The Orbit of Planet Nine

The existence of a giant planet beyond Neptune -- referred to as Planet Nine (P9) has been inferred from the clustering longitude perihelion and pole position distant eccentric Kuiper belt objects (KBOs). After updating calculations observational biases, we find that remains significant at 99.6\% confidence level. We thus use these observations determine orbital elements P9. A suite numerical simulations shows distribution KBOs is strongly influenced by mass P9 can be used infer parameters. Combining biases with simulations, calculate likelihood values for discrete set parameters, which then input into Gaussian Process emulator allows computation arbitrary all this in Markov Chain Monte Carlo analysis estimate parameters $6.2^{+2.2}_{-1.3}$ Earth masses, semimajor axis $380^{+140}_{-80}$ AU, inclination $16\pm5^\circ$ $300^{+85}_{-60}$ AU. Using samples estimates radius albedo such planet, probability function on-sky its brightness. For many reasonable assumptions, closer brighter than initially expected, though includes long tail larger distances, uncertainties could yield fainter objects.