While studying the Gaussian gravitational constant and its constant function I found that the function and the elliptical orbit remain unchanged in General Relativity's rotating (precessing) orbital plane. The equation for the orbit has an extra term, 3mu2 (u = 1/r), in GR. This shouldn't be surprising since motion in Relativity confuses space and time a little. The term is small compared to other terms in the equation of the motion and the solution for planetary orbits found in Eddington's The Mathematical Theory of Relativity used the classical orbit as a first approximation to derive a relativistic correction. Eddington also makes an assumption that the mass is constant since p = h2/μ is dependent on mass which relativistically varies with the speed at which a body is moving. For highly elliptical orbits the speed at perihelion near the Sun is much greater than at aphelion, the most distant point in the orbit, and we may expect the approximations made to break down a little.
But Relativity makes some assumptions like the speed of light being a constant which can be considered an approximation too. The results of Relativity are based on deduction which is more accurate than induction and it draws heavily on classical results such as the agreement of the form of the gravitational potential with classical theory. For a two-body problem in GR one has to work with two world lines and coupling their motion assumes a rigid rotor. This like all other constraints restricts the solution to the problem. The check on results is a correspondence principle which says that the results of GR should agree with classical results for low velocities and small masses but one is free to speculate about initial the possible changes that one can make.
The dependence of the results of Relativity on classical physics makes it appear somewhat juvenile. It doesn't appear to be able to stand on its own as one would expect of a more mature theory. The initial assumptions that one can make have a lot of room for error that the correspondence with the classical limit can't narrow down. The same is true for Quantum Mechanics which has a similar approach to the problem and has to deal with uncertainties of its own. In QM one seems to be solving for theories to fit the facts. The results can sometimes be confusing and contradictory which the Schrodinger's cat thought experiment tried to point out. In the quantum world one can never have a clear picture of what is happening and one tends lose track of events.
One's comprehension may be limited but that doesn't mean that theory itself is bounded by one's limits. Are we being held back by a juvenile world view or is there still room for change. We probably shouldn't forget that change comes from within. And additionally we need to narrow down what is "good conduct" in Science. That might be a sign of movement towards a more mature approach.