  Synchronous binary asteroids can experience libration about their
tidally-locked equilibrium, which will result in energy dissipation. This is an
important topic to the Asteroid Impact and Deflection Assessment, where
excitation caused by the DART kinetic impact in the Didymos binary asteroid
system may be reduced through dissipation before Hera arrives to survey the
effects of the impact. We develop a numeric model for energy dissipation in
binary asteroids to explore how different system configurations affect the rate
of energy dissipation. We find tumbling within the synchronous state eliminates
a systematic trend in libration damping on short timescales (several years),
but not over long times (hundreds of years) depending on the material
conditions. Furthermore, damping of libration, eccentricity, and fluctuations
in the semimajor axis are primarily dependent on the stiffness of the
secondary, whereas the semimajor axis secular expansion rate is dictated by the
stiffness of the primary, as expected. Systems experiencing stable planar
libration in the secondary can see a noticeable reduction in libration
amplitude after only a few years depending on the stiffness of the secondary,
and thus dissipation should be considered during Hera's survey of Didymos. For
a very dissipative secondary undergoing stable libration, Hera may be able to
calculate the rate of libration damping in Dimorphos and therefore constrain
its tidal parameters.
