The four longest period Kuiper Belt objects have orbital periods close to integer ratios with each other. A hypothetical planet with an orbital period of similar to 17,117 years and a semimajor axis similar to 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.
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