Exoplanet Systems

The orbital region where liquid surface water can exist under atmospheric pressure: $r_{in} \approx \sqrt{L/1.1}$, $r_{out} \approx \sqrt{L/0.53}\text{ AU}$, where $L = (M/M_\odot)^{3.5}$.

When an exoplanet crosses its host star, stellar brightness drops proportional to cross-sectional area: $\Delta F / F = (R_p / R_*)^2$.