On 20 Mar 1998 11:51:25 -0500 (EST) David Bowman commented on
"the usefulness of the pendulum analogy in the lunar context".
If the word "analogy" stands for the exact mathematical and conceptual
correspondance (as in an electrically oscillating L,C,R circuit versus
a mechanical mass-spring damped system) then I am sorry I used it.
I really ment a qualitative "similarity" not a quantitative "analogy"
in a mathematical, sense.
I was not aware of "the lunar libratory motions". The two textbooks I am
using to learn astronomy do not even have the word libration in the index.
They only say that the moon shows us the same face all the time. Now I am
aware that the face is oscillating so that eastern and western borders
are not identical all the time. This was know for very long time and
explained mathematically by Lagrande.
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).
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. The dominant factor is the
gravitational gradient acting on a large sphere. A perfectly rigid moon
would also librate. The disipative tidal effects accompany the process
but they are not causing it. In the context of this issue the term
"tidal effect" appears because the gradient of the lunar field, acting
on Earth, is responsible for common oceanic tides. It means "the same
effect that is responsible for tides".
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.
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?
Ludwik Kowalski