Stability indicator of orbital motion around asteroids with automatic domain splitting

Asteroids usually have irregular gravity field due to their non-spherical shapes. Moreover, their gravity fields are estimated with large uncertainty as a result of the limited ground observations. Resultantly, the orbital motion in their vicinity can be highly unstable and cannot be predicted accurately before reaching the asteroid. Therefore, the identification of stable orbital motion around asteroids is essential for robust mission design. In this study, the automatic domain splitting method (ADS) is introduced as a new tool of identifying the stable and unstable region in the phase space with gravity uncertainty. The ADS is actually based on the differential algebra (DA) method that approximates the dynamics with arbitrary order Taylor expansion and can replace thousands of pointwise integrations of Monte Carlo runs with the fast evaluation of the Taylor polynomials. The asteroid Steins is taken as an example. However, as the C20 and C22 harmonic terms are usually dominant over the nonspherical gravity, only their uncertainties are considered in the investigations. Given the required accuracy, the expansion order and the maximum splitting times are firstly determined, to balance efficiency. It is found that the orbital motion is more sensitive to the variation of the C22 term, compared with that of the C20 term. Then, the first split time of the orbits with different geometry is recorded on the semi-major axis and inclination plane, i.e. the a-i plane. Along the propagation the bounds of the state flow are evaluated. Resultantly, given the allowed first split time and bounds that are determined according to the real mission requirement, practical stable regions can be identified.