On Tue, Jul 24, 2018 at 06:36:19PM +0100, David Shaw wrote:
> Taking the Earth and its moon, would it be possible to add a second moon,
> smaller to the naked eye, but still visible and distinguishable as a moon
> and not a star or other planet in such an orbit - possibly retrograde -
> that one moon eclipses the other at the same time as the Earth eclipses
> both, or would this be an unstable system?

You could have a system where this occasionally happens.  Earth's moon
is large enough that for stability, a second moon would have to be
smaller and quite a lot closer to Earth.

You might be able to have a situation where the inner moon is also
eclipsed by the Earth during every lunar eclipse, but not for long in
astronomical terms.  That could only happen if the inner moon's
orbital period is a divisor of the outer moon's, and the repetition
will very slightly adjust the orbit of the inner moon in the same
direction each time.  So the orbit will shift until it is no longer in
resonance.

- Tim