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

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 of the GGT. We study the feasibility of recovering the trace[GTT] with the sensitivity of ${\cal O}(10^{-24}~{\rm s}^{-2})$ -- the level where some of the recently proposed cosmological models may have observable effects in the solar system. Specifically, we consider how a set of local measurements provided by precision laser ranging (to measure the inter-satellite ranges) and atom-wave interferometry (to correct for any local non-gravitational disturbances) can be used for that purpose. We report on a preliminary study of such an experiment and on the 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 placed on nearby elliptical orbits around the Sun. We develop analytical models for the relevant observables and study the conditions for setting up an optimal tetrahedral configuration. We formulate the observational equations to measure the trace[GTT] relying only on the observables that are available within the formation, such as those based on the laser ranging and the Sagnac interferometry. We demonstrate that Sagnac observable is a mission enabling capability that allows to measure the angular frequency of the tetrahedral rotation with respect to an inertial reference frame with an accuracy that is much higher than that available from any other modern navigational techniques. We show that the quality of the science measurements is affected by the tetrahedron evolution, as its orientation and the shape change while the spacecraft follow their orbits. We present the preliminary mission and instrument requirements needed to measure the trace[GTT] to the required accuracy and thus demonstrate the feasibility of satisfying the stated science objective.