We report the discovery of one newly confirmed planet ( P = 66.06 days , R _ { P } = 2.68 \pm 0.17 R _ { \oplus } ) and mass determinations of two previously validated Kepler planets , Kepler-289 b ( P = 34.55 days , R _ { P } = 2.15 \pm 0.10 R _ { \oplus } ) and Kepler-289-c ( P = 125.85 days , R _ { P } = 11.59 \pm 0.10 R _ { \oplus } ) , through their transit timing variations ( TTVs ) .
We also exclude the possibility that these three planets reside in a 1 : 2 : 4 Laplace resonance .
The outer planet has very deep ( \sim 1.3 \% ) , high signal-to-noise transits , which puts extremely tight constraints on its host star ’ s stellar properties via Kepler ’ s Third Law .
The star PH3 is a young ( \sim 1 Gyr as determined by isochrones and gyrochronology ) , Sun-like star with M _ { * } = 1.08 \pm 0.02 M _ { \odot } , R _ { * } = 1.00 \pm 0.02 R _ { \odot } , and T _ { eff } = 5990 \pm 38 K. The middle planet ’ s large TTV amplitude ( \sim 5 hours ) resulted either in non-detections or inaccurate detections in previous searches .
A strong chopping signal , a shorter period sinusoid in the TTVs , allows us to break the mass-eccentricity degeneracy and uniquely determine the masses of the inner , middle , and outer planets to be M = 7.3 \pm 6.8 M _ { \oplus } , 4.0 \pm 0.9 M _ { \oplus } , and M = 132 \pm 17 M _ { \oplus } , which we designate PH3 b , c , and d , respectively .
Furthermore , the middle planet , PH3 c , has a relatively low density , \rho = 1.2 \pm 0.3 g/cm ^ { 3 } for a planet of its mass , requiring a substantial H/He atmosphere of 2.1 ^ { +0.8 } _ { -0.3 } \% by mass , and joins a growing population of low-mass , low-density planets .