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

Measurement of planet masses with transit timing variations due to synodic "chopping" effects