Tidal Locking & Synchronous Rotation
How tidal torques drive a moon toward spin-orbit synchrony
Parameters
Initial spin rate ω₀/n:
2.0
Tidal Q factor:
20
Eccentricity e:
0.05
Triaxiality β:
0.3
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State
Spin ratio ω/n
—
Tidal torque
—
Locked?
No
Time (orbits)
0
Physics
τ_tidal ∝ (Gm²R⁵)/(Qa⁶) × f(e)
İ dω/dt = -τ sign(ω−n)
Locked when |ω−n| < δ_lock
t_lock ∝ Q·a⁶/(m_planet·R⁵)