Radial-Velocity Semi-Amplitude Budgets Across the Mass and Period Plane

This study computes a detection budget for a clearly bounded question: What radial-velocity semi-amplitude does a planet of given mass and period induce, and where in that plane does the signal fall below the noise floors of current and planned spectrographs? Earth at one year around a solar twin: K = 0.0894 m/s. At 100 days: 0.138 m/s. At 10 days: 0.297 m/s. A five-Earth-mass super-Earth at 100 days gives 0.69 m/s; a Neptune at one year gives 1.53 m/s. A Saturn at 1000 days still gives 6.08 m/s, while a Jupiter at 1000 days gives 20.32 m/s. All values are computed from published anchor values and stated assumptions by a deposited script; the study is simulated and computed throughout, not measured. Semi-amplitude budgets favour short periods and low-mass hosts so strongly that target selection, not spectrograph precision alone, decides which terrestrial planets are measurable.