You cannot measure the absolute speeds of the stars, but you can measure their relative speeds along the line of sight, because if a star is moving toward us its light is shifted to shorter wave lengths, and if it is moving away from us its light is shifted to longer wave lengths.

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If we see a star at a large distance from the center of the galaxy, that star is going to be mostly moving either away from the center or back toward the center. Almost certainly, most of its motion is perpendicular to our line of sight.

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