  The Moon is known to have a small liquid core, and it is thought that in the
distant past the core may have produced strong magnetic fields recorded in
lunar samples. Here we implement a numerical model of lunar orbital and
rotational dynamics that includes the effects of a liquid core. In agreement
with previous work, we find that the lunar core is dynamically decoupled from
the lunar mantle, and that this decoupling happened very early in lunar
history. Our model predicts that the lunar core rotates sub-synchronously, and
the difference between the core and the mantle rotational rates was significant
when the Moon had a high forced obliquity during and after the Cassini State
transition. We find that the presence of the lunar liquid core further
destabilizes synchronous rotation of the mantle for a wide range of semimajor
axes centered around the Cassini State transition. CMB torques make it even
more likely that the Moon experienced large-scale inclination damping during
the Cassini State transition. We present estimates for the mutual core-mantle
obliquity as a function of Earth-Moon distance, and we discuss plausible
absolute time-lines for this evolution. We conclude that our results are
consistent with the hypothesis of a precession-driven early lunar dynamo and
may explain the variability of the inferred orientation of the past lunar
dynamo.
