{"knowledge_schema": {"broad_category": "Physics \u2192 Astronomy \u2192 Stellar Observations", "refinement": "This problem involves understanding the relationship between parallax, distance, and the observed star count in a given area of the sky.", "specific_scope": "The focus is on how the star count changes with distance based on the given parallax relationship, specifically analyzing the mathematical implications of the parallax formula.", "goal": "Determine the mathematical relationship between star count and distance based on the provided parallax dependency."}, "summary": "This problem explores the relationship between star count and distance in astronomy, specifically how the count changes with parallax. Given that the star count varies as 1/plx^5, we need to derive how this translates to a change in star count with distance (r). The correct answer indicates that the star count changes with distance as r^3, which reflects the three-dimensional nature of space and how volume increases with distance."}