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The four longest period Kuiper belt objects have orbital periods close tointeger 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 periodratios with these four objects. The orbital geometries and dynamics of resonantorbits constrain the orbital plane, the orbital eccentricity and the mass ofsuch a planet, as well as its current location in its orbital path.

Corralling a distant planet with extreme resonant Kuiper belt objects