Global mapping of asteroids by frozen orbits: the case of 216 Kleopatra

In this paper, the global mapping of an irregular asteroid is studied referring to the ground track properties of a frozen orbit (at constant eccentricity and argument of pericentre on average). In fact, when the size of the asteroid is in the order of hundreds of kilometres or more, an appropriate design of the ground track becomes an important element to optimise the coverage and guarantee regular cycles of observation. To this end, the methodology used to design the ground track in missions for the observation of regular bodies, like planets, is extended to the case of irregular bodies, such as asteroids. Moreover, to manage the irregular shape of the asteroid, the classical spherical coordinates (geographical longitude and latitude) are replaced by cylindrical coordinates, whereas the regions that are not reached by the ground track are modelled by using appropriate tetrahedra, useful to plan the coverage. In this context, the case of asteroid 216 Kleopatra has been investigated.