# What is synchronous rotation and tidal coupling?

Synchronous rotation is a concept used in astronomy to describe the characteristic that occurs when a celestial body rotates on itself and in orbit around another celestial body, and the speed of rotation is the same as the speed of orbital translation.

Synchronous rotation has a very peculiar effect: the celestial body in synchronous rotation keeps the same hemisphere pointing towards its companion around which it is orbiting. The best known example is undoubtedly the synchronous rotation of the Moon around the Earth.

## Synchronous rotation and tidal coupling

Synchronous rotation between two celestial bodies occurs as a consequence of the so-called tidal coupling. Although there are no tides on other planets, at least not ocean tides as we know them on Earth, synchronous rotation occurs in a similar way on many natural satellites of the Solar System.

Generally, satellites are much smaller in size than the planets they orbit and only satellites achieve synchronous rotation, but in theory, if the difference in mass between the two bodies and the distance between them is small, both should achieve synchronous rotation. synchronous rotation with each other; this can be observed in some binary star systems.

In the specific case of the Moon, both the rotation on its axis and the translation around the Earth have a duration of 27.33 days (although the length of the lunar cycle is 29.53 days). Having the same duration, it does not matter when we observe the Moon, we will always see the same face.

The other side we don't see, or hidden side, was first observed in 1959 on the Soviet mission Luna 3 or E-2A (Russian Луна-3)

### Mechanism

Consider two co-orbitinating objects, A and B, such that A is the larger body and generates synchronous rotation in body B. For this to happen, body A has to modify the rotation that body B would have in gravitational equilibrium on its own.

First, the force of gravity from A causes a distortion in the shape of body B. Body B is elongated in the direction of gravity, causing it to lose its spherical shape. The deformation creates a gravitational gradient, larger on the deformation axis. This effect can be smaller or larger depending on the mass of B and the mass and strength of gravity of A.

At the beginning of the formation of both bodies, body B would rotate much faster on itself, and with the passage of time the gravity of A would slow down the speed of rotation of B.

The angular momentum of the whole system AB is maintained during the coupling, so that the reduction in rotational speed at B is accompanied by a equal magnitude increase in the speed of translation until they become equal and one hemisphere of B is blocked facing A. A torque would be created.

The effect of the gravity of B on A would also produce the coupling of the rotation and translation of A, but since the mass of B is much smaller, this effect would take many years to complete. In fact, with the use of atomic clocks it has been possible to estimate that the Moon reduces the rotation speed of the Earth by 15 microseconds each year; each passing year has days 15 microseconds shorter.

At this speed, the coupling of the Earth to the Moon will not be complete before the Sun goes extinct.

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