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Suppose there is a isolated system in which there is only one stationary rocket.

As the rocket is in a stationary position the initial momentum will be 0, now the nuclear engine is started, as a result momentum increases but in nuclear engine, there is no exhaust gases or such things to counteract the increase in momentum of rocket. So the total momentum in the system increases. As a result law of conservation of momentum is violated.

Can you please say what is the mistake in my thought experiment.

Edit: The question was a result of my misunderstanding of how nuclear engine works.

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    $\begingroup$ It's not clear to me,at least, how your nuclear engine works. What's coming out of the hot end of the rocket, particles, pure radiation, i. e. What's the working fluid? $\endgroup$ – user108787 Jul 10 '16 at 7:32
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It's unclear what you mean by "nuclear engine", but the main similar notion is a nuclear thermal rocket. Although it derives its energy from nuclear reactions, it uses this to heat gas (usually hydrogen) to very high velocity for propulsion. There is still matter being expelled.

More common in space travel is the radioactive thermal generator, which uses radioactive decay to create electricity. This powers computers and instruments on board a craft, but does not propel it.

The only designs people have discussed that don't have a material propellant fire photons for momentum. As you said, momentum must be conserved.

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    $\begingroup$ Also obligatory reading here is the insane Project Pluto nuclear powered ramjet known as the flying crowbar and Project Orion $\endgroup$ – WetSavannaAnimal Jul 10 '16 at 7:44
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    $\begingroup$ Also a 40 min YouTube video re nuclear powered aircraft youtu.be/c_yQOPZ5CY0 detailing the early days of nuclear power, and the optimism surrounding its applications. $\endgroup$ – user108787 Jul 10 '16 at 8:20
  • $\begingroup$ @WetSavannaAnimalakaRodVance: Ah, the good old illusions of the torch ship crowd will never die. Now all we need is a space amazon to really set the mood: i131.photobucket.com/albums/p295/lucyp_album/photos/famous/… $\endgroup$ – CuriousOne Jul 10 '16 at 8:34

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