From: henry@spsystems.net (Henry Spencer)
Newsgroups: sci.space.science
Subject: Re: Tide Locked body question
Date: Sun, 7 Nov 1999 21:10:23 GMT

In article <19991107031313.16689.00000582@ng-ct1.aol.com>,
V-Man <velovich@aol.com.CanDo> wrote:
>   What determines which planets or moons will become tidally locked, and which
>will have their own rotation?

Well, the fast answer is that they will *all* become tidally locked
eventually.  It just takes a long time in the less favorable cases.

A non-locked rotating body orbiting another body always experiences some
tidal drag, which tries to bring its rotation rate into lock with the
orbit.  Smaller and more rigid bodies experience less drag, and drag drops
off very sharply with distance.  (Mercury is in a 3:2 lock, rather than
usual 1:1 lock, with the Sun because its orbit is somewhat elliptical and
the tidal drag is much stronger at perihelion than over most of the rest
of the orbit.)  So in general, large soft objects in close orbits go into
lock very quickly, and small hard ones in distant orbits take a very long
time to be affected noticeably.

In our solar system...  All the major moons are locked to their planets,
as are the small close ones; some small distant ones are not.  Only one
small planet with a large close moon (Pluto) is locked to its moon,
although Earth, with a large but fairly distant moon, is measurably
working on it.  Mercury is locked to the Sun, Venus is *almost* locked
(although the history of its rotation is unclear and this might be a
coincidence), but nothing farther out shows any sign of solar lock.
--
The space program reminds me        |  Henry Spencer   henry@spsystems.net
of a government agency.  -Jim Baen  |      (aka henry@zoo.toronto.edu)

From: henry@spsystems.net (Henry Spencer)
Newsgroups: sci.space.science
Subject: Re: Tide Locked body question
Date: Thu, 18 Nov 1999 02:26:17 GMT

In article <383100F1.A1F651A5@mail.com>, Bill Bonde  <stderr@mail.com> wrote:
>> ...Thus, the moon has a 1:1 ratio. For Mercury, the ratio 3:2 means
>> that for 3 rotations of the planet, it orbits the sun twice.
>
>The thing that is confusing is WHY some objet would end up in these
>various ratios. 1/1 seems logical but the other ones seem amazingly
>convoluted.

It was quite a surprise when people discovered that Mercury was in a 3:2
lock; everyone had expected 1:1.  (A contributing factor was that
observing conditions for Mercury are most favorable at regular intervals
which happen to be an even number of Mercury orbits long, a situation in
which you can't tell the difference between 1:1 and 3:2.)

Almost all the tidally-locked rotations are in fact 1:1.  Mercury is an
exception because its orbit is quite significantly elliptical.  That means
its orbital motion at perihelion is substantially faster than its average
orbital motion.  And because tides follow an inverse-cube law, they are
*much* stronger at perihelion than during the rest of the orbit... so the
locking effect tends to lock Mercury's rotation to its faster perihelion
motion, not to its average orbital motion.

When the difference is small enough, you still get 1:1 lock -- Io is in
1:1 lock with Jupiter despite a slightly elliptical orbit.  But when the
difference is substantial, as with Mercury, you can get oddball forms of
lock like Mercury's 3:2.
--
The space program reminds me        |  Henry Spencer   henry@spsystems.net
of a government agency.  -Jim Baen  |      (aka henry@zoo.toronto.edu)