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The successful miniaturisation of extremely accurate atomic clocks and atominterferometers invites prospects for satellite missions to perform precisionexperiments. We discuss the effects predicted by general relativity andalternative theories of gravity that can be detected by a clock, which orbitsthe Earth. Our experiment relies on the precise tracking of the spacecraftusing its observed tick-rate. The spacecraft's reconstructed four-dimensionaltrajectory will reveal the nature of gravitational perturbations in Earth'sgravitational field, potentially differentiating between different theories ofgravity. This mission can measure multiple relativistic effects all during thecourse of a single experiment, and constrain the Parametrized Post-NewtonianParameters around the Earth. A satellite carrying a clock of fractional timinginaccuracy of $\Delta f/f \sim 10^{-16}$ in an elliptic orbit around the Earthwould constrain the PPN parameters $|\beta -1|, |\gamma-1| \lesssim 10^{-6}$.We also briefly review potential constraints by atom interferometers on scalartensor theories and in particular on Chameleon and dilaton models.

Testing General Relativity and Alternative Theories of Gravity with Space-based Atomic Clocks and Atom Interferometers