Arcturus Motion

When sunlight is passed through a prism, it splits into a spectrum of different wavelengths \(\lambda\) (different colors). On careful examination, we notice some missing bands, which indicate the presence of different elements such as hydrogen, sodium, and magnesium that absorb light of specific wavelengths.

The spectrum of a distant star, Hayesmark, which is known to have the same elemental composition as the Sun, was measured, and the data is shown below.

What can we infer from the spectra?

Hint: The Doppler effect tells us how the wavelength measured by an observer depends on their relative velocity, \(v,\) with the source. It changes according to \[\frac{\lambda_o}{\lambda_s} = \sqrt{\frac{c + v}{c - v}},\] where \(c\) is the speed of light.

This star is named in honor of Mark Hayes, who pointed out a problem with the star we originally chose.


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