Precision of spectroscopy for astronomy How precise can the measurements be when looking at spectral lines in astrophysics?
For example, suppose I have a telescope in orbit, and I am looking at $H_\alpha$ lines coming from a star at 613 pc. Is it realistic to observer the lines move from 626.282 nm to 656.282002854 nm? this would correspond to a radial velocity of about 1.3 m/s (I am not an astronomer, and I just want to get a feel for whether this is realistic to measure, or out of the question)
 A: While most measurements in astronomy are better in space, precision spectroscopy can actually do quite well on the ground. One of the best spectrographs (some would say the best) is HARPS, the High-Accuracy Radial Velocity Planetary Searcher used for finding extrasolar planets.
As described in its instrument paper (pdf; note that the sole purpose of this paper is for the team to tout its own accomplishments), it operates from $380\ \mathrm{nm}$ to $690\ \mathrm{nm}$. HARPS can reliably get down to $1\ \mathrm{m}/\mathrm{s}$ precision, so yes, this accuracy can be achieved.
HARPS, like other high-precision spectragraphs, is of the echelle variety. In a very complicated way it spreads the spectrum over many rows of a CCD.1 Even then, the shifts one extracts usually are on the sub-pixel level. This is done by fitting many spectral lines presumed to be Doppler shifted by the same amount. If you were only allowed one line this would be somewhat more difficult.
Given that the Sun's reflex motion due to Earth tugging on it is $10\ \mathrm{cm}/\mathrm{s}$, there is a big push in the exoplanet community to get even more precise measurements.

1 A traditional spectrograph spreads light from a slit in one direction, so the rectangular CCD will have one spectral axis and one spatial axis.
