{"knowledge_schema": {"broad_category": "Astronomy \u2192 Exoplanets \u2192 Thermal Properties", "refinement": "This problem involves calculating the equilibrium temperatures of exoplanets based on their orbital periods and albedo.", "specific_scope": "The focus is on determining the temperature ratio between two specific exoplanets (Planet_4 and Planet_2) that are in orbital resonance and have the same albedo.", "goal": "Calculate the ratio of the equilibrium temperatures of Planet_4 to Planet_2 using their orbital periods."}, "summary": "This problem is centered on the thermal properties of exoplanets, specifically calculating the equilibrium temperatures based on their orbital periods and albedo. Given that the planets have the same albedo and are in a specific ratio of orbital periods, the task is to find the temperature ratio between Planet_4 and Planet_2. The solution involves applying the formula for equilibrium temperature, which is influenced by the distance from the star and the albedo, to derive the required ratio."}