About how far does the Moon drift away from Earth each year?

Answer

Tides transfer energy from Earth's spin to the Moon's orbit, slowly pushing the Moon outward. Laser reflectors left by Apollo crews measure it.

Context

The 3.8 cm figure comes from lunar laser ranging. Apollo astronauts on Apollo 11, 14 and 15 placed corner-cube reflectors on the surface, and Soviet rovers carried two more. Observatories fire short laser pulses at them and time the round trip, which gives the Earth-Moon distance to within about a centimeter or better. Decades of such timing show the average separation of roughly 384,400 km growing by about 3.8 cm per year.

The cause is tides. The Moon's gravity raises ocean bulges on Earth, but Earth spins faster than the Moon orbits, so friction drags the bulges slightly ahead of the Earth-Moon line. Their gravity pulls the Moon forward along its orbit and adds energy, lifting it into a wider path. The same exchange takes angular momentum from Earth's spin, so the day lengthens by an amount on the order of 2 milliseconds per century, according to historical eclipse records and other evidence.

The present rate should not be extrapolated backward without caution. Tidal strength depends on the shape of the oceans and continents, which have changed, so the drift speed was not constant. Running today's rate back would put the Moon implausibly close to Earth too recently, which tells scientists the rate was lower in the past. Over hundreds of millions of years the Moon's apparent size will shrink enough that total solar eclipses are expected to stop, although that is a distant, approximate projection.