{"knowledge_schema": {"broad_category": "Physics \u2192 Astrophysics \u2192 Stellar Properties", "refinement": "This problem involves understanding the relationship between a star's radius, mass, temperature, and luminosity, particularly in the context of black body radiation.", "specific_scope": "The focus is on comparing the luminosities of two stars based on their physical properties (radius and mass) and their spectral characteristics (peak wavelength).", "goal": "Calculate the factor by which the luminosity of Star_A is greater than that of Star_B using the Stefan-Boltzmann law."}, "summary": "This problem is rooted in astrophysics, specifically in the study of stellar properties and their relationships. It examines two stars, Star_A and Star_B, with known differences in radius and mass, and requires the application of the Stefan-Boltzmann law to determine their luminosities. Given that both stars have the same peak wavelength, we can infer that they have the same temperature. The goal is to calculate the luminosity ratio, which is influenced by the stars' radii and temperatures, leading to the conclusion that Star_A's luminosity is approximately 3.92 times greater than that of Star_B."}