In a one-line reply to John M. (or was it to David B. ?) Brian W.
compared our Moon to a pendulum. Actually it is a good model for
describing the Interactive Physics simulation I was watching.
Do your own mental simulations (thinking) along the following line.
A point-like satellite, whose mass is very small in comparison with
the planet, orbits along a perfect circle. A sufficiently long simple
pendulum is "suspended" from it toward the planet. It start swinging
trying to "show us the same face". The situation is dominated by the
apparent forces, especially when the mass of the pendulum is not very
small in comparison with the mass of the satellite. By the way, the
ropes never break in I.P. It is not a "simple pendulum" with which we
are familiar.
My simulation does clearly display a pendulum-like behaviour of the
rigid double-moon orbiting Earth. The center of the satellite follows
more or less circular orbit but the axis of the satellite swings back
and forth. Actually it is back and forth spinning, like in a torsional
pendulum. Try it with I.P., you will like it. For a distance between
the half-moons, with which I was playing, the period of oscillation is
only slightly less than the orbiting period. But for another distance
it can be very different.
How accurate is our assumption that the Moon is a sphere? Perhaps it
is not a perfect circle (when viewed perpendiculary with respect to
the E-M line). Or perhaps the spherical Moon has an inner distribution
of mass which is not spherically symmetrical. This could, perhaps,
lead to an explanation of its "showing the same face" behaviour
without the invocation of "solid tides".
Ludwik Kowalski