The Onset of Chaos in Permanently Deformed Binaries from Spin–Orbit and Spin–Spin Coupling

Abstract

Permanently deformed objects in binary systems can experience complex rotation evolution, arising from the extensively studied effect of spin-orbit coupling as well as more nuanced dynamics arising from spin-spin interactions. The ability of an object to sustain an aspheroidal shape largely determines whether or not it will exhibit nontrivial rotational behavior. In this work, we adopt a simplified model of a gravitationally interacting primary and satellite pair, where each body's quadrupole moment is approximated by two diametrically opposed point masses. After calculating the net gravitational torque on the satellite from the primary, as well as the associated equations of motion, we employ a Hamiltonian formalism that allows for a perturbative treatment of the spin-orbit and retrograde and prograde spin-spin coupling states. By analyzing the resonances individually and collectively, we determine the criteria for resonance overlap and the onset of chaos, as a function of orbital and geometric properties of the binary. We extend the 2D planar geometry to calculate the obliquity evolution. This calculation indicates that satellites in spin-spin resonances undergo precession when inclined out of the plane, but they do not tumble. We apply our resonance overlap criteria to the contact binary system (216) Kleopatra, and find that its satellites, Cleoselene and Alexhelios, may plausibly be exhibiting chaotic rotational dynamics from the overlap of the spin-orbit and retrograde spin-spin resonances. While this model is, by construction, generalizable to any binary system, it will be particularly useful for studies of small bodies in the Solar System, whose irregular shapes make them ideal candidates for exotic rotational states.

Rotation-induced granular motion on the secondary component of binary asteroids: Application to the DART impact on Dimorphos

“…Observational evidence and theoretical arguments both indicate that chaotic rotation is not uncommon for secondaries in tight binary systems (Pravec et al 2016;Ćuk et al 2021;Seligman & Batygin 2021;Quillen et al 2022a), and it is plausible that many synchronous secondaries have undergone some level of chaotic rotation in their past or during their formation (Wisdom 1987;Jacobson & Scheeres 2011;Davis & Scheeres 2020b). Therefore, the methods and results presented here are also broadly applicable to the general binary asteroid population.…”

Shape-Driven Selection Effects for Aspherical Near-Earth Objects in Systematic Surveys

“…As such, we will display many of our results in terms of both (a/b) and the corresponding |∆m|. We also ignore modifications to lightcurves from non-principal axis rotation (Rafikov 2018), binary asteroids (Seligman & Batygin 2021), or sublimation-induced spin-up (Mashchenko 2019;Taylor et al 2022). These situations only apply to some NEOs and are unimportant at the population-level, but determining the detection probability of a specific small body could require a consideration of these effects.…”

Fitting the Light Curve of 1I/‘Oumuamua with a Nonprincipal Axis Rotational Model and Outgassing Torques

“…In this subsection, we calculate the effect of tidal forces on the rotation of an ellipsoidal body with semiaxes (a, b, c), a = b, a > c, and aspect ratio ò ≡ c/a. We approximate the permanent quadrupole moment of the object as two concentric point masses of mass m at a distance D from the center of mass, similar to the "dumbbell" model developed by Batygin & Morbidelli (2015) and Seligman & Batygin (2021). The use of this model is validated in Appendix A.…”