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The validity of General Relativity, after 100 years, is supported by solidexperimental evidence. However, there is a lot of interest in pushing thelimits of precision by other experiments. Here we focus our attention on theequivalence principle, in particular the strong form. The results of groundexperiments and lunar laser ranging have provided the best upper limit on theNordtvedt parameter {\eta} that models deviations from the strong equivalenceprinciple. Its uncertainty is currently {\sigma}[{\eta}] =4.4 $\times$$10^{-4}$. In the first part of this paper we will describe the experiment, tomeasure {\eta}, that will be done by the future mission BepiColombo. Theexpected precision on {\eta} is $\approx$ $10^{-5}$. In the second part we willconsider the ranging between the Earth and a spacecraft orbiting near theSun-Earth Lagrangian points to get an independent measurement of {\eta}. Inthis case, we forecast a constraint similar to that achieved by lunar laserranging.

Space tests of the strong equivalence principle: BepiColombo and the Sun-Earth Lagrangian points opportunity