{"knowledge_schema": {"broad_category": "Astronomy \u2192 Exoplanet Detection \u2192 Radial Velocity Method", "refinement": "This problem involves understanding the relationship between the mass of a planet, the mass of its host star, and the resulting radial velocity (RV) signal detected from the star's spectrum.", "specific_scope": "The focus is on comparing the periodic shifts in spectral lines caused by two exoplanets orbiting stars of similar mass, and how these shifts relate to the orbital periods of the planets.", "goal": "Determine the ratio of the orbital periods of the two planets based on the detected radial velocity shifts."}, "summary": "This problem involves the study of exoplanets and their detection through the radial velocity method, which measures shifts in spectral lines due to the gravitational influence of orbiting planets. The key to solving the problem lies in understanding that the amplitude of the radial velocity shift is related to the mass of the planet and the orbital period. By comparing the periodic shifts of the two planets, we can derive the ratio of their orbital periods. The goal is to find out how many times longer the orbital period of planet #2 is compared to planet #1."}