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The next generation of exoplanet space photometry missions proposed by bothNASA and ESA promise to discover small transiting planets around the nearestand brightest main-sequence stars. The physical and rotational properties ofthese stars, in conjunction with Gaia-precision distances, can be used todetermine the inclination of the stellar rotation axis. Given edge-on orbitalpaths for transiting planets, stellar inclinations can be interpreted asobliquities projected into the line of sight, which can be used to more clearlyreveal the system architectures of small planets and the factors that drivetheir orbital evolution. To demonstrate the method, we use a sample ofsimulated target stars for the NASA Transiting Exoplanet Survey Satellite(TESS) mission. Based on predicted characteristics of these stars and likelymeasurement uncertainties, we show that the expected TESS discoveries willallow us to finely differentiate the true underlying obliquity distribution.Under conservative assumptions in our illustrative example--in which the truedistribution is assumed to contain systems drawn from both well-aligned andisotropic distributions (e.g., due to multiple migration channels)--the correctfractions can be determined to within $0.15$, thus enabling constraints on theevolutionary processes that shape system architectures. Moreover, because ofthe excellent astrometric precision expected from Gaia, this technique willalso be applicable to the large number of planets already discovered by${\textit Kepler}$ orbiting much more distant stars.

Obliquities of Exoplanet Host Stars from Precise Distances and Stellar Angular Diameters