Calculation of the Uncertainties in the Planetary Precessions with the Recent EPM2017 Ephemerides and their Use in Fundamental Physics and Beyond

I tentatively compile the formal uncertainties in the secular rates of change of the orbital elements $a,~e,~I,~\Omega$ and $\varpi$ of the planets of the solar system from the recently released formal errors in $a$ and the nonsingular elements $h,~k,~p$ and $q$ estimated for the same bodies with the EPM2017 ephemerides by E.\,V. Pitjeva and N.\,P. Pitjev. The highest accuracies occur for the inner planets and Saturn in view of the extensive use of radiotechnical data collected over the last decades. For the inclination $I$, node $\Omega$ and perihelion $\varpi$ of Mercury and Mars, I obtain accuracies $\sigma_{\dot I},\,\sigma_{\dot\Omega},\,\sigma_{\dot \varpi}\simeq 1-10\,\mu\textrm{as~cty}^{-1}$, while for Saturn they are $\sigma_{\dot I},\,\sigma_{\dot\Omega},\,\sigma_{\dot \varpi}\simeq 10\,\mu\textrm{as~cty}^{-1}-1\,\textrm{mas~cty}^{-1}$. As far as the semimajor axis $a$ is concerned, its rates for the inner planets are accurate to the $\sigma_{\dot a}\simeq 1-100\,\textrm{mm~cty}^{-1}$ level, while for Saturn I obtain $\sigma_{\dot a}\simeq 17\,\textrm{m~cty}^{-1}$. In terms of the parameterized post-Newtonian (PPN) parameters $\beta$ and $\gamma$, a formal error as little as $8\,\mu\textrm{as~cty}^{-1}$ for the Hermean apsidal rate corresponds to a $\simeq 2\times 10^{-7}$ bias in the combination $\left(2 + 2\gamma- \beta\right)/3$ parameterizing the Schwarzschild-type periehlion precession of Mercury. The realistic uncertainties of the planetary precessions may be up to one order of magnitude larger. I discuss their potential multiple uses in fundamental physics, astronomy, and planetology.