Surfing in the phase space of spin--orbit coupling in binary asteroid systems

For a satellite with an irregular shape, which is the common shape among asteroids, the well-known spin--orbit resonance problem could be changed to a spin--orbit coupling problem since a decoupled model does not accurately capture the dynamics of the system. In this paper, having provided a definition for close binary asteroid systems, we explore the structure of the phase space in a classical Hamiltonian model for spin--orbit coupling in a binary system. To map out the geography of resonances analytically and the cartography of resonances numerically, we reformulate a fourth-order gravitational potential function, in Poincare variables, via Stokes coefficients. For a binary system with a near-circular orbit, isolating the Hamiltonian near each resonance yields the pendulum model. Analysis of the results shows the geographical information, including the location and width of resonances, is modified due to the prominent role of the semimajor axis in the spin--orbit coupling model but not structurally altered. However, this resulted in modified Chirikov criterion to predict onset of large-scale chaos. For a binary system with arbitrary closed orbit, we thoroughly surf in the phase space via cartography of resonances created by fast Lyapunov indicator maps. The numerical study confirms the analytical results, provides insight into the spin-orbit coupling, and shows some bifurcations in the secondary resonances which can occur due to material transfer. Also, we take the (65803) Didymos binary asteroid as a case to show analytical and numerical results.