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Manevis classical potential is known to successfully modify Newtonian celestial mechanics, in accordance with the general-relativistic description. The idea of replacing the exact solution of Einsteinis equations, describing orbiting bodies, with a classical potential is widely used today. These models are not restricted to planetary motion only, but also include numerous interesting astrophysical phenomena such as accretion of matter around black holes or massive stars.
Ivanov, R. & Prodanov, R. (2005). Manev Potential and General Relativity. Prof. G. Manev's Legacy in Contemporary Astronomy, Theoretical and Gravitational Physics, Heron Press, Sofia. doi:10.21427/saqk-qf53