While the vast majority of multiple-planet systems have orbital angular momentum axes that align 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 the rotation axis of 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 M _ { \textrm { Jup } } .
We also place a 95 % upper limit of 0.80 m s ^ { -1 } yr ^ { -1 } on long-term trends caused by additional , more distant companions .