{"knowledge_schema": {"broad_category": "Astronomy \u2192 Exoplanet Studies \u2192 Orbital Mechanics", "refinement": "This problem involves understanding the relationships between the physical properties of exoplanets, such as temperature and mass, and their orbital periods based on Kepler's laws.", "specific_scope": "The focus is on calculating the orbital period of Planet3 in relation to Planet1 using the given ratios of temperatures and masses, along with the assumption of equal albedo.", "goal": "Determine the factor by which the orbital period of Planet3 is larger than that of Planet1."}, "summary": "This problem is rooted in astronomy and orbital mechanics, specifically examining the relationships between the equilibrium temperatures and masses of three exoplanets to derive their orbital periods. By applying Kepler's laws and the given ratios of temperatures and masses, the objective is to calculate how much larger the orbital period of Planet3 is compared to Planet1. The solution will involve using the ratios provided and the assumption of equal albedo to find the correct factor from the given options."}