From Kepler to Doppler in Three Steps: A Novel Solution to the Galaxy Rotation Curve Anomaly

In this paper, we present a pragmatic, step-by-step solution to the anomalous galaxy rotation curve problem. We begin by comparing modern and ancient measuring techniques, which revealed an inverse relationship requiring a Doppler velocity correction factor of (-1), subsequently we found by vector analysis that instant orbital velocity when observed from outside the orbit appears faster by a factor of \( \sqrt{2} \) , and last but not least we found it necessary to make a relativistic correction, gamma \( \gamma = \frac{1}{\sqrt{2GM/rc^2}} \) to the luminous mass. These three corrections predicted galaxy rotation curves with excellent accuracy. Doppler data and luminous mass profiles from 5 well studied galaxies were analysed and found to be in excellent agreement. Moreover we found that it was possible using the inverse formula \( M_{r} = v^2 r / 2G \) to calculate the exact luminous mass profile from Doppler velocity data.