{"knowledge_schema": {"broad_category": "Astronomy \u2192 Exoplanets \u2192 Planetary Characteristics", "refinement": "This problem involves calculating the equilibrium temperatures of exoplanets based on their distance from a star and the star's properties.", "specific_scope": "The focus is on two exoplanets orbiting a star with known mass, radius, and temperature, and determining the ratio of their equilibrium temperatures given their orbital characteristics.", "goal": "Calculate the ratio of the equilibrium temperatures of the two exoplanets based on their distances from the star and the star's effective temperature."}, "summary": "This problem is centered on the study of exoplanets and their thermal characteristics, specifically their equilibrium temperatures. Given the properties of a star and two orbiting planets, the task is to calculate the ratio of their equilibrium temperatures, which depends on their distance from the star and the star's effective temperature. The solution involves applying the principles of thermal equilibrium and the Stefan-Boltzmann law, leading to the conclusion that the ratio of their equilibrium temperatures is 0.53."}