  Due to tidal interactions in the Earth-Moon system, the spin of the Earth
slows down and the Moon drifts away. This recession of the Moon is now measured
with great precision, but it has been realized, more than fifty years ago, that
simple tidal models extrapolated back in time lead to an age of the Moon that
is by far incompatible with the geochronological and geochemical evidence. In
order to evade this problem, more elaborate models have been proposed, taking
into account the oceanic tidal dissipation. However, these models did not fit
both the estimated lunar age and the present rate of lunar recession
simultaneously. Here we present a physical model that reconciles these two
constraints and yields a unique solution of the tidal history. This solution
fits well the available geological proxies for the history of the Earth-Moon
system and consolidates the cyclostratigraphic method. The resulting evolution
involves multiple crossings of resonances in the oceanic dissipation that are
associated with significant and rapid variations in the lunar orbital distance,
the Earth's length of the day, and the Earth's obliquity.
