DYK-07 How good is Newtonian mechanics for planetary motion?

Every physical theory must pass the test of describing experimental data within the domain of its applicability. So we may ask, `` How good is Newtonian mechanics in describing planetary motion?'' It is well known that some data has remained unexplained. Here a small piece of text from one the references [1].

A collection is made of presently unexplained phenomena within our Solar system and in the universe. These phenomena are (i) the Pioneer anomaly, (ii) the flyby anomaly, (iii) the increase  of the Astronomical Unit, (iv) the quadrupole and octupole anomaly, and (v) Dark Energy and (vi) Dark Matter. A new data analysis of the complete set of Pioneer data is announced in order to search for systematic effects or to confirm the unexplained acceleration. We also review
the mysterious flyby anomaly where the velocities of spacecraft after Earth swing–bys are larger than expected. We emphasize the scientific aspects of this anomaly and propose systematic and continuous observations and studies at the occasion of future flybys. Further anomalies within the Solar system are the increase of the Astronomical Unit and the quadrupole and octupole anomaly. We briefly mention Dark Matter and Dark Energy since in some cases a relation
between them and the Solar system anomalies have been speculated.

References

1. C.Lammerzahl, O. Preuss and H. Dittus, `` Is physics within the solar system really understoood?''
   arXiv:gr-qc/0604052v1 (2006)
2. John D. Andersonet al., "Indication from Pioneer 10/11,Galileo, and Ulysses Data of an Apparent  Anomloous, Weak, Long-Range Acceleration`` arXiv:gr-qc/9808081v2 (1998)