We always see the same side of the moon

Hi,

We always see the same side of the moon. I believe this is due to an equilibrium state that happens after a long term for a dumbell-shaped or ellipsoid object. Can someone confirm this?

What about other planetry systems? Do other moons constantly look at their respective planets with the same face? What are the precise conditions for this to happen (I assume distance, shape, initial rotation etc.)?

The condition that causes the moon's rotation and revolution periods to match, so that it always shows us the same side, is called "tidal locking." The tidal forces due to the Earth's gravity on a body like the Moon generate bulges which always lag a bit behind the line connecting the Earth and moon. Naturally, the bulges are acted upon by the Earth's gravity also, and the result is a torque which acts to slow the Moon's rotation.

The same effect is also causing the Earth's rotation to slow. The tides, which are visible mostly in water but indeed affect the ground too, are slowly sapping rotational inertia from the Earth, slowing its rotation and making the day longer.

There are many examples of tidal locking throughout the solar system; almost all the Moons in the solar system are tidally locked to their parent planets. There are also some resonances you may wish to study, like the 3:2 resonance of Mercury in its orbit around the Sun.

- Warren

Gonzolo said:

Hi,

We always see the same side of the moon. I believe this is due to an equilibrium state that happens after a long term for a dumbell-shaped or ellipsoid object. Can someone confirm this?

What about other planetry systems? Do other moons constantly look at their respective planets with the same face? What are the precise conditions for this to happen (I assume distance, shape, initial rotation etc.)?

Tidal locking happens naturally between any moon and the planet it circles. Sometimes it happens with planets close to a sun as well. (Mercury almost qualifies, but not quite, it's in a 3:2 resonance as was mentioned earlier.)

The simplest approach to examing tidal locking is to use the conservation of energy. Tidal forces go as the inverse cube of distance. Tidal energy storage goes as the square of the height of the tide. This leads to a tidal energy storage that varies as the sixth power of the distance between the moon and the object it orbits.

Some fraction of the stored tidal energy is dissipated every cycle when the moon rotates. In a complete rotation the moon is alternately stretched, compressed, stretched, compressed, stretched back to it's original shape. Because the moon is not perfectly elastic, this process dissipates energy.

By considering the fact that energy is being dissipated, and that angular momentum is conserved, one finds that rotational angular momentum of the moon is converted into orbital angular momentum, and the system moves into a lower overall energy state.

Because tidal energy is proportional to the sixth power of the radius, tidal locking occurs fast for close moons, slowly for distant ones. Tides as we have them on earth, with liquid oceans, are a bit unusual.

Thanks. I remember a colleague making a model with an orbiting dumbell. I was just not around when he finished the project.