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Model-independent constraints on r^-3 extra-interactions from orbital motions

Long-range constraints on the AdS radius of curvature L in the Randall-Sundrum (RS) braneworld model are inferred from orbital motions of well known artificial and natural bodies. Thus, they do not rely upon more or less speculative and untested theoretical assumptions, contrary to other long-range RS tests proposed in astrophysical scenarios in which many of the phenomena adopted may depend on the system's composition, formation and dynamical history as well. The perihelion precession of Mercury and its radiotechnical ranging from the Earth yield L <= 10 - 50 km. Tighter bounds come from the perigee precession of the Moon, from which it can be inferred L <= 500-700 m. The best constraints (L <= 5 m) come from the Satellite-to-Satellite Tracking (SST) range of the GRACE A/B spacecrafts orbiting the Earth: proposed follow-on of such a mission, implying a subnm s-1 range-rate accuracy, may constrain L at \sim 10 cm level. Weaker constraints come from the double pulsar system (L <= 80 - 100 km) and from the main sequence star S2 orbiting the compact object in Sgr A* (L <= 6.2 - 8.8 AU). Such bounds on the length L, which must not necessarily be identified with the AdS radius of curvature of the RS model, naturally translate into constraints on an, e.g., universal coupling parameter K of the r^-3 interaction. GRACE yields K <= 1 10^16 m^5 s^-2.