In what situations do Newton's law of universal gravity fail to predict correctly how matter moves? The examples I know of are frame dragging (around rotating BH), shifting of light paths, shifting orbits of planets. But does Newton's law really predict the magnitude of gravity accuratly? How does the predicted Newtonian value compare to the predicted relativistic value in different situations? Also, given the symmetry between the electromagnetic and gravitomagnetic forces, how come there isn't a spacetime-equivalent theory for electromagnetism? Am I wrong in my assuption of said symmetry? I hope to get some answeres on my questions. Any help/feedback is appreciated.