Transit Count, Geometric Probability and the Combined Detection Window as a Function of Orbital Period

This study computes a detection budget for a clearly bounded question: For a photometric survey of fixed duration, how do the number of observed transits and the geometric transit probability combine into a single detection window, and how steeply does that window close with orbital period? The geometric probability falls from 0.051 at 10 days to 0.0047 at one year and 0.0029 at two years. Expected transit counts over the effective baseline run from 134 at 10 days to 3.7 at one year. The three-transit probability is unity through 200 days, 0.69 at 500 days, and zero at 730 days in the phase-averaged model. All values are computed from published anchor values and stated assumptions by a deposited script; the study is simulated and computed throughout, not measured. Geometry and scheduling alone suppress year-long-period detections by about a factor of twenty relative to 50-day planets, before any photometric term is applied.