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

The gravitational acceleration imparted on the solar system’s rocky planets by a putative large body like a planet or a star located at hundreds/thousands AU from the Sun can be considered as a small constant and uniform perturbation A 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 A by finding a long-period harmonic signal which can be approximated by a secular precession over the typical timescales of the inner planets. We compared such predicted effects with the corrections ∆ ̟̇ to the standard Newtonian/Einsteinian perihelion precessions of 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. We obtained Ax = (−0.3± 1)× 10 m s, Ay = (2± 5)× 10 m s and Az = (−0.6 ± 3) × 10 m s for the Cartesian components of the perturbing acceleration, so that A = (0.6± 3)× 10 m s. Such a constrain is three orders of magnitude better than that recently obtained from the analysis of the timing data concerning the time derivative of the periods of a set of pulsars. As a result, the minimum distances at which putative bodies with the mass of the Earth, Mars, Jupiter and the Sun can be located are 250 AU, 750 AU, 13.5 kAU = 0.21 ly, 500 kAU = 7.9 ly, respectively. A brown dwarf with m ≈ 75−80 mJup cannot orbit at a distance smaller than about 1.8 − 1.9 ly from the Sun, while the minimum distance for a red dwarf (0.075 M⊙ ≤ m ≤ 0.5 M⊙) ranges from 2.1 ly to 5.6 ly. Subject headings: Solar system objects; Low luminosity stars, subdwarfs, and brown dwarfs; Kuiper belt, trans-Neptunian objects; Oort cloud; Celestial mechanics