{"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 orbital periods of two exoplanets detected around stars of similar mass using the radial velocity method, based on the amplitude of the spectral line shifts.", "goal": "Determine the ratio of the orbital periods of the two planets based on the differences in the detected radial velocity shifts."}, "summary": "This problem involves the study of exoplanets and their detection through the radial velocity method, which measures the periodic shifts in spectral lines due to the gravitational influence of orbiting planets. The key to solving this problem lies in understanding how the amplitude of the radial velocity shift relates to the orbital period of the planet. Given that both stars have similar masses and the planets have similar masses, the ratio of the shifts in the spectral lines can be used to determine how many times longer the orbital period of planet #2 is compared to planet #1."}