How precise can Doppler shift be measured in detecting exo-planets?

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Doppler shift measurements are crucial for detecting exo-planets by analyzing the spectral shifts of stars caused by their movement. State-of-the-art spectrographs can measure stellar velocities as low as 10 cm/s, allowing for precise calculations of the Doppler effect. Using Doppler's law, a velocity of 1 m/s can yield a wavelength shift of Δλ = λ0/10^8, indicating high sensitivity in measurements. Techniques such as comparing spectral lines to a frequency comb enhance this precision. Understanding these concepts is essential for exam preparation and grasping the intricacies of exo-planet detection.
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As the title says, I'm interested in the precision a Doppler shift can be revealed.

That's why I read that it's possible to detect exo-planets by measuring the Doppler shift of the star's spectra. Works like this: the stars moves, since it moves back and forth is spectrum suffer from Doppler shift, by measuring this shift you can deduce at which speed the star is moving.

Now, my professor said once that state of the art spectrographs can measure the star moving at 10 cm/s.

But, using Doppler's law: V = c \frac{\lambda -\lambda_0}{\lambda_0} \qquad \Rightarrow \qquad \Delta \lambda = \frac{\lambda_0 V}{c} and setting, for now, V = 1 m/s, c = 3 \cdot 10^{8} m/s that means that we can reveal a \Delta \lambda = \frac{\lambda_0}{10^8}.

My professer intended that they use a special tecnique to achieve this precision and that he would probably ask me this at my exam (which is tomorrow) so please, if someone could answer very fast i would be very grateful.
 
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To give two keywords: Compare spectral lines to a frequency comb.

As interesting comparison, our Earth drags around the sun with approximately 10cm/s.
 
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