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

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SUMMARY

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 while L4 and L5 positions are nominally stable, they are only metastable because of the gravitational influences from other celestial bodies, including the Sun, Venus, and Jupiter. However, halo orbits around these geometric positions can remain stable for extended periods despite these perturbations.

PREREQUISITES
  • Understanding of celestial mechanics and orbital dynamics
  • Familiarity with Lagrange points, specifically L4 and L5
  • Knowledge of gravitational influences from multiple celestial bodies
  • Concept of halo orbits in astrodynamics
NEXT STEPS
  • Research the properties and stability of Lagrange points L4 and L5
  • Study halo orbits and their applications in space missions
  • Explore gravitational perturbations in multi-body systems
  • Investigate the dynamics of binary star systems and their orbital mechanics
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Astronomers, astrophysicists, and space mission planners interested in orbital mechanics and stability in multi-body gravitational systems.

TheAwkwardEng
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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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