Excitation of tumbling in Phobos and Deimos

Abstract

Mass-spring model simulations are used to investigate past spin states of Phobos and Deimos. From an initially tidally locked state, we find crossing of a spin-orbit resonance with Mars or a mean motion resonance with each other does not excite tumbling in Phobos or Deimos. However, once tumbling these moons can remain so for an extended period and during this time their orbital eccentricity can be substantially reduced. We attribute the tendency for simulations of an initially tumbling body to drop into spin-synchronous state at very low eccentricity to the insensitivity of the tumbling chaotic zone width to eccentricity. After a tumbling body enters the spin synchronous resonance, it can exhibit long lived non-principal axis rotation and this too can prolong the period of time with enhanced tidally generated energy dissipation. We propose that the low orbital eccentricities of Phobos and Deimos could in part be due to spin excitation by impacts rather than tidal evolution following orbital resonance excitation.

Non-principal axis rotation in binary asteroid systems and how it weakens the BYORP effect

“…Long after (10 4 orbit periods after) the secondary enters the 1:1 spin-orbit resonance, its obliquity and non-principal axis rotation angle θ N P A,s remain high and vary chaotically. Similar long lasting obliquity and non-principal axis angle variations were seen in simulations of tidally evolving Phobos and Deimos (Quillen et al, 2020). We confirm the findings of Naidu and Margot (2015) who similarly emphasized that chaotic non-principal axis rotation of the secondary could be long-lived in binary asteroid systems.…”

“…Our numerical simulations confirm the work by (Naidu and Margot, 2015) who emphasized that non-principal axis rotation may be slowly damped. Long-lived non-principal axis rotation was also previously seen in some simulations of a tidally evolving Deimos (Quillen et al, 2020).…”

“…The secondary's short axis periodically rocks back and forth about the orbit normal because of rotation about its long axis. The jump in the non-principal axis angle θ N P A,s suggests that it is a resonant state, so it could last a really long time (10 to 100 times longer than the spin down time, as did resonant non-principal axis rotation states seen in simulations of Deimos; Quillen et al 2020). In future, the theoretical framework developed by Boué and Laskar (2009) for binary systems might be applied to better identify and create a model for this NPA rotation resonance.…”

“…As emphasized by Wisdom (1987), a non-round body must tumble before entering the spin-synchronous state. Numerical simulations show that the time for obliquity and libration and non-principal axis rotation to damp can substantially prolong the time it takes to reach a spin synchronous state with low obliquity, low free libration and undergoing principal axis rotation (Naidu and Margot, 2015;Quillen et al, 2020). Hence the long spin down time estimated for Dimorphos in equation 11 suggests that Dimorphos could have spent a long period of time in a complex spin state that is nearly synchronous but has non-principal axis (NPA) rotation, obliquity oscillations and high amplitude libration.…”

Evidence for a Past Martian Ring from the Orbital Inclination of Deimos

“…Yoder (1982) speculated that higher-than-expected tidal damping of eccentricity by Deimos (possibly due to resonantly excited rotational librations) could explain this discrepancy, but available data on the moments of inertia of Deimos do not support exceptionally large librational response (Thomas 1993). Recently, Quillen et al (2020) proposed that Deimos could have experienced enhanced dissipation due to chaotic rotation (c.f. Wisdom 1987) down to very low eccentricities.…”