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Re: moon's synchronism



At 10:50 3/21/98 -0400, you wrote:
....
What is the period of libration of the moon? ... What fraction of
the "projected circular face" keeps hiding from us periodically?...
... I have no idea what a Klein
bottle is for? ... Ludwik Kowalski


Periods:
Libration in latitude: month (sidereal month = 27d,7h,43m,11.5s)
Due to tilted axis of rotation vs axis of revolution (6.5deg.)

Libration in longitude: month
Due to elliptical orbit

Diurnal libration: day
Due to variation in viewing angle from Earth horizon to horizon.

Physical libration: "small pendulum-like rotational vibration of the
moon with respect to its radius vector." (Bowditch, 1984)
(Period and amplitude not specified)

Moon Area Never Visible from Earth: 41%
Note: this is NOT projected area, which would be quite a
bit different...

Klein: a 3-D analog of a Mobius strip.
A (not very good) picture of a Klein bottle is shown on page 104 of
Scientific American Apr 98
A Mobius strip may be prepared from a strip of paper 2 cm wide and
25 cm long. Using adhesive or scotch tape one end is fastened to the
other to form a paper ring, after a half turn is executed on one end.
This demonstrates the property of single-sidedness in topological terms:
a ball point pen can draw a line along the length of the total surface
without lifting the pen.