Nuclear Engine for Rocket Vehicle Application

From the beginning of the space age to the end of the Apollo program in 1972, the United States (and to a lesser extent the Soviet Union) took a serious look at using nuclear reactors for spacecraft propulsion. In the US, the program was known as Nuclear Engine for Rocket Vehicle Application, or NERVA, and resulted in a design deemed flightworthy by NASA before the program's cancellation. You can read more about it here:
NERVA

Rockets work by adding energy to a propellant, then using a nozzle to harness this energy into momentum used to drive the ship forward. Thermal rockets start the process by heating the propellant up, chemical thermal rockets in a combustion chamber, and nuclear thermal rockets in a reactor. Less dryly, you can think of a nuclear thermal rocket as a very hot teakettle, powered by a nuclear reactor, with the spout replaced with a nozzle intended to shoot out steam as fast as possible. By "very hot," I mean hot enough to melt steel, and by "as fast as possible," I mean faster than satellites in low Earth orbit. Uranium and plutonium pack a big kick in a small package.

Why go to all the political and, potentially, environmental trouble of launching a nuclear reactor into space? The answer has to do with the materials used to build the nozzle, and the propellant exhausted through it. The hotter the propellant is, the faster its molecules are going on average, and therefore the more thrust it delivers per gram of exhaust. This is why hotter-burning engines are more efficient, but there's a maximum temperature any practical nozzle can reach before it weakens, melts, or does something else bad from an engineering standpoint. For the same temperature, molecules with lower molecular weight move faster, so ideally you'd use the smallest molecules available. For practical engines, that turns out to be molecular hydrogen.

Chemical rockets burn fuel and oxidizer, releasing energy and creating propellant in the form of the reaction's product in the same step. This means that a chemical rocket designer doesn't have direct control over the exhaust composition. Adding unburned hydrogen to the exhaust (a trick used on the Space Shuttle Main Engines) only buys a little bit of performance until the exhaust temperature decrease nullifies any efficiency increase from reduced molecular weight. Since nuclear thermal rockets keep the fuel (the reactor's uranium) and propellant separate, virtually any propellant can be used. For this reason, nuclear thermal rockets typically were designed with hydrogen in mind, but ammonia has also been considered due to its relatively low molecular weight and excellent heat transfer properties.

Most spacecraft propulsion strategies offer high thrust but low efficiency (like chemical rockets) or high efficiency at low thrust (like ion engines). NERVA's thrust couldn't quite match that of chemical rockets like the SSME, and its thrust per unit propellant (specific impulse, a good measure of mission efficiency for spacecraft engines) wasn't as good as an ion thruster, but it packed a combination of both that was nearly perfect for sending large payloads from Earth to Mars in a short amount of time. Since the most sensible program for such an engine was human exploration of Mars, extensive NASA study began on this subject in the late-1960s and early-1970s, with a goal of boots on the red planet by 1980 if the funding held up. In the event, the funding was axed, and NASA barely survived the development of the Space Shuttle, a programmatic consolation prize for the loss of people on Mars in the 20th Century.

Still, the physics of nuclear reactions and hydrogen through the nozzle haven't changed since 1972. NERVA, or an engine much like it, will almost certainly be involved when people finally do start crossing deep space to venture to the planets. Ideas that make sense sometimes get shelved for a while, but one day NERVA's true time will come.