The next phase in the field of exoplanets lies in the study of temperate planets with sizes similar to our Earth around the nearest stars. This is most easily accomplished by targeting the smallest stars, which led to the discovery of the TRAPPIST-1 system using a ground-based transit survey. Subsequently, the Spitzer space telescope enabled detection of the complement of seven transiting planets, all of which are similar in size to our Earth. The host is barely a star with 9% of the mass of our Sun and 12% of its radius, and lies only 12 parsecs away, making the transiting planets more amenable to characterization.
The planets prove to be in a complex dynamical configuration, showing a (broken) chain of Laplace resonances, which led to the discovery of the period of the seventh planet using the repurposed Kepler space telescope. Further monitoring with the Spitzer space telescope has allowed the measurement of the masses of the planets to 5-12% precision using transit-timing variations which occur due to the gravitational interactions between these planets. I will describe the analysis challenges in deriving the dynamical state of this system, which I have addressed by using Hamiltonian Monte Carlo, requiring a differentiable N-body integrator. I will end by discussing prospects for characterization of this system with the James Webb Space Telescope, which may provide precise characterization of the bulk densities, the dynamical state, as well as perhaps the constraints atmospheric compositions of these planets.