If we observe a Doppler blue shift from a star, it means the star is moving towards us.

Here's why:

* Doppler Shift: The Doppler effect describes the change in frequency of a wave (like light) as the source of the wave moves relative to the observer.

* Blue Shift: When light from an object is shifted towards higher frequencies (the blue end of the visible spectrum), it indicates the object is moving towards the observer.

* Red Shift: Conversely, a shift towards lower frequencies (the red end of the visible spectrum) indicates the object is moving away from the observer.

So, a blue shift means the star is getting closer to Earth.