Expert: Philip Stahl - 4/4/2004

Question
Hello Mr. Stahl,
I don't quite understand how even if the moon is spinning, why is it not subject to tidal braking?

and what is different about mercury that causes its spin rate to be locked differently from the moon's?

thanks a lot

-raichu

Answer
Hello.

The basis of your question resides in the principle of conservation of angular momentum. To put it in simple terms, two bodies in a joint system cannot both 'spin up' at the same time, when tidal forces act. One will slow (in this case, the Earth), the other (moon) will acquire its 'lost' angular momentum. Ignoring external effects, you can summarize the transaction as a "zero sum" game.


Let's now fix ideas within the Earth-Moon system: The Earth rotates faster than the Moon moves in its orbit. Because the tides are linked to the more slowly moving Moon, they act by friction as a brake on Earth's rotation, gradually slowing it down.

The angular momentum lost by the rotating Earth in this process is transferred to the Moon's angular momentum. Thus, the Moon is accelerated in its orbit, causing it to slowly spiral outwards...away from Earth. The day and month are thus lengthening at different rates.

Calculations have actually been retro-worked to show how the length of month differed when the Moon was much closer to Earth in the past. For example, when the Moon was only 16,000 km away (10,000 miles) the month was apporximately seven mean solar days long.

Similar calculations based on the conservation of angular momentum also allow us to project into the future. Thus, about three billion years hence, the day and month will be equal - about 47 of our present days long -  and the Earth will always turn the same face towards the Moon.

In the case of Mercury a number of reasons might explain why its spin rate is locked differently.

One is that its resonance period is simply different. Thus, 59 days rotation period for Mercury equals roughtly two-thirds of its period of revolution (88 days). This suggests a resonance effect with the tidal forces of the Sun. (Resonance effects always mean the rotation, for example, is a whole number or integer *multiple* of the revolution(s). In this case: 3 rotation periods ~ 2 revolution periods).

Clearly, since Mercury is much much closer to the Sun than the Moon is, the role of the Sun would figure much more prominently in such 'resonance periods' for Mercury than for the Moon. This would surely lead to a different spin rate locked.

Another factor that may play a role is the particular shape of the Moon, which is a tri-axial ellipsoid, not a perfect sphere. In this case, its longer axis is always pointing more or less towards the Earth's center. Thus, the Moon's shape may well contribute to some degree to its differing 'lockage' of spin rate.

Hope this info helps.