Tidal Locking: Why We Never See the Dark Side of the Moon
Our Egg-Shaped Satellite
A Rising Tide Only Lifts SOME Boats
The Earth's moon always shows us the same face, no matter where it lies in its 27.3-day orbit of our planet. This orbital trait can seem mysterious at first, and indeed can lead some to speculate that our only natural satellite may be of artificial origin.
However, there is nothing mysterious or even unusual about the Moon's rotation - or apparent lack thereof. This is explained by a process known as tidal locking. Most satellites in our solar system are tidally-locked to their planets. This means that their period of rotation is equal to the period of revolution. This occurs, as the name implies, due to tidal forces between the two bodies.
The Tide Is High, But I'm Moving On
When one body orbits another, the force of gravity they exert on each other is not even across their diameters. Gravitational pull is strongest at the point facing the other body and weakest on the opposite sides. This is demonstrated by the way our Moon creates tides on the Earth's oceans - the tides are highest at the point near the Moon, where lunar gravity is strongest, and at the point opposite the Moon where lunar gravity is weakest. Ocean tides are lowest on the two sides of Earth in between - 90 and 270 degrees from the closest point. Seen in cross-section, this distorts the oceans - and in fact the entire planet - into a slight oval shape.
Just as the Moon exerts this kind of uneven gravitational force on the Earth, the Earth has also been exerting a much stronger force on the Moon for several billion years. This has distorted the Moon into an egg shape, as measured by the NASA Lunar Reconnaissance Orbiter and Clementine missions.
This constant distortion, over many millions of years, creates mechanical friction that absorbs the rotational energy of both bodies. Some of this energy is converted into heat - in the case of Jupiter's moon Io resulting in frequent volcanic activity.
Our Moon's rotation energy was absorbed billions of years ago, and it in turn is slowing down the Earth's rotation - in a few billion years the Earth will slow until on Earth day is the same length as a lunar orbit.
The time required for a body to become tidally locked can be estimated using the formula:
tlock ≈ w a6 I Q / 3 G mp2 k2 R5
Where w is the initial rate of spin, a is the semi-major axis of the satellite's orbit, I the satellite's rotational inertia, Q is the dissipation function (the rate at which mechanical energy is converted into heat, G is the gravitational function, mp is the mass of the main body, k2 is the rigidity of the satellite, and R is the radius of the satellite.
This formula, with some rough estimates for unmeasurable properties such as Q and k2, can be used to determine whether exosolar planets are tidally-locked to their parent stars, such as the potential exoplanet Gliese 581g.