We use 16 quarters of the Kepler mission data to analyze the transit timing variations ( TTVs ) of the extrasolar planet Kepler-46b ( KOI-872 ) .
Our dynamical fits confirm that the TTVs of this planet ( period P = 33.648 ^ { +0.004 } _ { -0.005 } days ) are produced by a non-transiting planet Kepler-46c ( P = 57.325 ^ { +0.116 } _ { -0.098 } days ) .
The Bayesian inference tool MultiNest is used to infer the dynamical parameters of Kepler-46b and Kepler-46c .
We find that the two planets have nearly coplanar and circular orbits , with eccentricities \simeq 0.03 somewhat higher than previously estimated .
The masses of the two planets are found to be M _ { b } = 0.885 ^ { +0.374 } _ { -0.343 } and M _ { c } = 0.362 ^ { +0.016 } _ { -0.016 } Jupiter masses , with M _ { b } being determined here from TTVs for the first time .
Due to the precession of its orbital plane , Kepler-46c should start transiting its host star in a few decades from now .