# The Doppler Shift

WARNING: This post involves copious amounts of semi-difficult math. If you don’t like the realm of radicals and fractions below radicals, I suggest you stay away from the math portions of this.

Most of you know of the existence of a phenomenon called the Doppler Shift (or Doppler Effect, they’re the same thing). You know, when a train moves towards you, the sound it makes is higher, when it moves away, the sound is lower. How high or low the sound is to you is referred to as the “pitch”. There’s another version of the Doppler Shift in relation to light and astronomy. It’s called the relativistic Doppler Shift.

The relativistic Doppler Shift works the same way the regular Doppler Shift does, only it’s with colours instead of pitch. When the train moves away from you, the pitch drops because the frequency of the waves that carry sound are dropping, and therefore the pitch goes down. (For those of you who have never taken physics, a lower frequency means a lower pitch. A higher frequency means a higher pitch.) In the same way, if an object moves towards you, it appears blue because of a shorter wavelength, and if it is moving away from you, it appears red because of a longer wavelength.  In light, a smaller wavelength means you go towards the blue end of the spectrum, and a larger wavelength means you go towards the red.

Basically, everything here is relative. The relative motion of the source (i.e. some star a few dozen light years away) makes the wavelength in front of it to look relatively decreased, and the wavelength behind it to look relatively increased. And when wavelengths appear decreased or increased, the colour appears different. That’s called shifted wavelength. (Definition of shifted wavelength: How short or long the wavelength appears to be from the vantage point of the observer.)

However, the relativistic Doppler Shift can only be observed from objects moving at very great speeds a great distance away—you aren’t going to see a relativistic Doppler Shift from a car. From Earth, the only objects that have a relativistic Doppler Shift are celestial objects. Stars, deep sky objects (DSOs), distant galaxies—you can see Doppler Shifts from those. The Doppler Shift is important for figuring out just how fast a DSO is moving away or toward us. That’s why you should learn this for astronomy.

The math for the Doppler Shift is annoying and long and involves a bunch of fractions and radicals. There are five equations: the blue-shift wavelength equation, the blue-shift frequency equation, the red-shift wavelength equation, the red-shift frequency equation, and the velocity equation. Four of the five equations look incredibly similar to one another.

And there you have it. A crash course in the relativistic Doppler Shift. It’s a total of 666 words. Not too bad, eh?

And this, kids, is how the Doppler Shift works.

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TL;DR

It’s not complicated. Really.