  The orbital dynamics of a spacecraft orbiting around irregular small
celestial bodies is a challenging problem. Difficulties to model the gravity
field of these bodies arise from the poor knowledge of the exact shape as
observed from the Earth. In order to understand the complex dynamical
environment in the vicinity of irregular asteroids, several studies have been
conducted using simplified models. In this work, we investigate the qualitative
dynamics in the vicinity of an asteroid with an arched shape using a tripole
model based on the existence of three mass points linked to each other by rods
with given lengths and negligible masses. We applied our results to some real
systems, namely, asteroids 8567, 243 Ida and 433 Eros and also Phobos, one of
the natural satellites of Mars.
