Day-night terminator

The day-night terminator is the boundary between the illuminated and dark hemispheres of a planet. During transit, stellar rays probe morning and evening limbs that can have different temperatures, clouds, and compositions.

If the morning and evening limbs have effective radii $R_m(\lambda )$ and $R_e(\lambda )$ and each occupies half the annulus, the transit area is $\pi [R_m^2(\lambda )+R_e^2(\lambda )]/2$.