Secular tidal torque 2026-10-14
A secular tidal torque is the torque remaining after averaging the changing tidal interaction over fast orbital and rotational motion. The misaligned tidal deformation lets the companion's gravity change the spin angular momentum; the orbit receives the opposite torque. Tidal dissipation converts mechanical energy into heat, while total angular momentum is conserved in an isolated system. Thus the spin-orbit coupling exchanges angular momentum rather than destroying it. [ref]
https://link.springer.com/article/10.1007/s11214-024-01055-4. Fuller, Guillot, Mathis and Murray (2024): tidal dissipation in giant planets
.For intuition near synchronous rotation on a circular orbit, hold mean motion and moment of inertia fixed and adopt the illustrative linear dissipative lawHere is spin angular velocity, is a marked surface direction in an inertial frame, and is a response coefficient, not a universal material constant. A faster spin is slowed and a slower prograde spin is accelerated. The solution and the associated mechanical power loss areThe orbital contribution to this power is , and the spin contribution is ; their sum becomes heat. Holding fixed is a local approximation to the coupled evolution. Actual secular tidal torque depends on the deformation response and orbital eccentricity, so this simple law does not establish which spin-orbit resonance an eccentric body captures into.
Spin-orbit resonance 2026-10-14
A prograde spin-orbit resonance relates mean spin angular velocity to mean motion by a ratio of small positive integers, : the body makes turns in orbital periods. Synchronous rotation is ; Mercury's spin-orbit resonance is nonsynchronous. The relevant combination of spin and orbital angles must stay bounded around a preferred orientation, not merely have a near-integer frequency ratio. For an elongated body on an eccentric orbit, the companion's gravitational torque on the permanent shape can sustain the resonance while tidal dissipation permits capture. [ref].
Synchronous rotation Created 2026-10-05 Updated 2026-10-14
Synchronous rotation means one prograde turn about the body's own axis per orbital period, measured against fixed directions in an inertial frame. This spin-orbit resonance approximately describes the Moon's synchronous rotation toward Earth. [ref].
The striking geometric idea is that one turn in space can keep one face toward the companion: a fixed orientation in the frame turning with the orbit is a changing orientation in an inertial frame. This distinction helps us predict illumination: a synchronously rotating exoplanet orbiting its illuminating star can have persistent day and night hemispheres, whereas the Moon, synchronized to Earth, receives changing illumination from a different body, the Sun.
Tidal locking Created 2026-10-05 Updated 2026-10-14
Tidal locking settles a body's spin into a sustained relation with its orbital motion through tidal forces and tidal dissipation. The simplest case is synchronous rotation, a spin-orbit resonance. On an ideal circular orbit, with spin axis perpendicular to the orbital plane, the body keeps the same face toward its companion, as the Moon approximately does toward Earth. [ref].
This article retains the broader sense of tidal locking as capture into a spin-orbit resonance; the term is also commonly used specifically for synchronous rotation. Tidally evolved rotation need not be : Mercury has a spin-orbit resonance with the Sun, turning three times in two orbital periods. The distinction matters when inferring illumination or climate from a spin period. [ref].
