This paper explores the possibility of passively controlling the reactivity of a nuclear thermal propulsion (NTP) reactor. The objective of this study is to limit the use of the radial control drums to start-up and shutdown procedures and ensure that the exact same operation is performed for each full-power burn. To achieve the goal, this work considers several design measures, which include a low-density burnable absorber in the tie-tube components of the core, the use of variable hydrogen density in the moderator element coolant passages, and the judicious selection of a modified mission profile to maximize the decay of 135Xe after operation. In addition, the improved stability from the enhanced fuel temperature feedback due to the implementation of low-enriched-uranium fuel is also exploited for the realization of passive reactivity control. In this work, a passive reactivity control system is implemented in the Superb Use of Low Enriched Uranium (SULEU) NTP core and analyzed in terms of its ability to fulfill a NASA Mars Mission Design Reference Architecture 5.0-style mission. It is concluded that the use of the control drums can be limited to start-up and shutdown operations only, eliminating operator input in order to maintain a constant power level in the core.