{"knowledge_schema": {"broad_category": "Physics \u2192 Astronomy \u2192 Orbital Mechanics", "refinement": "This problem involves understanding the relationship between the mass of a planet, its orbital period, and the gravitational influence it has on its host star, as indicated by the spectral line shifts.", "specific_scope": "The focus is on comparing the orbital periods of two planets based on the periodic shifts they cause in the spectral lines of their respective stars.", "goal": "Determine the ratio of the orbital periods of Planet A to Planet B based on the observed spectral shifts."}, "summary": "This problem falls under the category of orbital mechanics in astronomy, where we analyze the relationship between a planet's mass, its orbital period, and the gravitational effects it has on its star. The periodic shifts in spectral lines provide a way to infer the gravitational influence of the planets. The goal is to calculate how many times longer the orbital period of Planet A is compared to that of Planet B, based on the given shifts of 8 miliangstroms and 6 miliangstroms, respectively. The answer indicates that Planet A's orbital period is 1.68 times longer than that of Planet B."}