||The Solar System has multiple destinations that private and governmental space agencies are planning to explore. Missions within the Solar System are both exorbitantly expensive and time intensive projects that involve high risks for the organizations involved. A mission that is currently being developed by multiple agencies is a human mission to Mars. In planning a mission to Mars and other similar targets, a critical design parameter to consider is the most effective propulsion system to transport the crew and payload to the destination in a given time frame. To understand the most effective propulsion system for space exploration, this analysis will use current parameters for a mission to Mars to compare the advantages and disadvantages of the chemical rocket with nuclear thermal propulsion. This assessment compares the two rockets due to their similar thrust capabilities and years of testing and development. Through numerical, graphical, and simulation data, this study validates that nuclear thermal propulsion, perating under an initial thrust-to-weight ratio of 0.11, can complete a mission from low Earth orbit to low Mars orbit within the same ten-month time frame as a chemical rocket. The numerical data in this analysis also shows that the nuclear thermal rocket is able to deliver 127,727.11 kilograms of payload to low Mars orbit, which is an extra 50,807 kilograms of payload when compared to a chemical rocket of the same size. By utilizing the extra payload carried by a nuclear thermal rocket, and an estimated budget of $23 billion for NASA to develop a chemical rocket as part of the Space Launch System to be used for a crewed mission beyond the moon's orbit , this paper shows that a nuclear thermal rocket would decrease the overall payload cost per kilogram by $430,000. This decrease would result in a total payload cost difference of $9.18 billion when considering the single mission. Once future program budgets are developed showing the total life-cycle of the Space Launch System program, a new payload cost difference can be calculated to compare the costs of the rockets' payloads over multiple missions. Due to the nuclear thermal rocket's superior payload capacities, which results in a large difference in the cost per kilogram of payload, this analysis hopes to provide further evidence that nuclear thermal rockets should be seriously considered for space exploration missions. It is the recommendation of this study that an in -depth analysis of the total cost to design, build and launch a nuclear thermal rocket be performed. If the nuclear thermal rocket can provide future savings in space exploration, the government along with other private organizations need to devote more resources to designing a safe and efficient nuclear thermal rocket that will allow for better access to the Solar System.