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The Orbit and Mass of the Third Planet in the Kepler-56 System

While the vast majority of multiple-planet systems have their orbital angular momentum axes aligned with the spin axis of their host star, Kepler-56 is an exception: its two transiting planets are coplanar yet misaligned by at least 40 degrees with respect to their host star. Additional follow-up observations of Kepler-56 suggest the presence of a massive, non-transiting companion that may help explain this misalignment. We model the transit data along with Keck/HIRES and HARPS-N radial velocity data to update the masses of the two transiting planets and infer the physical properties of the third, non-transiting planet. We employ a Markov Chain Monte Carlo sampler to calculate the best-fitting orbital parameters and their uncertainties for each planet. We find the outer planet has a period of 1002 $\pm$ 5 days and minimum mass of 5.61 $\pm$ 0.38 Jupiter masses. We also place a 95% upper limit of 0.80 m/s/yr on long-term trends caused by additional, more distant companions.