Earth-moon Lagrangian points as a test bed for general relativity and effective field theories of gravity

We first analyze the restricted four-body problem consisting of the Earth, the Moon, and the Sun as the primaries and a spacecraft as the planetoid. This scheme allows us to take into account the solar perturbation in the description of the motion of a spacecraft in the vicinity of the stable Earth-Moon libration points L4 and L5 both in the classical regime and in the context of effective field theories of gravity. We also evaluate the impulse required to cancel out the perturbing force due to the Sun in order to force the spacecraft to stay precisely at L4 or L5. Performing such an experiment requires controlling the propulsion to precisely reach L1, using an instrumental accuracy comparable to the measurement of the lunar geodesic precession, and understanding systematic effects resulting from thermal radiation and multi-body gravitational perturbations. This will then be the basis to consider a second-generation experiment to study deviations of effective field theories of gravity from general relativity in the Sun-Earth-Moon system.