Integration time adjusted completeness

Future, large-scale, exoplanet direct-imaging missions will be capable of discovering and characterizing Earth-like exoplanets. These mission designs can evaluated using completeness, the fraction planets from some population that are detectable by a telescope at an arbitrary observation time. However, original formulation completeness uses instrument visibility limits ignores additional integration time planetary motion constraints. Some sampled used to calculate may transit in out instrument’s geometric photometric while they being observed, thereby causing agnostic calculation overestimate completeness. We present method for calculating accounts leave during period. define aggregate orbital period which detectable, calculated specific times enter To perform this calculation, we derive analytical methods finding planet-star projected separation extrema, past periastron these extrema occur, intersects circle. also provide efficient numerical difference magnitude corresponding values Δmag. Our adjusted shows that, planned star 25 pc with 1-day 5-day times, is reduced 1% 5% respectively. Integration manner provides computationally inexpensive dynamic completeness—the change on subsequent observations.