With the new NASA directive of returning to the Moon in 2024 as a stepping stone to missions to Mars and beyond, there is a renewed interest in developing nuclear thermal rockets (NTR) to reduce trip times. This thesis will focus on the analysis of a conceptual reactor design for use as an NTR. The low enriched uranium centrifugal gas core reactor (CGCR) is a low technology readiness level (TRL) concept that uses centrifuge technology to separate uranium gas from hydrogen propellant. There is also a new US directive for additional focus on research and development of reactors that utilize low enriched uranium (LEU) instead of high enriched uranium (HEU). The inclusion of a moderator in between the gas enables the use of LEU and a lower mass system compared to previous gas core concepts. In addition, the CGCR operates at lower temperatures than previous gas core concepts enabling higher uranium densities, which suggests that the centrifugal separation will aid in minimization of uranium entrainment. This research will cover a thorough analysis of neutronics, thermal transport, fluid dynamics, and comparison to alternative NTR designs utilizing computational methods, such as the Monte Carlo N-Particle transport code MCNP, and analysis software platforms Mathematica and MATLAB.