{"knowledge_schema": {"broad_category": "Astronomy \u2192 Stellar Density \u2192 Parallax and Distance", "refinement": "This problem examines the relationship between the observed number of stars and their distance from the observer, specifically how parallax affects star density.", "specific_scope": "The focus is on understanding how the number of stars varies with distance based on the given parallax relationship, which is inversely proportional to the fifth power of parallax.", "goal": "Determine the mathematical relationship between the number of stars and distance, leading to the conclusion that the number of stars changes with the cube of the distance."}, "summary": "In this problem, we explore how the number of stars in a specific region of the sky varies with distance based on the parallax effect. The relationship given is that the number of stars is inversely proportional to the fifth power of parallax (1/plx^5). Since parallax is inversely related to distance, we can derive that the number of stars changes with the cube of the distance (r^3). Thus, the correct answer is that the number of stars varies as r^3 with distance."}