Observation that make to classify a star according to its luminosity, and why does that method work?

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The Hα spectral line has a rest wavelength of 6562.8 ˚A (remember: 1 ˚A = 10−10 m). In star A, the lineis seen at 6568.4 ˚A, in star B it’s seen at 6560.3 ˚A, and in star C it’s seen at 6562.8 ˚A. Which star ismoving the fastest (along the line of sight) and what is the radial velocity of each star?

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Chapter 8, Problem 11RQ

To determine

Observation that make to classify a star according to its luminosity, and why does that method work?

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