Revisiting the border between Newtonian mechanics and General Relativity: The periastron advance

The problem of periastron advance, which is the basis of one of the three classical tests of relativity theory, is revised with respect to both Newtonian mechanics and General Relativity and updated in the light of recent astronomical measurements of binary pulsars. We show that in Newtonian mechanics the addition of a corrective term to Newton’s law of gravitation, consistent with the principles of Newtonian mechanics, leads to the same formula of periastron advance as that used in General Relativity, which proves to be valid in all astronomical cases known, even in the cases of binary pulsars such as PSR B1913+16, PSR J1141-6545 and the so-called double pulsar PSR J0737-3039A and PSR J0737-3039B, which are considered as natural relativity laboratories. Thus, among the relativistic phenomena, the periastron advance is one that can be also understood in Newtonian terms by means of an ad hoc assumption. Keywords: periastron · perihelion · gravitation · pulsar · Newtonian mechanic