Red Shift and Blue Shift: Is It Possible?

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BJRowlett
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I was thinking today and had an idea but didn't know if it was possible. When an object moves toward or away from an observer, the light (such as visible light) "shifts", the wavelengths become closer together (moving toward you) or further apart (moving away from you).

Say for example we have an object, that only emits infrared radiation, and not any visible light.

Is it possible for this object (because its wavelength is longer than visible light) to be moving toward you so fast (so the waves propagate closer together) that its wavelengths shift into visible light?

Or the opposite for ultraviolet radiation?

Thanks!
 
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Naturally thinking, my answer is Yes.