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Nuclear Fission

Extended Definition: Nuclear fission is a reaction in which the nucleus of an atom splits into two or more smaller nuclei. The fission process often produces gamma photons, and releases a very large amount of energy even by the energetic standards of radioactive decay. Furthermore, In a nuclear reactor, Uranium atoms split apart and release energy in a process called fission. This process creates heat that can be used to power a nuclear engine.
Detailed Explanation: The main goal of Nuclear Fission is to produce heat, in turn generating thrust. So, In a nuclear thermal propulsion (NTP) system, a liquid propellant, like hydrogen, is pumped through a reactor core. The Uranium atoms split and release heat, which in turn heats the propellant and turns it into a gas. The gas is then expanded through a nozzle to create thrust
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Figure 8: "Typical Fission Process of a Fissile Uranium-235 Atom." Disclaimer: This diagram was pulled from a NASA website
Within a nuclear reactor Uranium-235, or also Plutonium-239, undergoes the nuclear fission proccess, in which was described above, the splitting of nuclei within atoms into smaller particles which releases an imense amount of energy in the form of heat. That heat is then harnessed, and used to convert water into steam. Overall this process of fission reaction is conducted in a controlled manner so that stability is maintained allowing the facilitation of regulation of output.
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Figure 9: "Comparison of State of The Art Propulsion Concepts." Disclaimer: This flowchart was pulled from a NASA website.
This figure in particular doesn't necessarily have to deal directly with submarines and marine NTP systems, but overall it does give everyone an idea on how various energy sources are implemented into these systems with their correlating TSI (Theoretical Specific Impulse), which equals total impulse (change in momentum) delivered per unit of energy source consumed. With that number a mass ratio to escape Earths atmosphere in terms of a rocket and space (rocket) propulsion systems can be determined.
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