From: Henry Spencer <henry@zoo.toronto.edu>
Newsgroups: sci.space.science
Subject: Mercury's rotation (was Re: Unique ?)
Date: Mon, 16 Dec 1996 04:03:51 GMT

In article <slrn5b30a8.4n.bgoudem@qualiscope.axess.com> bgoudem@qualiscope.axess.com (Benoit Goudreault) writes:
>You're almost right.  Mercury does rotate, but very slowly.  It takes 3
>revolutions for Mercury to complete two rotation...

Vice-versa:  the period of the orbit is 88 days, while the period of
Mercury's rotation is 59 days.

>Does anyone have a precise explanation of resonance?  My astrophysics
>book just says it exists, without really explaining how it works.

It's a fancier version of tidal locking.  In hindsight, we should have
expected this, rather than expecting a 1:1 lock between orbit and rotation.

Skipping a lot of detail, the key thing is that Mercury's orbit is quite
noticeably elliptical.  This matters because tidal forces follow an
inverse-cube law, so they are *much* stronger at Mercury's perihelion
(closest approach to the Sun) than at other times.  So tidal forces tend
to set Mercury's rotation to a speed that makes its rotation match its
orbital motion *at perihelion* -- a time when Mercury's orbital motion is
at its fastest, considerably faster than the average over the whole orbit. 
So instead of settling into a 1:1 relationship with the orbital period,
its rotation settled into a 3:2 relationship instead.  This is, in
retrospect, what you would expect for a body in a moderately elliptical
orbit.

This was missed for a long time for two reasons.  One is that major bodies
in the solar system tend to be in near-circular orbits, so we didn't have
any other examples to look at.  The other is that by an accident of
orbital mechanics, particularly good opportunities to observe Mercury from
Earth come roughly every *two* Mercury orbits... so astronomers observing
Mercury (not an easy thing to do) tended to see the same side of Mercury
all the time, and naturally assumed that in the course of two orbits, it
had completed two rotations, when in fact it had completed three.
-- 
"We don't care.  We don't have to.  You'll buy     |       Henry Spencer
whatever we ship, so why bother?  We're Microsoft."|   henry@zoo.toronto.edu