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A rotation curve (or galaxy rotation curve) of a galaxy is a function over its radial dimension, that maps points along that dimension to the orbital speed of the stars located there.
Rotation curves are of interest in that they show a pattern other than that expected of Keplerian orbits based upon the mass observed in the galaxy's stars and clouds. The gravity of such mass generally observed in galaxies would produce a rotation curve such that orbital speed falls with distance from the center, but measurements of real galaxies indicate that for a considerable portion of the radius, the speed is relatively constant, or even slowly rises with distance from the center. This mismatch is a primary motivation for the concept of dark matter.
The determined rotation curve of the Milky Way is the basis for the concept of kinematic distance, determining the distance to Milky Way objects suggested by their radial velocity.