In April 2012, scientists discovered that a Kepler candidate known as KOI-142.01 (Kepler-88b) exhibited very significant transit-timing variations caused by a non-transiting planet.[4] The timing variations were large enough to cause changes to the transit durations of Kepler-88b as well. Large transit-timing variations helped to put tight constraints on the masses of both planets. The non-transiting planet, Kepler-88c, was further confirmed through the radial velocity method in November 2013.[3]
Kepler-88b is the innermost planet in the system and is Neptune-sized but almost half as massive. Kepler 88c is about 67% as massive as Jupiter, but its radius is not known due to not transiting the star.[5]
Kepler-88d orbits its star every four years, and its orbit is not circular, but elliptical. At three times the mass of Jupiter, it is the most massive planet known in the system. It was discovered based on six years of radial velocity (RV) follow-up from the W. M. Keck Observatory HIRES spectrograph.[5]