Visually Observing Lunar Rotation
Is it possible to actually see the Moon slowly
rotating, through a telescope while standing on Earth?
Yes, you can, but you would have to watch the moon very carefully
for a full month. What you are discussing is called lunar
longitudinal libration. Although the moon is in synchronous rotation
and shows the same face to the earth, its slightly elliptic orbit
allows us to see eight degrees of extra face on its right and left
side during its perigee and apogee, respectively.
Hope this helps.
Only very slightly. Gravity has caused the rotational period (about
its polar axis), and the orbital period (about the earth's orbital
axis) to be synchronous so that except for a little wobble, the
part of the moon that faces the earth is always the same. This is
difficult to describe verbally, but if you do a 'Google' search on
term(s) like "moon synchronous orbit" or similar you will find many
sites with pictures and diagrams explaining synchronous orbits.
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Update: June 2012