Let me just add a little to "dawgdays" response...
Newtonian gravitation is used in systems as large and diffuse as galaxies, because it resolves to closed-form solutions, so is much faster to compute results in multi-body systems. And it does not return really terrible results to do this, the errors are not large. But it does describe a different system from what we are presented with.
Here is a paper or two you might want to review:
... don't get too bogged down in the formalism.
The things to be concerned with are usually assuming rigid bodies, point mass sources, and the "butterfly effect". Planetary radii are constantly changing, very slightly. We don't even know if we've spotted all the planets of this solar system:
If you just "stick to Newton", you introduce known errors. So if you are only going to orbit once or twice, Newton is probably good enough, but returns uninteresting results. Only roughly describing gross results. Sort of like an over-compressed image (only worse):