How do we know the Moon is drifting away from Earth by 3.8 centimetres a year?

Because astronauts left mirrors on the Moon, and scientists have timed laser pulses bouncing off them. Lunar laser ranging measures the Earth-Moon distance from the round-trip time of laser pulses reflected by retroreflectors on the Moon. The crew of Apollo 11 installed the first array on July 21, 1969, and on August 1, 1969 the 3.1 m telescope at Lick Observatory reported the first successful measurements. The round trip takes about 2.5 seconds.

Run that experiment for decades and the answer creeps up: laser ranging shows the Moon spiraling away from Earth at 3.8 centimeters per year, a rate described as anomalously high.

The cause is the tides. The Moon raises a tidal bulge on Earth, and Earth's much faster rotation drags that bulge ahead of the Moon. The bulge's gravity then exerts a torque that lifts the Moon into a higher orbit and slows Earth's rotation: angular momentum is handed from Earth's spin to the Moon's orbit, so our days lengthen as the Moon backs away. It only works because of friction: without friction and heat dissipation, the bulge would be pulled back into line within two days and the Moon would stop receding.

The idea is older than the lasers. In 1898 George Darwin calculated that the Moon had once orbited much more closely and was drifting away, and laser targets on the Moon later confirmed that drift.

The pace has not always been the same. Tidal layers from 620 million years ago suggest an average recession of about 2.17 cm per year since then, about half the present rate, which may be high today because Earth's oceans are close to resonating with the tides.