Searching for new physics in the solar system with tetrahedral spacecraft formations

Abstract: Tetrahedral configurations of spacecraft on unperturbed heliocentric orbits allow for highly precise observations of small spatial changes in the gravitational field, especially those affecting the gravity gradient tensor (GGT). The resulting high sensitivity may be used to search for new physics that could manifest itself via deviations from general relativistic behavior yielding a non-vanishing trace[GGT]. We study the feasibility of recovering the trace[GGT] with the sensitivity of O(1e-24 s^-2) -- the level where some of the recently proposed cosmological models may have observable effects in the solar system. We consider how local measurements provided by precision laser ranging and atom-wave interferometry can be used for that purpose. We report on a preliminary study of such an experiment and precision that may be reached in measuring the trace[GGT], with the assumption of drag-compensated spacecraft by atom interferometer measurements. For that, we study the dynamical behavior of a tetrahedral formation established by four spacecraft on heliocentric nearby elliptical orbits. We formulate the observational equations to measure the trace[GGT] relying only on the observables available within the formation: laser ranging and the Sagnac interferometry. We demonstrate that Sagnac observable is a mission enabling and allows to measure the angular frequency of the tetrahedral rotation with respect to an inertial reference frame with an accuracy much higher than that available from any other modern navigational techniques. We show that the quality of the science measurements is affected by the changes in tetrahedron's orientation and shape as spacecraft follow their orbits. We present the preliminary mission and instrument requirements needed to measure the trace[GGT] to the required accuracy and demonstrate the feasibility of satisfying the science objectives.