2022AJ....163...91J

We apply AnalyticLC, an analytic model described in an accompanying paper, to interpret Kepler data of systems that contain two or three transiting planets. We perform tests to verify that the obtained solutions agree with full N-body integrations, and that the number of model parameters is statistically justified. We probe non-co-planar interactions via impact parameter variations (TbVs), enabled by our analytic model. The subset of systems with a valid solution includes 54 systems composed of 140 planets, more than half of which are without previously reported mass constraints. Overall we provide: (i) estimates of physical and orbital properties for all systems analyzed; (ii) 102 planets with mass detections significant to better than 3σ, 43 of which have masses below 5 m ⊕; and (iii) 35 TbVs significant to better than 3σ. We focus on select systems showing strong TbVs, which can result from either interaction among the known transiting planets, or with a nontransiting object, and provide: (iv) a method to constrain the parameters of such unseen companions. These results are enabled by an accurate 3D photodynamical model, of a kind expected to become increasingly important for modeling multidecade photometric and composite (radial velocity, astrometry) data sets.