We fit the Kepler photometric light curve of the KOI-368 system using an oblate, gravity-darkened stellar model in order to constrain its spin-orbit alignment. We find that the system is relatively well-aligned with a sky-projected spin-orbit alignment of λ = 10 • ± 2 • , a stellar obliquity of ψ = 3 • ± 7 • , and a true spinorbit alignment of ϕ = 11 • ± 3 • . Although our measurement differs significantly from zero, the low value for ϕ is consistent with spin-orbit alignment. We also measure various transit parameters of the KOI-368 system: R KOI−368 = 2.28 ± 0.02R , R p = 1.83 ± 0.02R jup , and i = 89.221 • ± 0.013 • . This work shows that our gravity-darkened model can constrain long-period, well-aligned planets and M-class stars orbiting fast-rotators, allowing for measurement of a new subcategory of transiting bodies.

We use rotational gravity darkening in the disk of Kepler star KOI-2138 to show that the orbit of 2.1 − R ⊕ transiting planet candidate KOI-2138.01 has a low projected spin-orbit alignment of λ = 1 • ± 13. KOI-2138.01 is just the second super-Earth with a measured spin-orbit alignment after 55 Cancri e, and the first to be aligned. With a 23.55-day orbital period, KOI-2138.01 may represent the tip of a future iceberg of solar-system-like terrestrial planets having intermediate periods and low-inclination circular orbits.Subject headings: planets and satellites: individual (KOI-2138)