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At the second post-Newtonian (2PN) order, the secular pericentre precession$\dot\omega^\mathrm{2PN}$ of either a full two-body system made of welldetached non-rotating monopole masses of comparable size and a restrictedtwo-body system composed of a point particle orbiting a fixed central mass havebeen analytically computed so far with a variety of approaches. We offer ourcontribution by analytically computing $\dot\omega^\mathrm{2PN}$ in aperturbative way with the method of variation of elliptical elements byexplicitly calculating both the direct contribution due to the 2PN acceleration${\boldsymbol A}^\mathrm{2PN}$, and also an indirect part arising from theself-interaction of the 1PN acceleration ${\boldsymbol A}^\mathrm{1PN}$ in theorbital average accounting for the instantaneous shifts induced by${\boldsymbol A}^\mathrm{1PN}$ itself. Explicit formulas are straightforwardlyobtained for both the point particle and full two-body cases without recurringto simplifying assumptions on the eccentricity $e$. Two different numericalintegrations of the equations of motion confirm our analytical results for boththe direct and indirect precessions. The values of the resulting effects forMercury and some binary pulsars are confronted with the present-day level ofexperimental accuracies in measuring/constraining their pericentre precessions.The supermassive binary black hole in the BL Lac object OJ 287 is considered aswell. A comparison with some of the results appeared in the literature is made.

Revisiting the 2PN pericentre precession in view of possible future measurements of it