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This is an outcome used to predict the motion of celestial bodies (stars!). When a visible object is located very long distances from an observer, it will be observed to make a color shift throughout the visible spectrum of light as it gains distance from the observer. As the object becomes farther away, the color of the object becomes shifted toward the highest wavelength of light in the visible spectrum (red). This is called Redshift, and is the application of this phenomenon to light waves.
What is the Doppler Effect?