After updating the observational bias calculations, we find that the cluster remains significant at the 99.6 \% confidence level. So we use these observations to determine the orbital elements of P9.

A set of numerical simulations shows that the orbital distribution of distant KBOs is strongly influenced by the mass and orbital elements of P9 and therefore can be used to infer these parameters.

Combining the biases with these numerical simulations, we calculate the likelihood values for a discrete set of P9 parameters, which we then use as input to a Gaussian Process emulator that allows a probability calculation for arbitrary values of all parameters.

We use this emulator in a Markov Chain Monte Carlo analysis to estimate the parameters of P9. We find a mass P9 of Earth masses, semi-major axis of 380 ^ {+ 140} _ {- 80} AU, slope of 16 \ pm5 ^ \ circ, and perihelion of 300 ^ {+ 85} _ {- 60} AU. Using samples of the orbital elements and estimates of the radius and albedo of such a planet, we calculate the probability distribution function of Planet Nine's position in the sky and its brightness.

For many reasonable assumptions, Planet Nine is closer and brighter than initially expected, although the probability distribution includes a long tail for greater distances, and uncertainties in Planet Nine's radius and albedo can result in weaker objects. 6.2+ 2.2- 1.3380+ 140- 8016 ±5∘300+ 85-60.

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