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 \lesssim 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 .