What is tidal locking?

Why the Moon is always facing the same side to Earth? The answer is tidal coupling or tidal locking and it is this post’s subject.

Why tidal locking happens?

Moon elliptical orbit, inclination between orbital planes of Earth and Moon and tilted axes of both, make possible observe more than half of lunar surface. Including the natural satellite’s north and south poles. However, 41% of lunar surface remains hidden for an Earth observer.

How it started?

At the time of formation, Moon and Earth rotated much faster than today. Both exert gravitational forces on each other, causing tides on Earth and a small stretching on Moon.

For having lower mass, Moon obtained tidal locking first. If the Moon rotated slower than Earth, tidal forces would have accelerated the rotation to achieve tidal locking. 

50 billion years from now, Earth will be locked and will have the same side to the Moon. Unless both are swallowed by the red giant the Sun will become in 5 billion years.

How long it takes to obtain tidal locking?

This is the simplified equation to calculate estimated time $t$, in years, to a moon achieve tidal locking in relation to its planet. This equation can only be used for spherical moons.

$t\approx 6\frac{a^{6}R\mu }{m_{s}m_{p}^{2}}\cdot 10^{10}$

Where:

• $m_{p}$ is the mass of primary body, or planet.
• $m_{s}$ is the mass of secondary body, or moon.
• $a$ is distance between two bodies.
• $R$ is satellite’s radius.
• $\mu$ is natural satellite’s rigidity, in $N/m^{2}$. Depends on moon’s composition, if it’s rocky, made of ice, etc.