  Three planets with minimum masses less than 10 Earth masses 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 a numerical integration shows that the eccentricities must be at
least 0.0001. Also, 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 a remnant eccentricity larger than 0.001, then,
going back in time, the system would have been unstable within the lifetime of
the star (which we estimate to be 6.1 +/- 1.6 Gyr). Moreover, if the
eccentricities are that large and the inner planet is rocky, then its tidal
heating may be an order of magnitude greater than extremely volcanic Io, on a
per unit surface area basis. If planet b is not terrestrial, e.g. Neptune-like,
these physical constraints would not apply. This analysis suggests the planets
are not terrestrial-like, and are more like our giant planets. In either case,
we find that the planets probably formed at larger radii and migrated early-on
(via disk interactions) 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.
