Corralling a distant planet with extreme resonant Kuiper belt objects

Abstract

The four longest period Kuiper belt objects have orbital periods close to integer ratios with each other. A hypothetical planet with orbital period $\sim$17,117 years, semimajor axis $\sim$665 AU, would have N/1 and N/2 period ratios with these four objects. The orbital geometries and dynamics of resonant orbits constrain the orbital plane, the orbital eccentricity and the mass of such a planet, as well as its current location in its orbital path.

Shortened version with a few changes in response to peer review, in press at ApJL. Corrected minor errors, Fig 4 is now higher resolution, Fig 5 is now in RA/Dec

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