Mass derivation of planets K2-21b and K2-21c from transit timing variations

While various indirect methods are used to detect exoplanets, one of the most effective and accurate is transit method, which measures brightness a given star for periodic dips when an exoplanet passing in front parent star. For systems with multiple transiting planets, gravitational perturbations between planets affect their times. The difference times allows measurement planet masses orbital eccentricities. These parameters help speculating on formation, evolution stability system. Using Transit Timing Variations (TTVs), we measure eccentricities two orbiting K2-21, relatively bright K7 dwarf exhibit measurable TTVs, have periods about 9.32 days 15.50 days, respectively, period ratio 1.66, near 5:3 mean motion resonance. We report that inner outer K2-21 system properties consistent presence hydrogen helium dominated atmospheres, as estimate be 1.59^{+0.52}_{-0.44} M_E 3.88^{+1.22}_{-1.07} densities 0.22^{+0.05}_{-0.04} rho_E 0.34^{+0.08}_{-0.06} rho_E, respectively (M_E mass density Earth, respectively). Our results show less dense than planet; more counter-intuitive exoplanetary such Kepler-105, LTT 1445, TOI-175 Kepler-279 systems.