With recent breakthroughs in AI and deep learning, applying these techniques to on-board computers for space applications has grown in interest to engineers on space applications. The space field brings its own challenges, such as reliability and power restrictions. The proposed solution in this work concerns a neuromorphic accelerator for a spiking neural network (SNN) designed using memristive devices (RRAM), dubbed the Newtype Learning Computer. To this end, this work presents the following contributions: A design for a behavioral VHDL implementation of a target SNN boasting software-level accuracy, specifically built for edge AI in space. We also present a characterized ASIC design of one layer of this SNN, analyzed using RTL design tools. An analysis of this same layer designed using Memristive Crossbar Arrays is also provided, and we present a comparison of both. When simulating 4096 neurons, the RRAM-based design shows 174x smaller area, power dissipation reduction of 27x energy reduction by 4 orders of magnitude and over 80x faster by latency compared to the CMOS-based design. This thesis presents a confident first step towards the use of RRAM-based neuromorphic accelerators for spiking neural networks in space-based applications.