The Orbit of Planet Nine
Abstract
The existence of a giant planet beyond Neptunereferred to as Planet Nine (P9)has been inferred from the clustering of longitude of perihelion and pole position of distant eccentric Kuiper belt objects (KBOs). After updating calculations of observational biases, we find that the clustering remains significant at the 99.6% confidence level. We thus use these observations to determine orbital elements of P9. A suite of numerical simulations shows that the orbital distribution of the distant KBOs is strongly influenced by the mass and orbital elements of P9 and thus can be used to infer these parameters. Combining the biases with these numerical simulations, we calculate likelihood values for discrete set of P9 parameters, which we then use as input into a Gaussianprocess emulator that allows a likelihood computation for arbitrary values of all parameters. We use this emulator in a Markov chain Monte Carlo analysis to estimate parameters of P9. We find a P9 mass of ${6.2}_{1.3}^{+2.2}$ Earth masses, semimajor axis of ${380}_{80}^{+140}$ au, inclination of 16 ± 5° and perihelion of ${300}_{60}^{+85}$ au. Using samples of the orbital elements and estimates of the radius and albedo of such a planet, we calculate the probabilitydistribution function of the onsky position of Planet Nine and of its brightness. For many reasonable assumptions, Planet Nine is closer and brighter than initially expected, though the probability distribution includes a long tail to larger distances, and uncertainties in the radius and albedo of Planet Nine could yield fainter objects.
 Publication:

The Astronomical Journal
 Pub Date:
 November 2021
 DOI:
 10.3847/15383881/ac2056
 arXiv:
 arXiv:2108.09868
 Bibcode:
 2021AJ....162..219B
 Keywords:

 Planetary dynamics;
 Solar system planets;
 Orbit determination;
 2173;
 1260;
 1175;
 Astrophysics  Earth and Planetary Astrophysics
 EPrint:
 AJ, in press. Previous version had outdated version of Figure 9 affecting the predicted magnitudes. New Figure 9 and fixed typos