Michael E. Brown Konstantin Batygin Division （迈克尔·e·布朗康斯坦丁Batygin部门）.pdfVIP

, A Preprint typeset using L T X style emulateapj v. 08/13/06 E OBSERVATIONAL CONSTRAINTS ON THE ORBIT AND LOCATION OF PLANET NINE IN THE OUTER SOLAR SYSTEM Michael E. Brown Konstantin Batygin Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125 Draft version March 17, 2016 ABSTRACT We use an extensive suite of numerical simulations to constrain the mass and orbit of Planet Nine, the recently proposed perturber in a distant eccentric orbit in the outer solar system. We compare our simulations to the observed population of aligned eccentric high semimajor axis Kuiper belt objects and determine which simulation parameters are statistically compatible with the observations. We find that only a narrow range of orbital elements can reproduce the observations. In particular, the combination of semimajor axis, eccentricity, and mass of Planet Nine strongly dictates the semimajor axis range of the orbital confinement of the distant eccentric Kuiper belt objects. Allowed orbits, which confine Kuiper belt objects with semimajor axis beyond 230 AU, have perihelia roughly between 200 and 350 AU, semimajor axes between 300 and 900 AU, and masses of approximately 10 Earth masses. Orbitally confined objects also generally have orbital planes similar to that of the planet, suggesting that the planet is inclined approximately 30 degrees to the ecliptic. We compare the allowed orbital positions and