On Sat, 28 Feb 2004 17:48:27 +0000 (UTC), Wal wrote:

According to a TV documentary last week the

moon is very slowly moving away from us.

Does it need to be accelerating to do that?

If that is the case were is acceleration coming from?

Yes, it is accelerated by tidal forces.

Gravity from the moon causes the facing earth's surface to bulge (also the
surface on the other side of the earth from the moon, but that's not
terribly important here). Because the earth rotates faster than the moon
revolves, that bulge is rotated out from below the moon.

Draw an imaginary line between the centers of the earth and moon. The
bulge will be continually carried to one side of the line, thereby causing
a slightly larger gravitional pull from that side. This pulls the moon
laterally a bit instead of directly towards the earth's center. This
accelerates the moon in a line tangential to its orbit. The energy
required to produce this acceleration comes from the earth's angular
momentum. So the earth slows down, and the moon moves faster (and as a
consequence of the latter, the moon's orbit recedes).

This is a vast oversimplification, of course. A bulging ocean has much
more of an effect than a bulging landmass, as it's fluid and is more
easily held back from rotation by the moon, thereby robbing angular
momentum via friction (it's much as if the crust of the earth is trying to
move through a stationary ocean). So, the rate of recession at any given
time will be affected greatly by the nature of the earth's surface below
the moon. At the present, the rate of recession is much larger than it
was in the past, despite the tidal forces being lower (since the moon is
further away).

The recession will continue until the period of rotation of the earth
slows down to match the period of revolution of the moon. Just as the
moon shows the same face to the earth, the earth will show the same face
to the moon. The tidal bulge then would not be rotated ahead of the moon,
and therefore no longer pull it laterally.

I believe the best calculations show that this state will be reached in
several billion years.

In the much more near future (though still well beyond our lifetime),
however, the moon will recede to the point where total solar eclipses will
never occur again. All eclipses from that point on will be annular.


--
- Mike

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