{"knowledge_schema": {"broad_category": "Astronomy \u2192 Stellar Properties \u2192 Luminosity", "refinement": "This problem involves understanding the relationship between a star's radius, mass, and luminosity, particularly in the context of black body radiation.", "specific_scope": "The focus is on comparing the luminosities of two stars with different radii and masses, while considering their spectral characteristics and radial velocities.", "goal": "Calculate the factor by which the luminosity of Star_1 exceeds that of Star_2 based on their physical properties."}, "summary": "This problem examines the luminosity of two stars with different sizes and masses, using the principles of black body radiation. Given that Star_1 has a radius and mass 1.5 times larger than Star_2, the task is to determine how much greater Star_1's luminosity is compared to Star_2's. The solution involves applying the Stefan-Boltzmann law, which relates a star's luminosity to its radius and temperature, to find that Star_1's luminosity is greater than Star_2's by a factor of 2.23."}