Nuclear fission does not have much to do with star formation, but if what you're thinking about is nuclear fusion, then it has a lot to do with the birth of stars.
Basically, a cloud of gas in space can start to collapse under the right conditions, and once the temperature and density (density is the amount of "stuff" in a given volume, so gases are not dense, but water is) become high enough, nuclear fusion starts. In some of these clouds, fusion happens to a specific type of hydrogen that's heavier than the hydrogen in our normal atmosphere.
During fusion, two or more of the centers of atoms (atomic centers are called nuclei) come together to make a different atom. During the fusion process that forms stars, the heavy hydrogen nucleus fuses with a normal hydrogen nucleus, and together, they form a helium nucleus that's lighter than normal helium. As fusion takes place, radiation is released, which slows down the collapse of the gas cloud. Fusion will then continue to give power to the star, but where the fusion happens and what fusion produces differ depending on how massive the star is. Deuterium fusion (fusion of the heavy hydrogen) can keep the center of the protostar (protostar is what we call the collapsing gas cloud in which fusion has started) below temperatures that are too hot. Without deuterium fusion, hydrogen fusion would take over, the central temperature would rise, and the protostar would not be able to continue gathering more materials from the gas cloud surrounding it.
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