{"knowledge_schema": {"broad_category": "Astronomy \u2192 Exoplanet Studies \u2192 Orbital Dynamics", "refinement": "This problem involves understanding the relationships between the physical properties of exoplanets, such as temperature and mass, and their orbital characteristics.", "specific_scope": "The focus is on calculating the orbital period of Exo3 in relation to Exo1 using the given ratios of temperature and mass, applying Kepler's laws of planetary motion.", "goal": "Determine the factor by which the orbital period of Exo3 is greater than that of Exo1 based on the provided ratios."}, "summary": "This problem is rooted in astronomy, specifically in the study of exoplanets and their orbital dynamics. It requires understanding how the equilibrium temperature and mass ratios of the planets relate to their orbital periods. By applying Kepler's laws, we can derive the relationship between the orbital periods of Exo1 and Exo3. The goal is to find the factor by which Exo3's orbital period exceeds that of Exo1, leading to the answer of 33.4."}