Constraints on planet X/Nemesis from Solar System’s inner dynamics

We use the corrections ∆$̇ to the standard Newtonian/Einsteinian perihelion precessions of the inner planets of the solar system, recently estimated by E.V. Pitjeva by fitting a huge planetary data set with the dynamical models of the EPM ephemerides, to put constraints on the position of a putative, yet undiscovered large body X of mass MX, not modelled in the EPM software. The direct action of X on the inner planets can be approximated by a Hooke-type radial acceleration plus a term of comparable magnitude having a fixed direction in space pointing towards X. The perihelion precessions induced by them can be analytically worked out only for some particular positions of X in the sky; in general, numerical calculations are used. We show that the indirect effects of X on the inner planets through its action on the outer ones can be neglected, given the present-day level of accuracy in knowing ∆$̇. As a result, we find that Mars yields the tightest constraints, with the tidal parameter KX = GMX/r X ≤ 3× 10−24 s−2. To constrain rX we consider the case of a rockice planet with the mass of Mars and the Earth, a giant planet with the mass of Jupiter, a brown dwarf with MX = 80mJupiter, a red dwarf with M = 0.5M and a Sun-mass body. For each of them we plot r 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 no less than 70− 85 AU: such bounds are 147− 175 AU, 1, 006− 1, 200 AU, 4, 334 − 5, 170 AU, 8, 113 − 9, 524 AU, 10, 222 − 12, 000 AU for a body with a mass equal to that of the Earth, Jupiter, a brown dwarf, red dwarf and the Sun, respectively. Subject headings: Solar system objects; Low luminosity stars, subdwarfs, and brown dwarfs; Kuiper belt, trans-Neptunian objects; Oort cloud; Celestial mechanics