Mapping the Milky Way's Rotation Curve from Archival 21-cm HI Observations

The 21-cm hyperfine line of neutral atomic hydrogen (H I) provides a direct spectroscopic probe of Galactic gas because radio emission penetrates interstellar dust and Doppler shifts encode line-of-sight motion. This work uses archival HI4PI data to construct a Galactic longitude–velocity (l–v) diagram, inspect representative spectra, identify terminal-velocity edges, and transform those measurements into an inner-Milky-Way rotation curve with the tangent-point method. In the supplied run, the displayed l–v product spans approximately 10◦ ≤ l ≤ 85◦ and averages a broader latitude strip |b| ≤ 2 ◦ . Terminal velocities are measured with an absolute brightness-temperature threshold of 20 K and a persistence requirement across adjacent channels. The real diagnostic figures show that this configuration is not uniformly successful: representative sightlines near l = 69.9 ◦ and 84.9 ◦ return no valid terminal velocity, and the intended high-longitude calibration interval begins beyond the available accepted terminal-velocity sequence. Consequently the displayed edge-bias correction is 0.0 kms−1 rather than a measured calibration. The derived curve extends from roughly 1.5 to 7.4 kpc and rises from about 95 kms−1 in the innermost sampled region to approximately 230–255 kms−1 over much of the outer part of the measured interval. The exercise therefore demonstrates both the astrophysical power of 21-cm kinematics and the importance of quality control: a plausible-looking rotation curve must be interpreted together with threshold diagnostics, missing detections, geometric validity, and calibration coverage. The analysis is presented as a reproducible undergraduate investigation rather than a precision Galactic mass mode