Recent trends are emerging in the use of Large Language Models (LLMs) as autonomous agents that take actions based on the content of the user text prompts. We intend to apply these concepts to the field of Guidance, Navigation, and Control in space, enabling LLMs to have a significant role in the decision-making process for autonomous satellite operations. As a first step towards this goal, we have developed a pure LLM-based solution for the Kerbal Space Program Differential Games (KSPDG) challenge, a public software design competition where participants create autonomous agents for maneuvering satellites involved in non-cooperative space operations, running on the KSP game engine. Our approach leverages prompt engineering, few-shot prompting, and fine-tuning techniques to create an effective LLM-based agent that ranked 2nd in the competition.