2016ApJ...828...44H

We develop and apply methods to extract planet masses and eccentricities from observed transit timing variations (TTVs). First, we derive simple analytic expressions for the TTV that include the effects of both first- and second-order resonances. Second, we use N-body Markov chain Monte Carlo simulations, as well as the analytic formulae, to measure the masses and eccentricities of 10 planets discovered by Kepler that have not previously been analyzed. Most of the 10 planets have low densities. Using the analytic expressions to partially circumvent degeneracies, we measure small eccentricities of a few percent or less.