Tidal locking Totally Explained

Everything about Tidal Locking totally explained

ť A separate article treats the phenomenon of tidal resonance in oceanography.: See the article tidal acceleration for a more quantitative description of the Earth-Moon system.

Tidal locking occurs when the gravitational gradient makes one side of an astronomical body always face another; for example, one side of the Earth's Moon always faces the Earth. A tidally locked body takes just as long to rotate around its own axis as it does to revolve around its partner. This synchronous rotation causes one hemisphere constantly to face the partner body. Usually, only the satellite becomes tidally locked around the larger planet, but if the difference in mass between the two bodies and their physical separation is small, both may become tidally locked to the other, as is the case between Pluto and Charon. This effect is employed to stabilize some artificial satellites.

Mechanism

The change in rotation rate necessary to tidally lock a body B to a larger body A is caused by the torque applied by A's gravity on bulges it has induced on B by tidal forces. Tidal bulges: A's gravity produces a tidal force on B which distorts its gravitational equilibrium shape slightly so that it becomes stretched along the axis oriented toward A, and conversely, is slightly compressed in the two perpendicular directions. These distortions are known as tidal bulges. When B isn't yet tidally locked, the bulges travel over its surface, with one of the two "high" tidal bulges traveling close to the point where body A is overhead. For large astronomical bodies which are near-spherical due to self-gravitation, the tidal distortion produces a slightly prolate spheroid or ellipsoid. Smaller bodies also experience distortion, but this distortion is less regular. Bulge dragging: The material of B exerts resistance to this periodic reshaping caused by the tidal force. In effect, some time is required to reshape B to the gravitational equilibrium shape, by which time the forming bulges have already been carried some distance away from the A-B axis by B's rotation. Seen from a vantage point in space, the points of maximum bulge extension are displaced from the axis oriented towards A. If B's rotation period is shorter than its orbital period, the bulges are carried forward of the axis oriented towards A in the direction of rotation, whereas if B's orbital period is shorter the bulges lag behind instead. Resulting torque: Since the bulges are now displaced from the A-B axis, A's gravitational pull on the mass in them exerts a torque on B. The torque on the A-facing bulge acts to bring B's rotation in line with its orbital period, while the "back" bulge which faces away from A acts in the opposite sense. However, the bulge on the A-facing side is closer to A than the back bulge by a distance of approximately B's diameter, and so experiences a slightly stronger gravitational force and torque. The net resulting torque from both bulges, then, is always in the direction which acts to synchronize B's rotation with its orbital period, leading eventually to tidal locking. Orbital changes: The angular momentum of the whole A-B system is conserved in this process, so that when B slows down and loses rotational angular momentum, its orbital angular momentum is boosted by a similar amount (there are also some smaller effects on A's rotation). This results in a raising of B's orbit about A in tandem with its rotational slowdown. For the other case where B starts off rotating too slowly, tidal locking both speeds up its rotation, and lowers its orbit. Locking of the larger body: The tidal locking effect is also experienced by the larger body A, but at a slower rate because B's gravitational effect is weaker due to B's smaller size. For example, the Earth's rotation is gradually slowing down because of the Moon, by an amount that becomes noticeable over geological time in some fossils. For similar sized bodies the effect may be of comparable size for both, and both may become tidally locked to each other. The dwarf planet Pluto and its satellite Charon are good examples of this— Charon is only visible from one hemisphere of Pluto and vice versa. Rotation-Orbit resonance: Finally, in some cases where the orbit is eccentric and the tidal effect is relatively weak, the smaller body may end up in an orbital resonance, rather than tidally locked. Here the ratio of rotation period to orbital period is some well-defined fraction different from 1:1. A well known case is the rotation of Mercury—locked to its orbit around the Sun in a 3:2 resonance.

Final configuration

There is a tendency for a moon to orient itself in the lowest energy configuration, with the heavy side facing the planet. Irregularly shaped bodies will align their long axis to point towards the planet. Both cases are analogous to how a rounded floating object will orient itself with its heavy end downwards. In many cases this planet-facing hemisphere is visibly different from the rest of the moon's surface.
The orientation of the Earth's moon might be related to this process. The lunar maria are composed of basalt, which is heavier than the surrounding highland crust, and were formed on the side of the moon on which the crust is markedly thinner. The Earth-facing hemisphere contains all the large maria. The simple picture of the moon stabilising with its heavy side towards the Earth is incorrect, however, because the tidal locking occurred over a very short timescale of a thousand years or less, while the maria formed much later.

Occurrence

Earth's Moon

The Moon's rotation and orbital periods are both just under 4 weeks, so no matter when the Moon is observed from the Earth the same hemisphere of the Moon is always seen. The far side of the Moon wasn't seen in its entirety until 1959, when photographs were transmitted from the Soviet spacecraft Luna 3.
Despite the Moon's rotational and orbital periods being exactly locked, we may actually observe about 59% of the moon's total surface with repeated observations from earth due to the phenomena of librations and parallax. Librations are primarily caused by the Moon's varying orbital speed due to the eccentricity of its orbit: this allows us to see up to about 6° more along its perimeter. Parallax is a geometric effect: at the surface of the Earth we're offset from the line through the centers of Earth and Moon, and because of this we can observe a bit (about 1°) more around the side of the Moon when it's on our local horizon.

Moons

Most significant moons in the Solar System are tidally locked with their primaries, since they orbit very closely and tidal force increases rapidly (as a cubic) with decreasing distance. Notable exceptions are the irregular outer satellites of the gas giant planets, which orbit much further away than the large well-known moons. Pluto and Charon are an extreme example of a tidal lock. Charon is a relatively large moon in comparison to its primary and also has a very close orbit. This has made Pluto also tidally locked to Charon. In effect, these two celestial bodies revolve around each other (their mass center lies outside of Pluto) as if joined with a rod connecting two opposite points on their surfaces.
The tidal locking situation for asteroid moons is largely unknown, but closely-orbiting binaries are expected to be tidally locked, as well as, obviously, contact binaries.

Planets

Until radar observations in 1965 proved otherwise, it was thought that Mercury was tidally locked with the Sun. Instead, it turned out that Mercury has a 3:2 spin-orbit resonance, rotating three times for every two revolutions around the Sun; the eccentricity of Mercury's orbit makes this resonance stable. The original reason astronomers thought it was tidally locked was because whenever Mercury was best placed for observation, it was always at the same point in its 3:2 resonance, so showing the same face, which would be also the case if it were totally locked.
A curious aspect of Venus' orbit and rotation periods is that the 583.92-day interval between successive close approaches to the Earth is almost exactly equal to 5 Venusian solar days (precisely, 5.001444 of these), making approximately the same face visible from Earth at each close approach. Whether this relationship arose by chance or is the result of some kind of tidal locking with the Earth is unknown .

Stars

Close binary stars throughout the universe are expected to be tidally locked with each other, and extrasolar planets that have been found to orbit their primaries extremely closely are also thought to be tidally locked to them. An unusual example, confirmed by MOST, is Tau Boötis, a star tidally locked by a planet. The tidal locking is almost certainly mutual.

Timescale

An estimate of the time for a body to become tidally locked can be obtained using the following formula :
ť ::

t_,

with masses in kg, distances in meters, and μ in Nm^-2. μ can be roughly taken as 3 Nm^-2 for rocky objects and 4 Nm^-2 for icy ones.
   Note the extremely strong dependence on orbital radius a.
   For the locking of a primary body to its moon as in the case of Pluto, satellite and primary body parameters can be interchanged.
   One conclusion is that other things being equal (such as Q and μ), a large moon will lock faster than a smaller moon at the same orbital radius from the planet because

m_s,

grows much faster with satellite radius than

R

. A possible example of this is in the Saturn system, where Hyperion isn't tidally locked, while the larger Iapetus, which orbits at a greater distance, is. This isn't clear cut because Hyperion also experiences strong driving from the nearby Titan, which forces its rotation to be chaotic.

List of known tidally locked bodies

Solar System

Locked to the Sun

Mercury (in a 3:2 rotation:orbit resonance) Locked to the Earth

Moon Locked to Mars

Phobos

Deimos Locked to Jupiter

Metis

Adrastea

Amalthea

Thebe

Europa

Ganymede

Callisto Locked to Saturn

Pan

Atlas

Prometheus

Pandora

Epimetheus

Janus

Mimas

Enceladus

Telesto

Tethys

Calypso

Dione

Rhea

Titan

Iapetus Locked to Uranus

Miranda

Ariel

Umbriel

Titania Locked to Neptune

Proteus

Triton Locked to Pluto

Charon (Pluto being itself locked to Charon)

Extra-solar

Tau Boötis is known to be locked to the close-orbiting giant planet Tau Boötis Ab

Bodies likely to be locked

Solar System

Based on comparison between the likely time needed to lock a body to its primary, and the time it has been in its present orbit (comparable with the age of the Solar System for most planetary moons), a number of moons are thought to be locked. However their rotations are not known or not known enough. These are:
Probably locked to Saturn

Daphnis

S/2004 S 6

S/2004 S 4

S/2004 S 3

Methone

Pallene

Helene

Polydeuces Probably locked to Uranus

Cordelia

Ophelia

Bianca

Cressida

Desdemona

Juliet

Portia

Rosalind

Cupid

Belinda

Perdita

Puck

Mab

Oberon Probably locked to Neptune

Naiad

Thalassa

Despina

Galatea

Larissa Probably locked to other dwarf planets and minor planets
Numerous asteroid and TNO moons are expected to be locked to their primaries. However, in the absence of direct observation reliable candidates are difficult to verify. While locking timescales can be estimated, the age of the primary+satellite system is difficult to gauge; most are thought to be the results of collisions in the last few hundred million years.

Extra-solar

Gliese 581 c may be tidally locked to its parent star Gliese 581.Further Information

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