Tidal Locking: Why the Moon Only Shows Us One Face

Two bulges, and a small delay that changes everything

Gravity from a planet pulls harder on the near side of an orbiting moon than on the far side, stretching the moon into a slight ellipsoid with a bulge pointing toward the planet and a matching bulge pointing away. If the moon were a perfectly rigid, instantly responsive body, those bulges would stay locked exactly on the planet-moon line and exert no rotational force at all. Real material has internal friction, so the bulge takes a short time to rise and fall as the moon spins, and by the time it reaches full height it has already been dragged slightly out of line by the moon's own rotation — a small lag angle between where the bulge points and where the planet actually is.

That lag is a lever arm

Because the misaligned bulge is not lined up with the planet, the planet's gravity now pulls on it at a slight angle, producing a torque. If the moon spins faster than it orbits, that torque acts as a brake, slowly transferring angular momentum from the moon's spin into its orbit. The process runs one way only, toward equilibrium — and equilibrium is reached exactly when the moon's rotation period matches its orbital period, because at that point the bulge stops being dragged out of alignment and the lag, and the torque, both go to zero.

tidal torque ≈ 0                     while rotation period = orbital period
tidal torque brakes spin             while rotation period < orbital period
                                       (spins the moon down toward the orbital rate)

locking timescale  t_lock ∝  a⁶ / (M_planet² · R_moon⁵)

a = orbital distance, R_moon = moon's radius, M_planet = planet's mass
— locking is dramatically faster for close, small moons around big planets

Why the Moon locked to Earth and not the reverse — yet

The locking timescale is extremely sensitive to the size of the body doing the spinning — it scales with the fifth power of that body's radius — and to the distance between the two bodies, to the sixth power. The Moon is small and close, so it locked to Earth roughly within the first tens of millions of years after formation, astronomically almost instantaneous. Earth is far larger, so the same torque acting the other way (raised by lunar tides on Earth) takes vastly longer to slow Earth's rotation to match the lunar month — an estimated 50 billion years, well beyond the Sun's remaining lifetime. In the meantime, the same physics is measurably lengthening Earth's day by about 1.7 milliseconds per century as the Moon steals a little of Earth's spin angular momentum and, in exchange, drifts about 3.8 cm farther away every year.

Beyond simple 1:1 locking

A 1:1 spin-orbit lock, where rotation period equals orbital period, is the most common outcome for a nearly circular orbit, but it is not the only stable one. Mercury is famously locked in a 3:2 resonance instead — it rotates three times for every two orbits around the Sun — because its orbit is eccentric enough that the tidal torque, which is strongest near perihelion, favours that ratio over the simple 1:1 case. This shows the mechanism generalises: tidal locking drives a body toward whichever spin state makes the average torque over an orbit vanish, and for an eccentric orbit that state is not always the "obvious" one-to-one match.

Frequently asked questions

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