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Earth is the only place in our solar system that has fire. Flames are known to require free atmospheric oxygen, and Earth has about 21% of it. The Sun, on the other hand, is composed mostly of hydrogen (91 %) and helium (8.9 %). The remainder, including oxygen, is a very small fraction of the mass.
The heat and light that are emitted by the Sun are produced by nuclear fusion occurring in its nucleus. This is a process in which atoms combine to form larger ones and release huge amounts of energy.