Photon-Noise Photometric Budgets and Magnitude Limits for Kepler and TESS

This study computes a detection budget for a clearly bounded question: Anchored to published noise levels, what signal-to-noise do Kepler and TESS actually deliver for standard transit cases as a function of stellar magnitude, and where does each mission's terrestrial-planet sensitivity end? Kepler's six-hour precision degrades from 23 ppm at Kp = 10 to 190 ppm at Kp = 16. A single Earth transit at Kp = 12 carries 2.94 sigma; four transits combine to 5.88 sigma, below the 7.1 pipeline threshold. The four-transit Earth limit falls at Kp approximately 11. All values are computed from published anchor values and stated assumptions by a deposited script; the study is simulated and computed throughout, not measured. Kepler's terrestrial sensitivity ends near twelfth magnitude for year-long periods, while TESS's budget is spent on bright stars and small hosts where single transits already carry large signal.