We analytically work out the long-term variations caused on the motion of a planet orbiting a star by a distant, pointlike massive object X. Apart from the semimajor axis a, all the other Keplerian orbital elements of the perturbed planet experience long-term variations which are complicated functions of the orbital configurations of both the planet itself and of X. We infer constraints on the minimum distance d_X at which the putative body X can exist by comparing, first, our prediction of the long-term variation of the longitude of the perihelion \varpi to the latest empirical determinations of the corrections \Delta\dot\varpi to the standard Newtonian/Einsteinian secular precessions of several planets of the solar system recently obtained. Independent teams of astronomers estimated them by fitting accurate dynamical force models$-$not including the action of X itself$-$to observational data records covering almost one century. Then, we numerically compute the perturbations induced by X on the range \rho, the right ascension \alpha and the declination \delta of Saturn. We compare them with the latest residuals produced by analyzing records of radiotechnical data from the Cassini spacecraft spanning some years. Tighter constraints on d_X are, thus, obtained. The combined use of all the methods adopted yield the following lower bounds on d_X for the assumed masses of X quoted in brackets: 141-281 au (Mars), 300-600 au (Earth), 771-1542 au (Neptune), 2037-4074 au (Jupiter), 8784-17568 au (brown dwarf with m_X = 80 m_Jup), 16434-32868 au (red dwarf with m_X = 0.5 M_Sun), 20709-41418 au (Sun). Alternative strategies which could be followed are pointed out. Constraints on the adimensional parameter -q of the External Field Effect within the MOdified Newtonian Dynamics are obtained from the range residuals of Saturn: it turns out -q\approx 0.01-0.04 (at 1/3-\sigma level of rejection).