## Thursday, February 1, 2018

### Selected Questions -Answers From All Experts Astronomy Forum (Tidal locking, resonance)

Question:

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?

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,

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 approximately 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 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 roughly 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 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 the locking
In of a different spin rate .

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.