Near/far side asymmetry in the tidally heated Moon

Abstract

Using viscoelastic mass spring model simulations to track heat distribution inside a tidally perturbed body, we measure the near/far side asymmetry of heating in the crust of a spin synchronous Moon in eccentric orbit about the Earth. With the young Moon within 8 Earth radii of the Earth, we find that tidal heating per unit area in a lunar crustal shell is asymmetric due to the octupole order moment in the Earth's tidal field and is 10 to 20% higher on its near side than on its far side. Tidal heating reduces the crustal basal heat flux and the rate of magma ocean crystallization. Assuming that the local crustal growth rate depends on the local basal heat flux and the distribution of tidal heating in latitude and longitude, a heat conductivity model illustrates that a moderately asymmetric and growing lunar crust could maintain its near/far side thickness asymmetry but only while the Moon is near the Earth.

Excitation of tumbling in Phobos and Deimos

“…We have used the model to explore resonant obliquity evolution in long term integrations of rapidly spinning and non-round satellites (Quillen et al, 2017) and with shorter integrations we resolve the internal tidal heating distribution in a spin synchronous Moon in eccentric orbit (Quillen et al, 2019a). Comparison between numerically measured and analytically predicted wobble (or non-principal axis) damping rates illustrate that the code is accurate and that we understand how the simulation dissipation rates depend on the simulated rheology (Quillen et al, 2019b).…”

Simulations of wobble damping in viscoelastic rotators

“…Our numerical simulations are complimentary to analytic computations of the wobbling or precession damping rate (Burns & Safronov 1973;Sharma et al 2005;Efroimsky & Lazarian 2000;Breiter et al 2012;Frouard & Efroimsky 2018). Moreover, the simulations are flexible as they can be used to model complex body shapes (e.g., Quillen et al 2019b), bodies with inhomogeneous in-E-mail: alice.quillen@rochester.edu ternal composition (e.g., Quillen et al 2016b) and the distribution of internally dissipated heat (e.g., Quillen et al 2019a). At a given total rotational angular momentum, the most stable rotational state of a rigid object is that with the least rotational kinetic energy.…”

Mass Spring Models of Amorphous Solids

“…Their potential applications include computer games, animations, virtual reality environments as well as engineering of structures or materials in which deformation under stress is considered, crack propagation studies or human tissue simulations. Related fields range from ultramicroscopy to astrophysics [1][2][3][4][5][6]. Specific needs of specific application may vary, but the general theory of how mass spring models (MSM) deform concerns all of them.…”