Inferring Planet Properties from Transit Timing Variations

Transit timing variations (TTV) are a powerful tool for characterizing the properties of transiting exoplanets. We derive analytical expression for TTV using a geometrical approach for orbital perturbations. Unlike previous works, our approach does not assume proximity to mean-motion-resonance. We introduce the concept of TTV modes - a set of three orthogonal functions that linearly span the space of TTV signals of planet pairs with a given period ratio. Utilizing these modes, we are able to infer the planet masses and free eccentricities without resorting to numerous computationally expensive N-body simulations. We demonstrate our method on a few Kepler systems that were previously analyzed by Hadden & Lithiwick (2017), inferring masses that are consistent with their values. Finally we apply our method on Kepler planets that did not have previously reported mass estimates. Our method is expected to be particularly beneficial for systems with a small number of detected transits, as will be the case in many of TESS's detections

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