To understand Jet propulsion, read this.
Answer by Robert Frost:
There are a couple of concepts about power and propulsion being confused, here.
In a submarine, a nuclear reactor uses fission to generate substantial heat that is used to produce steam that turns turbines to both generate electricity and turn the main propeller. Because a submarine is in water, it can be propelled forwards or backwards just by mechanical energy of turning the propeller.
In a spacecraft, nuclear energy can be used to generate electricity. We’ve done so on many small unmanned spacecraft, such as Voyager, Galileo, and Cassini. On those vehicles we use a radioisotope thermoelectric generator (RTG). Plutonium 238 decay releases smaller amounts of heat and we use a thermocouple to convert some of that heat energy into electrical energy. But while that electrical energy is useful to power the radio, the computer, and the science instruments, it is useless in propelling the spacecraft. In the vacuum of space, one can’t move forward simply by pushing backwards, because there is nothing to push. With current and near future technology, in order to move a spacecraft forwards we need to expel mass. Conservation of momentum means if we shoot a small amount of mass at very high speed out of the back of the spacecraft, the much larger spacecraft mass will move forward slightly faster than it was.
The potential role for nuclear energy, here, is to provide electricity that can be used to accelerate that outgoing fuel so that less fuel needs to be used (ion engines). But that requires very powerful and thus massive reactors, outweighing the benefits (today). So, nuclear energy just isn’t a panacea for spacecraft propulsion.
Even if it were, there are complications that make it undesirable. One is environmental risk. NASA does use plutonium RTGs because they are small and can be encapsulated to ensure that even if the launch vehicle explodes during ascent, the capsule will remain intact and not release radioactive material into the environment. Even though the engineers are confident there is no risk, every time we launch one there are protests, and court injunctions, and lawsuits from environmental groups. Even though uranium reactors could provide more electrical energy than plutonium RTGs, NASA does not use uranium reactors because they aren’t as easy to secure as a plutonium RTG. I can’t imagine NASA ever getting approval for uranium reactors. The Soviet Union, however, did not have to worry about such things as protests from citizens and the legal process. They did in fact launch uranium reactors into space (with mixed results). In 1978, one of those uranium powered satellites re-entered the atmosphere and released uranium over Canada. The Canadians were not pleased.