Large language models (LLMs) demonstrate strong performance in natural language processing but often generate factual errors when relying solely on parametric knowledge. Retrieval-Augmented Generation (RAG) mitigates these errors by grounding responses in external evidence, yet conventional retrieve-and-dump approaches frequently introduce irrelevant context that degrades answer quality. In this work, we present AstroRAG -- a PageRank-based retrieval-augmented generation (RAG) pipeline adapted for question answering in astronomy. The system performs token-aware chunking and per-instance, ephemeral indexing in Elasticsearch, then executes a two-stage retrieval: (i) Maximal Marginal Relevance (MMR) to obtain a small, diverse candidate set and (ii) a reader-driven PageRank (PR) re-ranking on a similarity graph to identify a compact, mutually supportive context under a strict token budget. Our design is training-free, privacy-preserving, and reproducible, as each instance is processed through transient indexing to prevent cross-task leakage. We evaluate the pipeline on the AstroQA benchmark for astronomy QA, and demonstrate competitive performance across all difficulty levels. In particular, the RAG-enhanced Mistral-7B achieves \textbf{79.49\% accuracy} and \textbf{79.49\% F1-score}, nearly doubling the performance of its non-RAG counterpart. These results highlight the effectiveness of disciplined retrieval and refinement in boosting domain-specific reasoning, establishing a robust foundation for extending RAG to other scientific fields.