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

Published onAug 03, 2020
The Onset of Chaos in Permanently Deformed Binaries from Spin-Orbit and Spin-Spin Coupling

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 a permanent aspheroidal shape largely determines whether or not it will exhibit non-trivial rotational behavior. We propose 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, and the associated equations of motion, we develop a Hamiltonian formalism which recovers 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. With an analytical 3-dimensional extension of the model, we evaluate the linear stability of each of the resonances with respect to oscillations out of the orbital plane, where instability is a proxy for the onset of non-principle axis tumbling. While this model is by construction generalizable to any binary system, it will be particularly useful to study small binaries in the Solar System, whose irregular shapes make them ideal candidates for exotic rotational states.


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