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I understand how infrared spectroscopy works for determining molecules in the atmosphere of a transiting object (like Venus from Earth). But how does this work for objects that don't pass between us and the sun? If the IR spectra is an absorption spectra, is the light emitted by a planet, like Uranus, enough for us to determine its atmoshpere's composition via IR spectroscopy?

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Yes it is. As long as light is produced by a source and then passes through a medium, we can perform spectroscopy on it. When considering a planet like Uranus, most of the light that it emits is actually reflected light or re-emitted light from the Sun. Uranus produces very little light by its own merit. For light that is directly reflected (by that I mean the light from the Sun goes into the atmosphere, hits molecules, and gets scattered out of the atmosphere again), this is directly equivalent to the standard transiting planets you mention in your question. For light that is re-emitted, you still see absorption spectra, but the black body background has changed. In this scenario, the light is absorbed lower in the atmosphere and re-emitted at a longer wavelength, but that emitted light must still try to leave the atmosphere and will experience some absorption along the way, creating absorption lines.

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