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Grades 9–12 · Earth & Space

How can tides make a moon keep the same face toward its planet?

Earth's Moon turns on its axis, yet nearly the same side faces Earth throughout an orbit. Its spin period matches its orbital period. This synchronous rotation is a result of tidal evolution, not a requirement that the Moon stop rotating. A marking on the illustrated moon makes one complete turn relative to distant space during one trip around the planet.

E37 visual explanationOrbital angular speed is normalized to one. Spin 1 gives mismatch 0, torque 0 and nonnegative normalized dissipation 0. The four moon positions separately show synchronous geometry, not the selected transient spin. This is not an evolution-timescale model.One turn per orbit keeps one face planetwardPlanetFour synchronous positionsSeparate torque modelOrbit rate n = 1Spin rate ω = 1Mismatch ω − n = 0Torque = 0Dissipation = 0Synchronous stateRates and torque use normalized model units.

In the diagramOne turn per orbit keeps one face planetwardPlanetFour synchronous positionsSeparate torque modelOrbit rate n = 1Spin rate ω = 1Mismatch ω − n = 0Torque = 0Dissipation = 0Synchronous stateRates and torque use normalized model units.

Four synchronous positions show a moon rotating once per orbit while its marked side faces the planet. The separate toy torque opposes a mismatch between spin and orbital angular speeds.

A planet's gravity is stronger on its moon's near side than on its far side. This difference deforms the moon. When its material response is delayed, the tidal deformation can be misaligned with the line joining the two bodies. The planet's pull on that misaligned deformation exerts a torque that changes the moon's spin. Internal deformation dissipates mechanical energy as heat, while angular momentum is exchanged with orbital motion.

The small model separates the direction of this tendency from a complete evolution calculation. With orbital angular speed normalized to one, the supplied torque opposes the difference between spin and orbital speed. A spin rate of two gets a negative torque; a rate of one half gets a positive torque. Both tend toward the same rate in this circular ideal. The model's nonnegative dissipative term becomes zero when that difference vanishes.

The four orbital positions show the resulting synchronous geometry. The planet-facing mark changes direction in space as the moon travels. Actual tidal evolution depends on internal structure and orbital conditions, and eccentric orbits can produce other spin-orbit resonances. The real Moon also rocks slightly in our view, an effect called libration; same face is therefore an approximation, not a claim that precisely half its surface is ever visible.

About this explanation

Starting knowledge: Understand orbital motion, spin, angular speed and a torque changing rotation.

Sources

  • NASA — Tidal Locking
  • NASA — Secular Acceleration of the Moon
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