It would be unstable. Even a far orbit would have the Sun, Venus and Jupiter tugging at the additional satellite, changing it's eccentricity.

The only 'stable' orbits around the Earth-Moon system are the L4 and L5 locations. L1, L2, and L3 can 'orbited'

Now regarding the eclipses, once the Earth has eclipsed Luna, it would not matter if the new satellite were orbiting inside or outside the Moon's orbit, it would be said to be eclipsed by the Earth also.

I would suggest trying out Kerbal Space program. The primary planet, Kerbin, has two satellites, the Mün and Moho, that orbit in the same plane as Kerbin's orbit around it's primary, Kerbol, so this scenario can be tried out.

Jeffrey

On Tue, Jul 24, 2018 at 10:37 AM David Shaw <xxxxxx@gmail.com> wrote:

Apologies if this is a basic question.

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?

Many thanks,

David Shaw

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