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Published November 2021 | Submitted + Published
Journal Article Open

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 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 Gaussian-process 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^(+2.2)_(-1.3) Earth masses, semimajor axis of 380^(+140)_(-80) au, inclination of 16 ± 5° 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 the on-sky 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.

Additional Information

© 2021. The American Astronomical Society. Received 2021 May 4; revised 2021 August 19; accepted 2021 August 22; published 2021 October 28. This manuscript owes a substantial debt to the participants at the MATH + X Symposium on Inverse Problems and Deep Learning in Space Exploration held at Rice University in 2019 January with whom we discussed the issue of inverting the observations of KBOs to solve for Planet Nine. We would also like to thank two anonymous reviewers of a previous paper whose excellent suggestions ended up being incorporated into this paper and @Snippy_X 2 and @siwelwerd 3 on Twitter for advice on notation for our likelihood functions. Software: HEALPix (Gorski et al. 2005), astropy (Astropy Collaboration et al. 2013), scikit-learn (Pedregosa et al. 2011), emcee (Foreman-Mackey et al. 2013), corner (Foreman-Mackey 2016).

Attached Files

Published - Brown_2021_AJ_162_219.pdf

Submitted - 2108.09868.pdf


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