Transit Timing Precision and Ephemeris Decay Budgets for Follow-Up Observations

This study computes a detection budget for a clearly bounded question: How precisely can a transit mid-time be measured from ground and space photometry, how does the period uncertainty derived from a discovery baseline grow into future timing error, and after how many cycles is a fresh transit observation required? Ground-based mid-time precision for the worked hot Jupiter is 1.42 minutes; from space, 0.142 minutes. The derived period uncertainty is 0.0184 minutes per cycle. Predicted timing error grows to 2.3 minutes at 100 cycles and 18 minutes at 1000 cycles. All values are computed from published anchor values and stated assumptions by a deposited script; the study is simulated and computed throughout, not measured. Ephemeris uncertainty grows linearly in cycle count from a measurable starting precision, giving every transit discovery a computable date by which it must be refreshed.