Three planets with minimum masses less than 10 $\mearth$ orbit the star HD
40307, suggesting these planets may be rocky. However, with only radial
velocity data, it is impossible to determine if these planets are rocky or
gaseous. Here we exploit various dynamical features of the system in order
to assess the physical properties of the planets.  Observations allow for
circular orbits, but an N-body model shows that the eccentricities must be
at least $10^{-4}$. Planets b and c are so close to the star that tidal
effects are significant. If planet b has tidal parameters similar to the
terrestrial planets in the Solar System and an eccentricity larger than
$10^{-3}$, then, going back in time, the system would have been unstable
within the lifetime of the star (which we estimate to be 6.1$\pm$1.8 Gyr).
Moreover, with the best-fit eccentricity, the tidal heating of a rocky
planet b is similar to Io's, which may produce volcanic outgassing with
signatures detectable in transit spectra. If planet b is not terrestrial,
\eg more similar to Neptune, these physical constraints would not apply.
In either case, we find that the planets probably formed at larger radii
and migrated into their current orbits. This study demonstrates how the
orbital and dynamical properties of exoplanet systems may be used to
constrain the planets' physical properties.