Do the L4 and L5 points travel in a geodesic?

[kmarinas86]

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?

 

[Garth]

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