2009MNRAS.400..346I

We use the corrections to the standard Newtonian/Einsteinian perihelion precessions of the inner planets of the Solar system, recently estimated by E.V. Pitjeva by fitting a huge planetary data set with the dynamical models of the EPM ephemerides, to put constraints on the position of a putative, yet undiscovered large body X of mass M_X, not modelled in the EPM software. The direct action of X on the inner planets can be approximated by a elastic Hooke-type radial acceleration plus a term of comparable magnitude having a fixed direction in space pointing towards X. The perihelion precessions induced by them can be analytically worked out only for some particular positions of X in the sky; in general, numerical calculations are used. We show that the indirect effects of X on the inner planets through its action on the outer ones can be neglected, given the present-day level of accuracy in knowing . As a result, we find that Mars yields the tightest constraints, with the tidal parameter. To constrain r_X we consider the case of a rock-ice planet with the mass of Mars and the Earth, a giant planet with the mass of Jupiter, a brown dwarf with M_X= 80m_Jupiter, a red dwarf with M = 0.5M_☉ and a Sun-mass body. For each of them we plot r^min_X as a function of the heliocentric latitude β and longitude λ. We also determine the forbidden spatial region for X by plotting its boundary surface in the three-dimensional space; it shows significant departures from spherical symmetry. A Mars-sized body can be found at not less than 70-85 au: such bounds are 147-175 au, 1006-1200 au, 4334-5170 au, 8113-9524 au and 10222-12000 au for a body with a mass equal to that of the Earth, Jupiter, a brown dwarf, red dwarf and the Sun, respectively.