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We present an efficient, robust computational method for modeling theNewtonian dynamics for rotation curve analysis of thin-disk galaxies. For adisk galaxy with a typical flat rotation curve, our modeling results show thatthe surface mass density monotonically decreases from the galactic centertoward periphery, according to Newtonian dynamics. In a large portion of thegalaxy, the surface mass density follows an approximately exponential law ofdecay with respect to the galactic radial coordinate. Yet the radial scalelength for the surface mass density seems to be generally larger than that ofthe measured brightness distribution, suggesting an increasing mass-to-lightratio with the radial distance in a disk galaxy. In a nondimensionalized form,our mathematical system contains a dimensionless parameter which we call the"galactic rotation number" that represents the gross ratio of centrifugal forceand gravitational force. The value of this galactic rotation number isdetermined as part of the numerical solution. Through a systematiccomputational analysis, we have illustrated that this galactic rotation numberremains within $\pm 10%$ of 1.70 for a wide variety of rotation curves. Thisimplies that the total mass in a disk galaxy is proportional to $V_0^2\,R_g$,with $V_0$ denoting the characteristic rotation velocity and $R_g$ the radiusof the galactic disk. The predicted total galactic mass of the Milky Way is ingood agreement with the star-count data.

Modeling the Newtonian Dynamics for Rotation Curve Analysis of Thin-Disk Galaxies