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The NASA MESSENGER mission explored the innermost planet of the solar system and obtained a rich data set of range measurements for the determination of Mercury’s ephemeris. Here we use these precise data collected over 7 years to estimate parameters related to general relativity and the evolution of the Sun. These results confirm the validity of the strong equivalence principle with a significantly refined uncertainty of the Nordtvedt parameter  η  = (−6.6 ± 7.2) × 10 −5 . By assuming a metric theory of gravitation, we retrieved the post-Newtonian parameter  β  = 1 + (−1.6 ± 1.8) × 10 −5  and the Sun’s gravitational oblateness,    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${{J}}_{2 \odot }$$\end{document}J    2  ⊙ = (2.246 ± 0.022) × 10 −7 . Finally, we obtain an estimate of the time variation of the Sun gravitational parameter,    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$\dot{{G} {{M}}_ \odot} {\mathrm{/}}{{G}}{{M}}_ \odot$$\end{document}G    M    ⊙°   ∕  G    M    ⊙ = (−6.13 ± 1.47) × 10 −14 , which is consistent with the expected solar mass loss due to the solar wind and interior processes. This measurement allows us to constrain    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$\left| {{\dot{ G}}} \right|{\mathrm{/}}{{G}}$$\end{document}G   °∕  Gto be <4 × 10 −14  per year.

Solar system expansion and strong equivalence principle as seen by the NASA MESSENGER mission