In the present paper, using the first-order approx-
imation of the n-body Lagrangian (derived on the basis of
the post-Newtonian gravitational theory of Einstein, Infeld,
and Hoffman), we explicitly write down the equations of
motion for the planar circular restricted three-body problem
in the Solar system. Additionally, with some simplified as-
sumptions, we obtain two formulas for estimating the val-
ues of the mass-distance and velocity-speed of light ratios
appropriate for a given post-Newtonian approximation. We
show that the formulas derived in the present study, lead to
good numerical accuracy in the conservation of the Jacobi
constant and almost allow for an equivalence between the
Lagrangian and Hamiltonian approaches at the same post-
Newtonian order. Accordingly, the dynamics of the sys-
tem is analyzed in terms of the Poincaré sections method
and Lyapunov exponents, finding that for specific values of
the Jacobi constant the dynamics can be either chaotic or
regular. Our results suggest that the chaoticity of the post-
Newtonian system is slightly increased in comparison with
its Newtonian counterpart.

EB00000004140K

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• On the conservation of the Jacobi integral in the post-Newtonian circular restricted three-body problem