Mechanism Tidal locking

1 mechanism

1.1 orbital changes
1.2 locking of larger body
1.3 rotation–orbit resonance

mechanism

if tidal bulges on body (green) misaligned major axis (red), tidal forces (blue) exert net torque on body twists body toward direction of realignment

the change in rotation rate necessary tidally lock body b larger body caused torque applied s gravity on bulges has induced on b tidal forces.

the gravity of body produces tidal force on b distorts gravitational equilibrium shape becomes elongated along axis oriented toward a, , conversely, reduced in dimension in directions orthogonal axis. these distortions known tidal bulges. when b not yet tidally locked, bulges travel on surface, 1 of 2 high tidal bulges traveling close point body overhead. large astronomical bodies spherical due self-gravitation, tidal distortion produces prolate spheroid, i.e. axially symmetric ellipsoid elongated along major axis. smaller bodies experience distortion, distortion less regular.

the material of b exerts resistance periodic reshaping caused tidal force. in effect, time required reshape b gravitational equilibrium shape, time forming bulges have been carried distance away a–b axis b s rotation. seen vantage point in space, points of maximum bulge extension displaced axis oriented toward a. if b s rotation period shorter orbital period, bulges carried forward of axis oriented toward in direction of rotation, whereas if b s rotation period longer, bulges instead lag behind.

because bulges displaced a–b axis, s gravitational pull on mass in them exerts torque on b. torque on a-facing bulge acts bring b s rotation in line orbital period, whereas bulge, faces away a, acts in opposite sense. however, bulge on a-facing side closer bulge distance of approximately b s diameter, , experiences stronger gravitational force , torque. net resulting torque both bulges, then, in direction acts synchronize b s rotation orbital period, leading tidal locking.

orbital changes

if rotational frequency larger orbital frequency, small torque counteracting rotation arises, locking frequencies (situation depicted in green)

the angular momentum of whole a–b system conserved in process, when b slows down , loses rotational angular momentum, orbital angular momentum boosted similar amount (there smaller effects on s rotation). results in raising of b s orbit in tandem rotational slowdown. other case b starts off rotating slowly, tidal locking both speeds rotation, , lowers orbit.

locking of larger body

the tidal locking effect experienced larger body a, @ slower rate because b s gravitational effect weaker due b s smaller mass. example, earth s rotation gradually being slowed moon, amount becomes noticeable on geological time revealed in fossil record. current estimations (together tidal influence of sun) has helped lengthen earth day 6 hours current 24 hours. currently, atomic clocks show earth s day lengthens 15 microseconds every year. given enough time, create mutual tidal locking between earth , moon, length of day has increased , length of lunar month has shortened until 2 same. however, earth not expected become tidally locked moon before sun becomes red giant , engulfs earth , moon.

for bodies of similar size effect may of comparable size both, , both may become tidally locked each other on shorter timescale. example dwarf planet pluto , satellite charon. have reached state charon visible 1 hemisphere of pluto , vice versa. pluto same age planets in solar system.

rotation–orbit resonance

finally, in cases orbit eccentric , tidal effect relatively weak, smaller body may end in so-called spin-orbit resonance, rather being tidally locked. here, ratio of rotation period of body own orbital period simple fraction different 1:1. known case rotation of mercury, locked own orbit around sun in 3:2 resonance.

many exoplanets (especially close-in ones) expected in spin–orbit resonances higher 1:1. mercury-like terrestrial planet can, example, become captured in 3:2, 2:1, or 5:2 spin-orbit resonance, probability of each being dependent on orbital eccentricity.