I doubt General Relativity will ever be "overthrown" as Newton's theory of gravity has never been overthrown despite being "wrong".
Physical theories evolve and a theory which replaces its predecessor needs to make the same successful predictions as per the theory it replaces.
What a new theory does as General Relativity did in replacing Newton's theory is to add corrective terms.
The above equation is the potential energy for orbital motion.
The first two terms in the right hand side of the equations are the Newtonian terms describing the gravitational and centrifugal potentials respectively.
The last term is a General Relativity term which is usually extremely small and can be ignored.
It becomes significant when planets are very close to the Sun such as Mercury where the effects of space-time curvature become apparent leading to non Newtonian behaviour such as the perihelion advance of Mercury's orbit.
In most cases Newtonian gravity is satisfactory to use, it is an incomplete theory like General Relativity both of which are not likely to overthrown but incorporated into a more general theory such as a Quantum theory of gravity.