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

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, J2⊙\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} = (2.246 ± 0.022) × 10−7. Finally, we obtain an estimate of the time variation of the Sun gravitational parameter, GM⊙°∕GM⊙\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} = (−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 G°∕G\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} to be <4 × 10−14 per year.