  Geological evidence suggests liquid water near the Earth's surface as early
as 4.4 billion years ago when the faint young Sun only radiated about 70% of
its modern power output. At this point, the Earth should have been a global
snowball if it possessed atmospheric properties similar to those of the modern
Earth. An extreme atmospheric greenhouse effect, an initially more massive Sun,
release of heat acquired during the accretion process of protoplanetary
material, and radioactivity of the early Earth material have been proposed as
reservoirs or traps for heat. For now, the faint-young-sun paradox persists as
an important problem in our understanding of the origin of life on Earth. Here
we use the constant-phase-lag tidal theory to explore the possibility that the
new-born Moon, which formed about 69 million years after the ignition of the
Sun, generated extreme tidal friction - and therefore heat - in the Hadean and
possibly the Archean Earth. We show that the Earth-Moon system has lost about
$3~ \times ~10^{31}$ J (99% of its initial mechanical energy budget) as tidal
heat. Tidal heating of roughly 10 W/m$^{-2}$ through the surface on a time
scale of 100 million years could have accounted for a temperature increase of
up to 5 degrees Celsius on the early Earth. This heating effect alone does not
solve the faint-young-sun paradox but it could have played a key role in
combination with other effects. Future studies of the interplay of tidal
heating, the evolution of the solar power output, and the atmospheric
(greenhouse) effects on the early Earth could help in solving the
faint-young-sun paradox.
