http://arxiv.org/abs/1603.02196
The four longest period Kuiper belt objects have orbital periods close to small 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.
R. Malhotra, K. Volk and X. Wang
Tue, 8 Mar 16
32/83
Comments: 16 pages, 5 figures