{"knowledge_schema": {"broad_category": "Astronomy \u2192 Exoplanetary Systems \u2192 Orbital Dynamics", "refinement": "This problem involves understanding the relationship between the orbital periods of planets and their sizes in relation to their host star, as well as the conditions for transit and occultation events.", "specific_scope": "The focus is on determining the maximum orbital period of a second planet that can transit and occult a star, given the parameters of a first planet that is already transiting.", "goal": "Calculate the maximum orbital period of the second planet based on its size and the conditions required for it to transit and occult the star."}, "summary": "This problem is rooted in astronomy and involves calculating the orbital dynamics of exoplanets. It requires understanding how the size of a planet and its orbital period relate to the ability to transit and occult a star. Given a first planet with a known orbital period and size, the task is to determine the maximum orbital period of a second, larger planet that can still exhibit both transit and occultation events. The solution involves applying Kepler's laws and geometric considerations related to the sizes of the planets and the star."}