{"knowledge_schema": {"broad_category": "Physics \u2192 Astronomy \u2192 Stellar Brightness", "refinement": "This problem examines the relationship between the brightness of stars and their distance from the observer, specifically in the context of parallax measurements.", "specific_scope": "The focus is on understanding how the brightness of stars changes with distance based on the given relationship of brightness varying with the inverse fourth power of parallax.", "goal": "Determine the mathematical relationship between the brightness of stars and their distance, expressed in terms of distance (r)."}, "summary": "This problem involves the study of stellar brightness in astronomy, specifically how it varies with distance. The brightness of stars is given to vary as 1/plx^4, where plx (parallax) is inversely related to distance. By understanding that parallax is inversely proportional to distance (plx \u221d 1/r), we can derive that brightness varies with the square of the distance (r^2). Thus, the answer to how brightness changes with distance is r^2."}