Transit timing variations - deviations from strict periodicity betweensuccessive passages of a transiting planet - can be used to probe the structureand dynamics of multiple-planet systems. In this paper, we examine prospectsfor numerically solving the so-called inverse problem, the determination of theorbital elements of a perturbing body from the transit timing variations itinduces. We assume that the planetary systems under examination have a limitednumber of Doppler velocity measurements, and show that a more extensive radialvelocity characterization with precision comparable to the semiamplitude of theperturber may remove degeneracies in the solution. We examine severalconfigurations of interest, including (1) a prototypical non-resonant system,modeled after HD40307 b and c, which contains multiple super-Earth massplanets, (2) a hypothetical system containing a transiting giant planet with aterrestrial-mass companion trapped in low-order mean motion resonance, and (3)the HAT-P-13 system, in which forced precession by an outer perturbing bodythat is well characterized by Doppler radial velocity measurements can giveinsight into the interior structure of a perturbing planet, and for which thedetermination of mutual inclination between the transiting planet and itsperturber is a key issue.
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