Official NASA model of the C-5 Nuclear Booster. Cast aluminum painted black & white with two nose cones for two versions of the last stage.
The Saturn C-5N was a successor design for Apollo’s Saturn V launch vehicle which would have had a nuclear thermal third stage. This one change would have increased the payload of the standard Saturn V to Low Earth orbit from 118,000 kg to 155,000 kg.
In the solid core nuclear design (see diagram below), liquid hydrogen is heated to a high temperature in a nuclear reactor and then expands through a rocket nozzle to create thrust. The external nuclear heat source theoretically allows a higher effective exhaust velocity and is expected to double or triple payload capacity compared to chemical propellants that store energy internally. Here’s a nice video overview by Amy Shira Teitel, and written summary here.
The NERVA (Nuclear Engine for Rocket Vehicle Application) Program was a collective effort between the US Atomic Energy Commission and NASA.
The Saturn C-5N was designed as an evolutionary successor to the Saturn V, intended for the planned crewed mission to Mars by 1980, it would have cut crewed transit times to Mars to about 4 months, instead of the 8–9 months of chemical rocket engines. However the Mars mission, along with all work related to the evolutionary successors of the Saturn V, was cancelled in 1972 by the Nixon Administration.
The ground testing of the Nuclear thermal rocket engines intended for the Saturn C-5N still hold a number of combined rocket thrust and specific impulse records.
Fully stacked model: 
In 1969, NERVA’s successes spurred NASA-Marshall Space Flight Center director, Dr. Wernher von Braun, to suggest sending 12 astronauts to Mars aboard two rockets. Each propelled by three NERVA rocket engines. That mission would launch in November 1981 and arrive at Mars in August 1982.
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