{"knowledge_schema": {"broad_category": "Astronomy \u2192 Stellar Properties \u2192 Effective Temperature and Luminosity", "refinement": "This problem involves calculating the luminosity of a star based on its effective temperature and radius, considering the effects of dark spots on its surface.", "specific_scope": "The focus is on a specific star with given parameters (radius, mass, and effective temperature) and how these parameters relate to its luminosity when dark spots are present.", "goal": "Determine the luminosity of the star in solar units, taking into account the changes in effective temperature due to dark spots."}, "summary": "This problem falls under the category of astronomy, specifically dealing with the properties of stars. It requires calculating the luminosity of a star based on its effective temperature and radius, while also considering the impact of dark spots on its surface. The goal is to find the luminosity in solar units, which involves applying the Stefan-Boltzmann law and understanding how effective temperature influences luminosity. The answer provided is 4.2, indicating the calculated luminosity of the star."}