A global binary asteroid system model with irregularly shaped components via iterated surface integral

The dynamics of binary asteroid systems are referred to as the full two-body problem (F2BP), which is one of the principal problems in astrodynamics. The gravitational interactions, including the mutual potential, force, and torque, are necessary quantities to acquire the solution of F2BP. However, it is usually difficult to balance accuracy with efficiency of the evaluations, due to the highly irregular shapes of the asteroids and the close distance between the two components. In this paper, a global model is proposed for evaluating the interactions between two polyhedral asteroids with arbitrary separating distances. First, the interactions are represented as the double surface integrals through the iterated divergence theorem, which is lossless. The integrals over the complex boundaries of bodies are then converted to the sum of subdomain integrals over triangular facets which are compatible with the polyhedron model. Finally, these integrals are conveniently approximated through the numerical quadrature. This work provides a general solution that avoids the divergence problem of most traditional models. The benchmarking tests against the exact solution between two ellipsoids verify its high precision even if the bodies are almost touching. Considering asteroids with irregular shapes, we investigate the evolution of the Moshup-Squannit system and compare the results with the traditional series-based model. The developed model makes a reasonable balance between accuracy and efficiency with different quadrature strategies. The simulations show that the developed model achieves a comparable precision with the 4th-order series solution and a relatively fast computation speed with an appropriate quadrature strategy.