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Re: moon's synchronism



What is the period of libration of the moon? I want to compare this with
what I simulated for two rigidly connected half-moons. What fraction of
the "projected circular face" keeps hiding from us periodically? I guess
I can check it myself with a pair of binoculars but learning it from
somebody who already knows will save a lot of time. (Both Igal and Leigh
would probably agree, in this particular case).

I'm afraid the topic is long and complex. You should obtain a copy
of the "Explanatory Supplement to the Astronomical Almanac and the
American Ephemeris and Nautical Almanac" and consult the section on
the ephemeris for physical observations of the Moon. (I note here
that the ESAAAENA style is that of scientists rather than sci-fi
fans. Earth, Moon, and Sun are capitalized when they refer to our
Earth, Moon, and Sun.) This will give you a complete treatment.

For your purposes I suspect that you are treating a simulated Moon
in a circular equatorial plane orbit. That is a long way from the
real situation, and without working on it a lot myself I wouldn't
be confident in giving you my answer. Suffice it to say that the
dominant period is one month *roughly*, and at least four different
but nearly one-month periods are involved here since the Moon's
orbit is not circular, or equatorial, or even elliptical, and
librations occur both in longitude and latitude. You won't have to
consider topocentric librations which have a diurnal period, so if
you are browsing indices for "libration" pass up those entries.

Another thing I learned under this thread (please confirm or contradict)
is that the disipation of mechanical energy (frictional solid tides)
is not necessary to explain librations.

That is certainly true, but the topic under discussion is not the
status of the Moon today; it is the evolutionary proces by which
the Moon approached the condition in which we now find it. Earlier
librational motion certainly played the major role in the evolving
kinematics of the Moon, and dissipation was very important in
explaining that evolution. These dissipating solid tides are still
active in the Moon, and the system is still evolving. You may say
to yourself "Yes, but very slowly"; that is not true. The evolution
is measurable and if one were able to harnes the energy dissipated
for useful purposes there would never again be a shortage of energy
on Earth!

I also learned about the two meanings of the word libration. The first
has to do with lunar face changes, the second is more general. According
to my reference, "it signifies that a particle at the libration point is
in balance, at rest in the rotating frame, the centrifugal forces and
the gravitational pulls of the two larger bodies just canceling". (In
"Celestial Encounters", by Diacu and Holmes, Princeton University
Press, 1996). Libratio means balance in Latin. Five Lagrange points
are equilibrium points when a small satellite is in motion in the field
created by two much larger objects. The satellite has a negligible effect
on the motions of large objects. I know this was already discussed here.
Forgive me if I am wrong by assuming that I was not the only one who did
not know what it was about.

There are even more meanings. The well known libration in mean
motion of the three inner galilean satellites of Jupiter is yet
another common application of the word.

Would you excomunicate me if I admit that I have no idea what a Klein
bottle is for? I resisted another "what is it?" reply when the Jack's
message appeared because I hoped to learn from what follows. No help
so far. Am I the only one who is so ignorant?

Given that now probably twice as many people in this group know
what "libration" means than knew before this discussion started,
mostly thanks to you, how could anyone think of such a thing?
Klein bottles have nothing to do with physics. It is a
topological curiosity, a closed surface which has only one side
or, alternatively, has neither an inside nor an outside.

Leigh