{"knowledge_schema": {"broad_category": "Astronomy \u2192 Stellar Distribution \u2192 Parallax", "refinement": "This problem examines the relationship between the observed number of stars and their parallax measurements, considering a uniform distribution of stars in space.", "specific_scope": "The focus is on understanding how the density of stars changes with varying parallax values, which are inversely related to the distance of stars from the observer.", "goal": "Identify the mathematical relationship that describes how the number of stars per unit range of parallax decreases as the parallax increases."}, "summary": "In this problem, we explore how the number of stars per unit range of parallax changes as the parallax value varies, assuming a uniform distribution of stars in the sky. The relationship is derived from the fact that as parallax increases (indicating that stars are farther away), the volume of space that each star occupies increases significantly, leading to a decrease in the number of stars observed per unit range of parallax. The correct answer is that the number of stars per unit range of parallax changes as 1/plx^4, reflecting the three-dimensional nature of space and the inverse square law."}