Orbital evolution around irregular bodies

The new profiles of the space missions aimed at asteroids and comets, moving from fly-bys to rendezvous and orbiting, call for new spaceflight dynamics tools capable of propagating orbits in an accurate way around these small irregular objects. Moreover, interesting celestial mechanics and planetary science problems, requiring the same sophisticated tools, have been raised by the first images of asteroids (Ida/Dactyl, Gaspra and Mathilde) taken by the Galileo and NEAR probes, and by the discovery that several near-Earth asteroids are probably binary. We have now developed two independent codes which can integrate numerically the orbits of test particles around irregularly shaped primary bodies. One is based on a representation of the central body in terms of "mascons" (discrete spherical masses), while the other one models the central body as a polyhedron with a variable number of triangular faces. To check the reliability and performances of these two codes we have performed a series of tests and compared their results. First we have used the two algorithms to calculate the gravitational potential around non-spherical bodies, and have checked that the results are similar to each other and to those of other, more common, approaches; the polyhedron model appears to be somewhat more accurate in representing the potential very close to the body's surface. Then we have run a series of orbit propagation tests, integrating several different trajectories of a test particle around a sample ellipsoid. Again the two codes give results in fair agreement with each other. By comparing these numerical results to those predicted by classical perturbation formulae, we have noted that when the orbit of the test particle gets close to the surface of the primary, the analytical approximations break down and the corresponding predictions do not match the results of the numerical integrations. This is confirmed by the fact that the agreement gets better and better for orbits farther away from the primary. Finally, we have found that in terms of CPU time requirements, the performances of the two codes are quite similar, and that the optimal choice probably depends on the specific problem under study.