  I present an initial investigation into a new planet detection technique that
uses the transit timing of a known, transiting planet. The transits of a
solitary planet orbiting a star occur at equally spaced intervals in time. If a
second planet is present, dynamical interactions within the system will cause
the time interval between transits to vary. These transit time variations can
be used to infer the orbital elements of the unseen, perturbing planet. I show
analytic expressions for the amplitude of the transit time variations in
several limiting cases. Under certain conditions the transit time variations
can be comparable to the period of the transiting planet. I also present the
application of this planet detection technique to existing transit observations
of the TrES-1 and HD209458 systems. While no convincing evidence for a second
planet in either system was found from those data, I constrain the mass that a
perturbing planet could have as a function of the semi-major axis ratio of the
two planets and the eccentricity of the perturbing planet. Near low-order,
mean-motion resonances (within about 1% fractional deviation), I find that a
secondary planet must generally have a mass comparable to or less than the mass
of the Earth--showing that these data are the first to have sensitivity to sub
Earth-mass planets orbiting main sequence stars. These results show that TTV
will be an important tool in the detection and characterization of extrasolar
planetary systems.
