  Gravitational interactions between planets in transiting exoplanetary systems
lead to variations in the times of transit that are diagnostic of the planetary
masses and the dynamical state of the system. Here we show that synodic
"chopping" contributions to these transit timing variations (TTVs) can be used
to uniquely measure the masses of planets without full dynamical analyses
involving direct integration of the equations of motion. We present simple
analytic formulae for the chopping signal, which are valid (generally <10%
error) for modest eccentricities e <~ 0.1. Importantly, these formulae
primarily depend on the mass of the perturbing planet, and therefore the
chopping signal can be used to break the mass/free-eccentricity degeneracy
which can appear for systems near first order mean motion resonances. Using a
harmonic analysis, we apply these TTV formulae to a number of Kepler systems
which had been previously analyzed with full dynamical analyses. We show that
when chopping is measured, the masses of both planets can be determined
uniquely, in agreement with previous results, but without the need for
numerical orbit integrations. This demonstrates how mass measurements from TTVs
may primarily arise from an observable chopping signal. The formula for
chopping can also be used to predict the number of transits and timing
precision required for future observations, such as those made by TESS or
PLATO, in order to infer planetary masses through analysis of TTVs.

Earth and Planetary Astrophysics