Do the L4 and L5 points travel in a geodesic?

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SUMMARY

In a two-body system such as the Sun and Earth, the L4 and L5 Lagrange points are indeed associated with geodesic motion. While the Sun and Earth follow geodesics in General Relativity (GR), test particles co-orbiting at the L4 and L5 points also experience free fall and travel along geodesics. The complexity of the two-body problem in GR necessitates numerical solutions, but the behavior of particles at these points is well-defined within the framework of GR.

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kmarinas86
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Given a two body system like the sun and the earth:

Do the L4 and L5 points travel in a geodesic, or is it just the sun and the Earth which do so?
 
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The two body problem in GR is fiendishly complicated and can only be solved numerically.

However, having said that, test-particles co-orbiting in the L4 or L5 points are in free fall, and in GR they would travel along geodesics.

Garth
 

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