The shift of the hydrogen absorption spectrum of a galaxy provides evidence for the following three:
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Expansion of the universe - The redshift observed in the hydrogen absorption spectrum indicates that galaxies are moving away from us, supporting the notion that the universe is expanding.
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Motion of the galaxy - The shift in the spectrum can provide information about the velocity and direction of a galaxy’s movement relative to Earth.
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Composition of the universe - The absorption lines in the spectrum can reveal the presence of hydrogen and other elements, which helps in understanding the composition of the galaxy and, by extension, the universe.
The remaining options, such as the number of stars in the galaxy, temperature of the galaxy, and The Big Bang theory, are not directly indicated by the shift of the absorption spectrum.