Newton, Einstein and the Advance of Planets’ Orbits

The recent result in C. Corda, Phys. Dark Un. 32,100834 (2021) is re-analyzed. It is indeed shown that, contrary to a longstanding conviction older than 160 years, the advance of Mercury’s orbit can be achieved in Newtonian gravity with a very high precision by correctly analysing the situation without neglecting Mercury’s mass. General relativity remains more precise than Newtonian physics, but Newtonian framework appears to be more consistent than researchers and astronomers were thinking till now, at least for the case of Mercury. This remarkable result depends on the fact that in Newtonian physics the distance travelled by a body changes with the frame of reference that is used in the analysis, while time intervals are absolute for all the observers. The Newtonian formula of the precession of planets’ orbits breaks down for the other planets. In fact, the predicted Newtonian result becomes too large for Venus and Earth. Hence, it is also shown that corrections depending on gravitational and rotational time dilation, in an intermediate framework which analyzes gravity between Newton and Einstein, can solve the problem. Such corrections permit indeed to obtain a result consistent with the one of general relativity. Summarizing, the most important results re-obtained in this paper are two: (i) It is not correct that Newtonian theory cannot predict the anomalous rate of advance of planets’ orbit. The real problem is instead that a pure Newtonian prediction is too large. (ii) The advance of planets’ orbit can be achieved with the same precision of general relativity if one extends Newtonian gravity via the inclusion of gravitational and rotational time dilation effects. This second result is consistent with a couple of recent and interesting papers of Hansen, Hartong and Obers. Differently from such papers, the importance of rotational time dilation is also highlighted in the present work.