Extrasolar planets that pass in front of their host star (transit) cause a temporary decrease in the apparent brightness of the star once per orbit, providing a direct measure of the planet's size and orbital period. In some systems with multiple transiting planets, the times of the transits are measurably affected by the gravitational interactions between neighbouring planets 1,2 . In favorable cases, the departures from Keplerian orbits implied by the observed transit times permit planetary masses to be measured, which is key to determining bulk densities 3 . Characterizing rocky planets is particularly difficult, since they are generally smaller and less massive than gaseous planets. Thus, few exoplanets near Earth's size have had their masses measured. Here we report the sizes and masses of three planets orbiting Kepler-138, a star much fainter and cooler than the Sun. We measure the mass of the Mars-sized inner planet based on on the transit times of its neighbour and thereby provide the first density measurement for an exoplanet smaller than Earth. The middle and outer planets are both slightly larger than Earth. The middle planet's density is similar to that of Earth, while the outer planet is less than half as dense, implying that it contains a greater portion of low density components such as H 2 O and/or H 2 .NASA's Kepler mission has discovered thousands of candidate transiting exoplanets, with a wide range of planetary sizes 4,5,6 . A small fraction of these planets have had their masses characterized, by either radial velocity spectroscopy (RV) or via transit timing. The latter probes the gravitational perturbations between planets in multi-planet systems by precisely measuring transit times and fitting dynamical models to the observed transit timing variations (TTV) 1,2 . Both RV and TTV signals are larger for more massive planets, improve with greater planetary masses, although the two techniques sample different populations of exoplanets. The RV technique measures the motion of a host star induced by its planet's gravity, and hence the signal declines with increasing orbital distance. The majority of planets with mass determinations via RV from Kepler's dataset have orbital periods shorter than one week. For Kepler-discovered planets characterized as rocky by this method, the orbital periods are all less than one day. Of the RV detections, Kepler-78 b has the lowest mass, (1.7 M Earth ), and the shortest orbital period-0.35 days 7,8 . Characterizing planets by transit timing is quite complementary to RV because transit timing is very sensitive to perturbations between planets that are closely spaced or near orbital resonances 3,9 . Note that most systems with detected TTVs are not in resonance, but rather near enough to resonance for the perturbations to be coherent for many orbital periods, while also far enough from resonance that the planetary """""""""""""""""""""""""""""""""""""""""""""""""""""""" 1 "Department"of"Astronomy,"Pennsylvania"State"University,"Davey"Lab,"University"Park," PA"1680...