Lunar Laser Ranging: Millimetre Precision on the Moon
🌐 Measuring the Earth from space
Question
How do we measure the distance to the Moon to the millimetre?
Observatories fire lasers at retroreflectors left on the Moon by the Apollo missions (and the Soviet Lunokhod rovers) and time the round trip of the light. The distance varies exactly as predicted by an elliptical orbit around a spherical Earth - and the timing of the return depends on the Earth's rotation and curvature. It is the longest baseline in the solar system, measured to the millimetre.
The math
385,000.6 km (centre to centre). Round-trip light time = 2 × 385,000.6 / 299,792.458 = 2.57 s. The elliptical orbit: perigee ~363,300 km, apogee ~405,500 km. The Moon is also spiralling away from Earth at 3.8 cm per year - measured by the same lasers.
Why it matters
Millimetre precision on a 385,000 km baseline (Murphy calls it 'the millimetre challenge'). The Earth-Moon geometry is impossible in flat-earth cosmology, and the retroreflectors are out there - anyone with a big telescope can bounce a laser off them.