{"knowledge_schema": {"broad_category": "Astronomy \u2192 Stellar Distribution \u2192 Parallax", "refinement": "This problem examines the relationship between the observed parallax of stars and their distribution in space, considering the effects of distance on brightness and visibility.", "specific_scope": "The focus is on understanding how the number of stars per unit range of parallax changes as the parallax value varies, under the assumption of uniform distribution of stars in the sky.", "goal": "Identify the correct mathematical relationship that describes how the number of stars per unit range of parallax (plx) changes with plx."}, "summary": "In this problem, we are exploring the relationship between the parallax of stars and their distribution in the sky, assuming a uniform distribution. The goal is to determine how the number of stars per unit range of parallax changes with varying parallax values. The correct answer reflects the inverse relationship between the number of stars and the square of the parallax, which is represented by the option 3: 1/plx^2. This indicates that as the parallax decreases (indicating greater distance), the number of stars per unit range of parallax increases significantly."}