Yesterday, in Data Group Meeting at Flatiron, Lily Zhao (Flatiron) showed a formula for the effectiveness of a spectrograph for measuring a radial velocity that she was confused about. It appeared in a paper by someone who builds spectrographs. We discussed it and ended up a bit confused. So today I sat down and wrote a short document, which represents my Official Position (tm) on spectrograph radial-velocity precision. My loyal reader will not be surprised to learn that I think the right way to compare is by looking at radial-velocity information per unit time where “information” is inverse variance (Fisher information). In that context, the answer is that you get more information linearly with wavelength coverage and you get more information linearly with spectrograph resolution. It's that simple!
[Note added later: This post is WRONG. See here.]
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