Knowledge of the Solar System is increasing with data coming from space missions to small bodies. A mission to those bodies offers some problems, because they have several characteristics that are not well known, like their shapes, sizes and masses. The present research has the goal of searching for trajectories around the double asteroid 2002CE 26 , a system of Near-Earth Asteroids (NEAs) of the Apollo type. For every trajectory of the spacecraft, the evolution of the distances between the spacecraft and the two bodies that compose the system is crucial, due to its impact in the quality of the observations made from the spacecraft. Furthermore, this study has a first objective of searching for trajectories that make the spacecraft remain as long as possible near the two bodies that compose the asteroid system, without the use of orbital maneuvers. The model used here assumes elliptical orbits for the asteroids. The effect of the solar radiation pressure is also included, since it is a major perturbing force acting in spacecrafts traveling around small bodies. The natural orbits found here are useful for the mission. They can be used individually or combined in several pieces by orbital maneuvers. Another point considered here is the importance of the errors in the estimation of the physical parameters of the bodies. This task is very important, because there are great uncertainties in these values because the measurements are based on observations made from the Earth. It is shown that a variation of those parameters can make very large modifications in the times that the spacecraft remains close to the bodies of the system (called

The main goal of this paper is to search for orbits that can be used in the Brazilian proposed Aster mission. This mission is under study and its objective is to use a spacecraft to observe the system 2001SN263, which is a triple asteroid system. With respect to the two-body problem (spacecraft and the main asteroid), the symmetries of the orbits are broken by the oblateness of the main body of the system, the solar radiation pressure, and the gravitational attraction of the two moons of the main body. Additionally, the masses of these two moons have errors associated with their predicted values, which reinforce the asymmetry and require extra effort to maintain the observational objectives of the mission. The idea is to find orbits that remain for some time observing the three bodies of that system, even if the physical parameters of the bodies are not the ones expected from observations made from the Earth. This is accomplished by studying the effects of errors in all the physical properties of the three asteroids in the trajectories described by a spacecraft that is orbiting this system. Several important and useful trajectories are found, which are the ones that can observe the desired bodies, even if the physical parameters are not the expected ones. To express our results, we built time histories of the relative distances between each of the asteroids and the spacecraft. They are used to select the trajectories according to the amount of time that we need to observe each body of the system. In this way, the first objective of this research is to search for trajectories to keep the spacecraft close to the three bodies of the system as long as possible, without requiring orbital maneuvers. The errors for the masses of the two smaller and lesser known bodies are taken into consideration, while the mass of the most massive one is assumed to be known, because it was determined with higher precision by observations.

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