  The majority of extrasolar planets discovered to date have significantly
eccentric orbits, some if not all of which may have been produced through
planetary migration. During this process, any planets interior to such an orbit
would therefore have been susceptible to resonance capture, and hence may
exhibit measurable orbital period variations. Here we summarize the results of
our investigation into the possibility of detecting low-mass planets which have
been captured into the strong 2:1 resonance. Using analytical expressions
together with simulated data we showed that it is possible to identify the
existence of a low-mass companion in the internal 2:1 resonance by estimating
the time-dependant orbital period for piecewise sections of radial velocity
data. This works as long as the amplitude of modulation of the orbital period
is greater than its uncertainty, which in practice means that the system should
not be too close to exact resonance. Here we provide simple expressions for the
libration period and the change in the observed orbital period, these being
valid for arbitrary eccentricities and planet masses. They in turn allow one to
constrain the mass and eccentricity of a companion planet if the orbital period
is sufficiently modulated.
