Solar activity, including solar flares, coronal mass ejections (CMEs), and geomagnetic storms, can significantly impact satellites, aviation, power grids, data centers, and space missions. Extreme solar events can cause substantial economic damage if not predicted in advance, highlighting the importance of accurate forecasting and effective education in space science. Although large language models (LLMs) perform well on general tasks, they often lack domain-specific knowledge and pedagogical capability to clearly explain complex space science concepts. We introduce SolarGPT-QA, a question answering system based on a domain-adapted large language model built on the LLaMA-3 base model. The model is trained using scientific literature and large-scale question-answer data generated with GPT-4 and refined using Grok-3 in a student-friendly storytelling style. Human pairwise evaluations show that SolarGPT-QA outperforms general-purpose models in zero-shot settings and achieves competitive performance compared to instruction-tuned models for educational explanations in space weather and heliophysics. A small pilot student comprehension study further suggests improved clarity and accessibility of the generated explanations. Ablation experiments indicate that combining domain-adaptive pretraining with pedagogical fine-tuning is important for balancing scientific accuracy and educational effectiveness. This work represents an initial step toward a broader SolarGPT framework for space science education and forecasting.