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

TL;DR

This paper investigates the phase space structure of spin-orbit coupling in binary asteroid systems, combining analytical Hamiltonian modeling with numerical resonance cartography to understand resonance locations, widths, and chaos onset.

Contribution

It introduces a Hamiltonian model reformulated with Stokes coefficients for binary asteroids and combines analytical and numerical methods to analyze resonance structures and chaos in spin-orbit dynamics.

Findings

Resonance geography is modified by semi-major axis effects.

Chirikov criterion is adapted for chaos prediction.

Numerical FLI maps confirm analytical resonance structures.

Abstract

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 semi-major 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 (FLI) 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.