  The early evolution of the Earth-Moon system prescribes the tidal environment
of the Hadean Earth and holds the key to the formation mechanism of the Moon
and its thermal evolution. Estimating its early state by backtracking from the
present, however, suffers from substantial uncertainties associated with ocean
tides. Tidal evolution during the solidification of Earth's magma ocean, on the
other hand, has the potential to provide robust constraints on the Earth-Moon
system before the appearance of a water ocean. Here we show that energy
dissipation in a solidifying magma ocean results in considerably more limited
lunar recession than previously thought, and that the Moon was probably still
at the distance of $\sim$7-9 Earth radii at the end of solidification. This
limited early recession aggravates the often overlooked difficulty of modeling
tidal dissipation in Earth's first billion years, but it also offers a new
possibility of resolving the lunar inclination problem by allowing the
operation of multiple excitation mechanisms.
