Re: Moon's synchronism

[brian whatcott <inet@intellisys.net>]

At 15:15 3/17/98 -0800, John Mallinckrodt wrote:

> > "resonant frequency" of what?
>
> Of the moon's rotational velocity perturbations due to the periodic tidal
> torque.  I just did a "back of the envelope" (actually more like "two
> sheet of paper") derivation of the period for small oscillations of a
> nearly spherical but slightly prolate ellipsoid in a gravitational field
> gradient and got the sensible result that
>
>  T = 2 pi/sqrt(f g')
>
> where f is the fractional difference between the maximum and minimum
> rotational inertias about axes through the CM and g' is the local field
> gradient.  For the moon g' is about 1.4 x 10^-11 s^-2.  I don't know the
> value of f, but if it were as large as 1% (which I sincerely doubt), the
> period would still be over 6 months.
>
> John


There is at least ONE simple soul who would have preferred more
symmetry with the well-known relation

T = 2 pi sqrt( L/g)

L length of pendulum
g the local field

The natural period of a slightly displaced pendulum.

Whatcott  Altus