The Alpha component has a peculiar number of 12 equilibrium points, all of them located very close to its surface. In the cases of Beta and Gamma, we found four equilibrium points not so close to their surfaces. Then, performing numerical experiments around their equilibrium points, we identified the location and size of just one stable region, which is associated with an equilibrium point around Beta. Finally, we integrated a spherical cloud of particles around Alpha and identified the location on the surface of Alpha where the particles have fallen.