When I first learned about the Doppler effect, I found that the easiest way to think about it was to imagine an ambulance driving past me at a very high speed. When the ambulance is approaching me, the sound its siren makes is higher because its waves are more compressed, and when it passes me, I hear the sound get lower in pitch because when it is traveling away from me, the sound waves are less compressed. I found this concept relatively easy to translate into my understanding of Doppler shifts in terms of spectroscopy and wavelengths of light.
However, one thing that puzzled me was what occurs when a star, for example, isn’t moving directly toward or away from Earth, but away at a diagonal. What sort of shift do we observe then? Once I discovered that the observed shift had to do with radial velocity, I was surprised to discover that Doppler shifts are actually key to our observation and discovery of extrasolar planets, as seen in the image above.