This paper studies the secondary's rotation in a synchronous binary asteroid system in which the secondary enters the 1:1 spin-orbit resonance. The model used is the planar full two-body problem composed of a spherical primary plus a tri-axial ellipsoid secondary. Compared with classical spin-orbit work, there are two differences: (1) Influence on the mutual orbit from the secondary's rotation is considered; (2) Instead of the Hamiltonian approach, the approach of periodic orbits is adopted. Our studies find: (1) Genealogy of the two families of periodic orbits is same as that of the families around triangular libration points in the restricted three-body problem. That is, the long-period family terminates onto a short-period orbit travelling N times; (2) In the limiting case where the secondary's mass is negligible, our results can be reduced to the classical spin-orbit theory, by equating the long-period orbit with the free libration, and by equating the short-period orbit with the forced libration caused by orbit eccentricity. However, the two models show obvious differences when the secondary's mass is non-negligible. (3) By studying the stability of periodic orbits, for a specific binary asteroid system, we are able to obtain the maximum libration amplitude of the secondary (which is usually less than 90°), and the maximum mutual orbit eccentricity which does not break the secondary's synchronous state. We also find the anti-correlation between the secondary's libration amplitude and the orbit eccentricity. The (65803) Didymos system is taken as an example to show the results.
This paper continues the authors’ previous work and presents a coplanar averaged ellipsoid-ellipsoid model of synchronous binary asteroid system (BAS) plus thermal and tidal effects. Using this model, we analyse the breakup mechanism of the synchronous BAS. Different from the classical spin-orbit coupling model which neglects the rotational motion’s influence on the orbital motion, our model considers simultaneously the orbital motion and the rotational motions. Our findings are following. (1) Stable region of the secondary’s synchronous state is mainly up to the secondary’s shape. The primary’s shape has little influence on it. (2) The stable region shrinks continuously with the increasing value of the secondary’s shape parameter aB/bB. Beyond the value of $a_B/b_B=\sqrt{2}$, the planar stable region for the secondary’s synchronous rotation is small but not zero. (3) Considering the BYORP torque, our model shows agreement with the 1-degree of freedom adiabatic invariance theory in the outwards migration process, but an obvious difference in the inwards migration process. In particular, our studies show that the so-called ‘long-term’ stable equilibrium between the BYORP torque and the tidal torque is never a real equilibrium state, although the binary asteroid system can be captured in this state for quite a long time. (4) In case that the primary’s angular velocity gradually reduces due to the YORP effect, the secondary’s synchronous state may be broken when the primary’s rotational motion crosses some major spin-orbit resonances.
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