Retrograde Moon?

Almost all the planets and satellites in the solar system rotate in 
the same direction as they revolve.  However, there are some notable 
exceptions.  For example, radar measurements made in 1961 showed that 
the planet Venus not only rotates very slowly (one rotation taking 
243 days, so the "day" on Venus is actually longer than the "year"), 
but that the direction of rotation is retrograde, i.e., it rotates 
in the opposite direction to its orbital revolution. No one really 
knows why Venus has such an unusual rotation.  I believe Pluto also 
has retrograde rotation.

Anyway, this got me wondering about our own Moon.  Of course, the 
Moon (presently) rotates in the same direction as it revolves, and 
it is gravitationally locked into a 1:1 synchronization because 
the "tides" in the formerly molten rock have cooled and solidified, 
and the resulting elipsoidal shape is permamently oriented with its 
major axis pointing toward the earth.  (This type of gravitational 
synchronization is fairly common in the solar system, almost always
with a ratio of 1:1.  The exception is Mercury, whose rotation is 
locked in a 3:2 coupling.)

However, it's believed that in former times the Moon rotated more 
rapidly and was closer to the Earth.  Over millions of years the 
Moon's rotation was slowed due to the tidal drag (with energy being 
disipated in friction with the constant reshaping of the Moon), and 
to conserve angular momentum the radius of the Moon's orbit has 
increased.  So the point is that at some time in the past the Moon 
had enough rotational momentum to spin it completely around relative 
to the Earth.  For a while it may have been locked in various other 
rotation/revolution proportions like 3:2.  But then one day it just 
couldn't quite make it all the way around, so it's rotation (relative 
to the rotating frame of its orbit around the Earth) actually stopped 
and reversed itself, and it swung back the other way.  Then it couldn't 
quite get around that way either, so it "rang like a bell" for awhile 
until the oscillations finally dissipated (although they aren't 
completely gone, since the Moon still "librates" a little.)

This raises some interesting and perhaps unanswerable questions.  The 
first time the Moon was unable to complete it's rotation relative to 
the Earth, did it then also fail to complete a rotation in the opposite 
direction?  Ideally one would think so, since the potential "hill" it 
had to climb would be the same height in both directions, but with 
variations in the Earth-Moon distance and non-ideal shapes, etc, it 
isn't obvious to me that the Moon couldn't have successfully completed 
a rotation in the retrograde direction (again, relative to the frame 
of its orbit around the Earth).

But this raises an even more fundamental question:  In which direction 
was the Moon originally spinning?  I have always presumed it was the 
"forward" direction, but now that I think about it I'm not sure the 
motion we observe today necessarily rules out the possibility that 
the Moon originally had retrograde spin.  If it's original spin had 
been retrograde, tidal forces would have slowed its spin (relative to 
the earth) just the same as it would if it had forward spin, and when 
it finally couldn't quite complete a retrograde rotation relative to 
the Earth, it would have gotten locked into a 1:1 orbit that (I think) 
would be indistinguishable from what we observe today.

The only thing that might rule out the retrograde possibility is the 
idea that the Moon was originally closer to the Earth, and it's been 
moving farther away to conserve angular momentum. If the Moon originally 
had retrograde spin then its slowing would (I think) tend to shrink the 
Moon's orbit and bring it closer to the Earth.  Of course, we know that 
the Moon is slowly receeding today, but that is due to the slowing of 
the Earth's rotation.  The Moon's spin is already 1:1 so it no longer 
has any secular changes in spin rate (aside from that due to the 
slowing of the Earth's spin).

Assuming a retrograde Moon, it could still have been the case that the 
Moon has been always receeding, because the slowing of the Earth's 
rotation might be the dominant factor.  On the other hand, even if the 
Moon's spin is the biggest factor, I'm not sure what evidence we have 
(aside from physical inferences based on the *assumption* of forward 
Moon spin) to tell us that the Moon's mean distance has changed 
monotonically.  It's conceivable that the Moon was originally in a 
more distant orbit with a retrograde spin, then approached as the 
Moon's spin slowed, and now is receeding based on the slowing of the 
Earth's spin.

I suppose the answer to these questions depends on the still 
unresolved issue of the Moon's origin, i.e., was it co-formed 
along with the Earth or was it formed elsewhere and then captured. 
In any case, the example of Venus shows that retrograde spins are 
not impossible.  It's an interesting physics question to decide
whether it is possible, even in principle, for us to infer the 
Moon's original direction of spin from it's present pattern of 
motion.

Return to MathPages Main Menu
Сайт управляется системой uCoz