  A method for classifying orbits near asteroids under a polyhedral
gravitational field is presented, and may serve as a valuable reference for
spacecraft orbit design for asteroid exploration. The orbital dynamics near
asteroids are very complex. According to the variation in orbit characteristics
after being affected by gravitational perturbation during the periapsis
passage, orbits near an asteroid can be classified into 9 categories: (1)
surroundingto-surrounding, (2) surrounding-to-surface, (3)
surroundingto-infinity, (4) infinity-to-infinity, (5) infinity-to-surface, (6)
infinity-to-surrounding, (7) surface-to-surface, (8) surfaceto-surrounding, and
(9) surface-to- infinity. Assume that the orbital elements are constant near
the periapsis, the gravitation potential is expanded into a harmonic series.
Then, the influence of the gravitational perturbation on the orbit is studied
analytically. The styles of orbits are dependent on the argument of periapsis,
the periapsis radius, and the periapsis velocity. Given the argument of
periapsis, the orbital energy before and after perturbation can be derived
according to the periapsis radius and the periapsis velocity. Simulations have
been performed for orbits in the gravitational field of 216 Kleopatra. The
numerical results are well consistent with analytic predictions.
