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For approximately circular motion in a spherically dominated Newtonian gravitational field, $v_c^2(r)=GM(<r)/r$. If most gravitating mass followed the concentrated luminous galaxies, then beyond their main light distribution the enclosed mass would nearly saturate, giving a declining Keplerian galaxy rotation curve, $v_c\propto r^{-1/2}$.

Instead, extended galaxy rotation curves commonly remain roughly flat. The spherical mass profile for a flat rotation curve then requiresThe inferred mass continues growing where the luminous contribution is small, so the mass-to-light ratio increases outward. Under the assumed gravitational dynamics this is evidence for an extended dark matter halo. Measurements of neutral-gas motion can probe radii beyond the bright stellar disk. A realistic disk contribution must be computed using its flattened geometry; the spherical formula describes a halo-dominated region and does not turn every disk rotation curve into a spherical mass profile.