If you mean that the "expected" trajectory is different than the "observed" one, it's not that we don't have examples where the simpler calculations result in d

If you mean that the "expected" trajectory is different than the "observed" one, it's not that we don't have examples where the simpler calculations result in difference from the observations, but then the newer, better calculations find these older simply insufficient. See the famous "Pioneer anomaly": https://en.wikipedia.org/wiki/Pioneer_anomaly https://en.wikipedia.org/wiki/Pioneer_anomaly "The anomalous acceleration was first noticed as early as 1980 but not seriously investigated until 1994." "Various explanations, both of spacecraft behavior and of gravitation itself, were proposed to explain the anomaly." "By 2012 several papers by different groups, all reanalyzing the thermal radiation pressure forces inherent in the spacecraft, showed that a careful accounting of this explains the entire anomaly; thus the cause is mundane and does not point to any new phenomenon or need for a different physical paradigm."