{"knowledge_schema": {"broad_category": "Astronomy \u2192 Stellar Characteristics \u2192 Stellar Observations", "refinement": "This problem involves analyzing the effects of surface features (dark spots) on the observed properties of a star.", "specific_scope": "The focus is on calculating the effective brightness or luminosity of a star with a specific filling factor of dark spots on its surface.", "goal": "Determine the effective brightness ratio of the star with dark spots compared to a star without spots."}, "summary": "This problem falls under the category of astronomy, specifically focusing on the characteristics of stars and how surface features like dark spots affect their observed properties. The task is to calculate the effective brightness of a star with a radius equal to that of the Sun, where one hemisphere has dark spots covering 20% of its surface. The goal is to find the effective brightness ratio, which will help in understanding how these spots influence the star's overall luminosity."}