Transit timing variations (TTVs) are a powerful tool for characterizing the properties of transiting exoplanets. However, inferring planet properties from the observed timing variations is a challenging task, which is usually addressed by extensive numerical searches. We propose a new, computationally inexpensive method for inverting TTV signals in a planetary system of two transiting planets. To the lowest order in planetary masses and eccentricities, TTVs can be expressed as a linear combination of three functions, which we call the TTV modes. These functions depend only on the planets' linear ephemerides, and can be either constructed analytically, or by performing three orbital integrations of the three-body system. Given a TTV signal, the underlying physical parameters are found by decomposing the data as a sum of the TTV modes. We demonstrate the use of this method by inferring the mass and eccentricity of six Kepler planets that were previously characterized in other studies. Finally we discuss the implications and future prospects of our new method.
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