Might the 2PN Perihelion Precession of Mercury Become Measurable in the Next Future?

Abstract

The Hermean average perihelion rate (Formula presented.), calculated to the second post-Newtonian (2PN) order with the Gauss perturbing equations and the osculating Keplerian orbital elements, ranges from (Formula presented.) to (Formula presented.) microarcseconds per century (Formula presented.), depending on the true anomaly at epoch (Formula presented.). It is the sum of four contributions: one of them is the direct consequence of the 2PN acceleration entering the equations of motion, while the other three are indirect effects of the 1PN component of the Sun’s gravitational field. An evaluation of the merely formal uncertainty of the experimental Mercury’s perihelion rate (Formula presented.) recently published by the present author, based on 51 years of radiotechnical data processed with the EPM2017 planetary ephemerides by the astronomers E.V. Pitjeva and N.P. Pitjev, is (Formula presented.), corresponding to a relative accuracy of (Formula presented.) for the combination (Formula presented.) of the PPN parameters (Formula presented.) and (Formula presented.) scaling the well known 1PN perihelion precession. In fact, the realistic uncertainty may be up to ≃10–50 times larger, despite reprocessing the now available raw data of the former MESSENGER mission with a recently improved solar corona model should ameliorate our knowledge of the Hermean orbit. The BepiColombo spacecraft, currently en route to Mercury, might reach a (Formula presented.) accuracy level in constraining (Formula presented.) and (Formula presented.) in an extended mission, despite (Formula presented.) seems more likely according to most of the simulations currently available in the literature. Thus, it might be that in the not-too-distant future, it will be necessary to include the 2PN acceleration in the Solar System’s dynamics as well.