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].
For intuition near synchronous rotation on a circular orbit, hold mean motion and moment of inertia fixed and adopt the illustrative linear dissipative law
Here 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 are
The 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.
Tidal deformation 2026-10-14
Tidal deformation is the change in a body's shape caused by differential gravity across it, that is, by a tidal force. The familiar two-bulge picture represents an elongated response along the companion direction, rather than a separate force pulling only the nearest surface. If spin and orbital motion differ, the forcing sweeps through the body's material. With tidal dissipation, the response is out of alignment with the instantaneous forcing, allowing a net torque. [ref].
Tidal dissipation Created 2026-10-06 Updated 2026-10-14
Tidal dissipation converts mechanical energy associated with a time-varying tidal deformation into heat. It can reduce orbital eccentricity, drive synchronous rotation, and contribute deep planetary heating. A circular orbit with exact synchronous rotation, perpendicular spin axis and no additional forcing has a static tidal deformation in the body's frame and need not sustain substantial tidal heating.
Tidal heating Created 2026-10-05 Updated 2026-10-14
Tidal heating converts mechanical energy of tidal deformation into internal heat through tidal dissipation. Sustained orbital eccentricity or a spin axis tilted relative to the orbital plane's perpendicular can maintain changing tidal deformation and heat an exoplanet interior. Thus synchronous rotation alone does not eliminate tidal heating.