Astronomers use earth-based spectroscopy

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How can astronomers use earth-based spectroscopy to determine the chemical composition of nebulae, stars, planets etc. when the light has to pass through the Earth's atmosphere before it's detected? Does the chemical composition of the Earth's atmosphere pose a problem?
 
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Not much of one - there are two possible problems

The spectral line being absorbed by the same atom in the Earth's atmosphere. In the visible band the atmosphere is relatively thin compared to a star and most of the elements found in a star are rare. So very little of a hydrogen line from the sun would be absorbed.
This isn't true for high energy lines in the ultra violet which can be absorbed which is why UV telescopes have to go in space.

The background from the same line (or something at the same wavelength) is also a problem. But since the lines in the visible are very narrow, with a high resolution spectra you can work between the lines in the atmopshere. This is a big problem in the near IR because the O-H bond in water has 1000s of emission lines which make the sky very bright and it's difficult to work between them. At longer infrared wavelengths the blackbody emission from the atmopshere swamps all the lines an you have to go into space.
 


Should they use reference? The resulted spectrum is the subtraction of the light beam from the star (planet etc) and the blank
 


Not generally for spectra.
The emission lines in the atmosphere are strong enough that if they occur on top of a line from a star you aren't going to easily subtract them. Also spectra of anything faint take a long time to measure an the sky brightness can change on much shorter timescales.

In the far-IR and microwave the sky is brighter than the source and you o have to do complex background subtraction to see anything at all.
 


Space based telescopes are also used for spectroscopy so calibration is not an issue. If you are asking if spectroscopy could be suspect, the answer is no.
 

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