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The vestibular system detects gravity, linear acceleration and angular velocity through two types of organs: the utricle and saccule (linear acceleration and gravity, through otoliths) and the three semicircular canals (angular acceleration in the three planes of space). The physics of the system is that of an inertial mechano-sensor with viscous damping.

The otolith (CaCO, 2700 kg/m³) is much denser than the surrounding endolymph ( 1003 kg/m³): the density difference 1700 kg/m³ generates a net force F_g = ·V·g that deflects the stereocilia of the hair cells below. The deflection x_eq is proportional to the acceleration (including g), allowing the brain to infer orientation relative to the vertical.

The dynamics of the semicircular canal is that of an underdamped oscillator: the equation I·d/dt + b· = has the solution (t) exp(-t/_sc) with _sc = b_cup/k_cup 515 s. The channel responds to angular velocity (not angular position): it detects the beginning and end of a rotation. When the body rotates at a constant speed, _dome decays and the system adapts (gyroscope illusion).

Mechanoelectric transduction (MET) of hair cells follows a sigmoidal curve I_MET(x) = I_max/(1 + exp(-(x-x)/_MET)): the ionic current through channels at the tip of the stereocilia is maximum when they are inclined towards the kinocilium and minimum in the other direction. The scale _MET 110 nm is the deflection distance to go from 10% to 90% saturation extraordinarily small, comparable to an atomic bond.

Gravity is used as an absolute vertical reference by practically all organisms with a nervous system. Statocysts in marine invertebrates, the vestibular system in vertebrates, and plant statocysts (amyloplasts in root cells) use the same physical principle: a dense body sediments under gravity and deforms elastic structures that activate sensors. The angular resolution of the human vestibular system is 0.5°, sufficient for postural control.

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