The relativistic precession of Mercury -43.1 seconds of arc per century, is the result of a secular addition of 5.02×10-7 rad. at the end of every orbit around the Sun. The question that arises in this paper, is to analyse the angular precession at each single point of the elliptic orbit and determine its magnitude and oscillation around the mean value, comparing key theoretical proposals. Underline also that, this astronomical determination has not been yet achieved, so it is considered that Messenger spacecraft, now orbiting the planet or the future mission BepiColombo, should provide an opportunity to perform it. That event will clarify some significant issues, now that we are close to reach the centenary of the formulation and first success of General Relativity.