Relaxation of Viscoelastic Tumblers with Application to 1I/2017 (`Oumuamua) and 4179 Toutatis

Abstract

Motivated by the observation of comets and asteroids rotating in non-principal axis (NPA) states, we investigate the relaxation of a freely precessing triaxial ellipsoidal rotator towards its lowest-energy spin state. Relaxation of the precession arises from internal dissipative stresses generated by self-gravitation and inertial forces from spin. We develop a general theory to determine the viscoelastic stresses in the rotator, under any linear rheology, for both long-axis (LAM) and short-axis (SAM) modes. By the methods of continuum mechanics, we calculate the power dissipated by the stress field and the viscoelastic material strain which enables us to determine the timescale of the precession dampening. To illustrate how the theory is used, we apply our framework to a triaxial 1I/2017 (`Oumuamua) and 4179 Toutatis under the Maxwell regime. For the former, employing viscoelastic parameters typical of very cold monolithic asteroids renders a dampening timescale longer by a factor of $10^{10}$ and higher than the timescales found in the works relying on the $Q$-factor approach, whilst the latter yields a significantly shorter timescale as a consequence of including self-gravitation. We further reduce our triaxial theory to bodies of an oblate geometry and derive a family of relatively simple analytic approximations determining the NPA dampening times for Maxwell rotators, as well as a criterion determining whether self-gravitation is negligible in the relaxation process. Our approximations exhibit a relative error no larger than $0.2\%$, when compared to numerical integration, for close to non-dissipative bodies and $0.002\%$ for highly energy dissipating rotators.

References in corpus (17)

• Interstellar Interloper 1I/2017 U1: Observations from the NOT and WIYN Telescopes
• Bodily tides near spin-orbit resonances
• A framework to combine low- and high-resolution spectroscopy for the atmospheres of transiting exoplanets
• The Natural History of 'Oumuamua
• The Ginger-shaped Asteroid 4179 Toutatis: New Observations from a Successful Flyby of Chang'e-2
• The tumbling rotational state of 1I/`Oumuamua
• Tidal Evolution of Asteroidal Binaries. Ruled by Viscosity. Ignorant of Rigidity
• The Excited Spin State of 1I/2017 U1 `Oumuamua
• Relaxation of Wobbling Asteroids and Comets. Theoretical Problems. Perspectives of Experimental Observation
• Inelastic Dissipation in Wobbling Asteroids and Comets
• Spin Evolution and Cometary Interpretation of the Interstellar Minor Object 1I/2017 'Oumuamua
• Precession Relaxation of Viscoelastic Oblate Rotators
• Stress field and spin axis relaxation for inelastic triaxial ellipsoids
• Asteroid rotation excitation by subcatastrophic impacts
• Precession of a Freely Rotating Rigid Body. Inelastic Relaxation in the Vicinity of Poles
• Euler, Jacobi, and Missions to Comets and Asteroids
• Simulations of wobble damping in viscoelastic rotators

Cited by in corpus (2)

• Interstellar Asteroid Rotation with the Mechanical Torque Produced by Interstellar Medium
• Confined tumbling state as the origin of the excess of slowly rotating asteroids