Can There Be a Stable Figure-Eight Orbit Between Earth and the Moon?

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A stable figure-eight orbit between the Earth and the Moon is not feasible due to gravitational perturbations from the Sun. The discussion highlights that even the L4 and L5 points, which are considered stable, are only metastable because of various gravitational influences, including those from other planets. While these points can be affected by solar gravity and the elliptical nature of Earth's orbit, a halo orbit around these positions can remain stable for extended periods. The complexities of celestial mechanics make such orbits challenging to maintain. Overall, the gravitational dynamics involved prevent the existence of a stable figure-eight orbit in this context.
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Hello! I don't know if this is in the right place or not. So if it's not, I won't misplace it in the future.

Anyway, I was recently thinking about the orbits of planets around Binary Stars, and was wondering if it's possible to have a similar orbit around the Earth and the Moon. Have a figure-eight like Orbit that would stay stable even with the movement of the Moon and the varying distance. Do you know if it's possible?
 
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No, sadly, because it would soon be perturbed by Sun's gravity...

On a local scale, this even applies to the nominally stable L4 & L5 positions. IIRC, they are only metastable due to solar gravity, Earth's slightly elliptical orbit, Venus & Jupiter etc etc. However, a 'halo orbit' around those geometric positions *will* survive for a long time...
 

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