Constraints on long-range power-law modifications Upert ∝ r-3 of the usual Newtonian gravitational potential UN ∝ r-1 are inferred from orbital motions of well known artificial and natural bodies. They can be interpreted in terms of a characteristic length ℓ which may be identified with, e.g., the anti-de Sitter (AdS) radius of curvature ℓ in the Randall-Sundrum (RS) braneworld model, although this not a mandatory choice. Our bounds, complementary to those from tabletop laboratory experiments, 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. Independently of the interpretation of ℓ, 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 sub-nm s-1 range-rate accuracy, may constrain ℓ at ∼ 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 of the extra r-3 interaction. GRACE yields ≤ 1 × 1016 m5 s-2.