Gravitational anomaly detection using a satellite constellation: Analysis and simulation

We investigate the utility of a constellation of four satellites in heliocentric orbit, equipped with accurate means to measure intersatellite ranges, round-trip times and phases of signals coherently retransmitted between members of the constellation. Our goal is to reconstruct the measured trace of the gravitational gradient tensor as accurately as possible. Intersatellite ranges alone are not sufficient for its determination, as they do not account for any rotation of the satellite constellation, which introduces fictitious forces and accelerations. However, measuring signal round-trip time differences among the satellites supplies the necessary observables to estimate, and subtract, the effects of rotation. Utilizing, in addition, the approximate distance and direction from the Sun, it is possible to approach an accuracy of $10^{-24}~{\rm s}^{-2}$ for a constellation with typical intersatellite distances of 1,000 km in an orbit with a 1 astronomical unit semi-major axis. This is deemed sufficient to detect the presence of a galileonic modification of the solar gravitational field.Comment: 24 pages, 5 figure