Transit Duration Geometry: Impact-Parameter Distributions and Per-Transit Signal Budgets

This study computes a detection budget for a clearly bounded question: How is the duration of a transit distributed over the allowed range of impact parameters, how much signal does a high-impact-parameter transit lose, and what fraction of transits are grazing? Central Earth-analogue duration at one year is 13.09 hours; at b = 0.5 it is 11.37 hours and at b = 0.9, 5.92 hours. The impact-parameter-averaged Earth duration is 10.34 hours, about thirty percent below the central value. A Jupiter's central duration is 14.28 hours, with a mean of 11.92 hours. All values are computed from published anchor values and stated assumptions by a deposited script; the study is simulated and computed throughout, not measured. Impact-parameter averaging reduces typical transit durations well below the central value, and completeness calculations that ignore the distribution overstate terrestrial signal by tens of percent.