Re: moon's synchronism

[Leigh Palmer <palmer@sfu.ca>]

> Date: Tue, 17 Mar 1998 10:42:39 -0800
> From: Leigh Palmer <palmer@sfu.ca>
> Subject: Re: Moon's synchronism
>
> > ... It's slower/higher, actually. This sort of tidal interaction
> > has resulted in the tidal spin-orbit locking of most of the large
> > planetary satellites in the solar system. It is also responsible
> > for the volcanism on Io and the librating orbital resonance lock
> > of the inner three Jovian satellites. ...
>
> 1) Is it correct to think that for ideal rigid (spherical or ellipsoidal)
>   Earth and Moon, synchrinization would be an infinitely long process?
>   It could only occur by coincidence.

Spherical - yes. No tides, no synchronization. Ellipsoidal - I don't
think synchronization is possible, but the orbit could get funny if
it was small enough, parhaps even to the point that a collision
occurs. I don't know if anyone has explored the two-spinning-orbiting
ellipsoid problem. Given the lack of naturally occurring instances
for which it could be a model I don't think I'll be the one to do so.

> 2) Is it correct to think that for ideally elastic (deforming slightly
>   without internal friction) Earth and Moon, synchrinization would be
>   an infinitely long process? It could only occur by coincidence.

Yes. There must be a dissipative process operating. Somehow the
system must find a state with the same total angular momentum
and the same total kinetic energy. That's hard to do if one takes
angular momentum away from the spins, because putting it into the
orbital motion invariably leads to lower total kinetic energy.

Leigh