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# Tidal lock

Due to tidal locking the inhabitants of central celestial body will never be able to see the green area of the satellite.

Tidal lock is a state in which any celestial body in orbit around another, usually heavier body keeps the same face toward the other body. The rotation of such a body is thus synchronous. The classic example of tidal lock is the attitude of the Moon of Earth.

## Mechanism

When one body is in orbit around another, each body induces tides in the other. In the case of the earth, the tides manifest themselves as a rising or lowering of the level of the ocean. But a solid body will bulge, both toward and away from the other body, while the other parts of the body will compress toward the center.

Once a bulge forms, if that bulge does not resolve itself, the other body in the orbital configuration will exert more force on it as it passes, simply because it is closer to the barycenter. With each successive seizure, the body's rotation will slow. Eventually the body will turn its greatest concentration of mass toward the other body and maintain that orientation. But as the body slows, it will move to a more-distant orbit from its primary, in order to satisfy the Law of Conservation of Angular Momentum. Hence the Moon recedes as its rotation continues to slow.

In theory, this could happen to the earth as well, and in fact many secular astronomers say that it is happening.

## Time scale

The time required for tidal lock is difficult to estimate, primarily because it depends on many factors, unique to any given satellite or primary, that are difficult to measure. The formula for the time required for any moon to enter tidal lock with its primary is:[1]

$t_{{{\textrm {lock}}}}={\frac {16\rho \omega a^{6}Q}{45Gm_{p}^{2}k_{2}}}$

where

• $\rho \,$ is the density of the moon
• $\omega \,$ is the initial rotation rate in rad s⁻¹
• $a\,$ is the semi-major axis of the moon's orbit.
• $Q\,$ is the dissipation function of the moon (not to be confused with its apoapsis).
• $G\,$ is the gravitational constant.
• $m_{p}\,$ is the mass of the primary.
• $k_{2}\,$ is the tidal second-order Love number of the moon.

Thus the time required is very sensitive to orbital distance and somewhat less sensitive to the mass of the primary. Thus dense moons relatively close to their primaries are more likely to be in tidal lock.

## Problems for uniformitarianism posed by tidal lock

Tidal locking is as likely to happen to the primary as to the moon. Indeed Pluto and Charon are mutually locked. But tidal lock has its most profound implications for the Earth-Moon system. Though the presence of tidal locking might appear to militate in favor of a great age for the solar system, the dynamics of tidal lock suggest youth, not age.

As earth's rotation decreases, the moon must recede from the earth, or else angular momentum is not conserved (see above). Therefore the rate of deceleration of Earth's rotation must itself decelerate over time. For that reason alone, the Earth-Moon system cannot be more than 1.2 billion years old, because at such a time the Earth would have been rotating dangerously fast, and the Moon would have been touching the Earth.

## References

1. Gladman B., Quinn D. D., Nicholson P., and Rand R. "Synchronous Locking of Tidally Evolving Satellites." Icarus 122(1):166-192, July 1996. doi:10.1006/icar.1996.0117 Accessed July 4, 2008.
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