  The Kepler-11 planetary system contains six transiting planets ranging in
size from 1.8 to 4.2 times the radius of Earth. Five of these planets orbit in
a tightly-packed configuration with periods between 10 and 47 days. We perform
a dynamical analysis of the system based upon transit timing variations
observed in more than three years of \ik photometric data. Stellar parameters
are derived using a combination of spectral classification and constraints on
the star's density derived from transit profiles together with planetary
eccentricity vectors provided by our dynamical study. Combining masses of the
planets relative to the star from our dynamical study and radii of the planets
relative to the star from transit depths together with deduced stellar
properties yields measurements of the radii of all six planets, masses of the
five inner planets, and an upper bound to the mass of the outermost planet,
whose orbital period is 118 days. We find mass-radius combinations for all six
planets that imply that substantial fractions of their volumes are occupied by
constituents that are less dense than rock. The Kepler-11 system contains the
lowest mass exoplanets for which both mass and radius have been measured.

Earth and Planetary Astrophysics