The detection and characterization of a nontransiting planet by transit timing variations

The Kepler mission is monitoring the brightness of ∼150,000 stars, searching for evidence of planetary transits. As part of the Hunt for Exomoons with Kepler (HEK) project, we report a planetary system with two confirmed planets and one candidate planet discovered with the publicly available data for KOI-872. Planet b transits the host star with a period P_b = 33.6 days and exhibits large transit timing variations indicative of a perturber. Dynamical modeling uniquely detects an outer nontransiting planet c near the 5:3 resonance (P_c = 57.0 days) with a mass 0.37 times that of Jupiter. Transits of a third planetary candidate are also found: a 1.7-Earth radius super-Earth with a 6.8-day period. Our analysis indicates a system with nearly coplanar and circular orbits, reminiscent of the orderly arrangement within the solar system.