Constraints on Planet X and Nemesis from Solar System’s inner dynamics

The gravitational acceleration imparted on a solar system’s rocky planet by a putative large body X like a planet or a star located at hundreds/thousands AU from the Sun can be considered as a small Hooke-type perturbation AX = Kr over the characteristic temporal and spatial scales of the inner planetary regions (Pb . 1 yr, r . 1.5 AU). We computed the variation of the longitude of the perihelion ̟ averaged over one orbital revolution due to AX by finding a secular precession proportional to MX/r 3 X. We compared such predicted effects with the corrections ∆ ̟̇ to the standard Newtonian/Einsteinian perihelion precessions of Mercury, Venus, Earth and Mars recently estimated by E.V. Pitjeva by fitting almost one century of observations with the dynamical force models of the EPM ephemerides which did not include the force imparted by the aforementioned body. As a result, the data from Mars yield the tightest dynamical constraints on the minimum distances at which putative bodies with the mass of Mars, Earth, Jupiter and the Sun can be located; they are 62 AU, 130 AU, 886 AU, 8, 995 AU, respectively. A brown dwarf with m ≈ 75− 80 mJup cannot orbit at a distance smaller than 3, 736− 3, 817 AU from the Sun, while the minimum distance for a red dwarf (0.075 M⊙ ≤ m ≤ 0.5 M⊙) ranges from 3, 793 AU to 7, 139 AU. Such dynamical, model-independent constraints are tighter than those obtainable from the upper bound on the solar system barycenter’s acceleration recently derived from pulsar timing data. Subject headings: Solar system objects; Low luminosity stars, subdwarfs, and brown dwarfs; Kuiper belt, trans-Neptunian objects; Oort cloud; Celestial mechanics