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