{"knowledge_schema": {"broad_category": "Physics \u2192 Relativity \u2192 Time Dilation", "refinement": "This problem involves the effects of special relativity, particularly time dilation experienced by an astronaut traveling at a significant fraction of the speed of light.", "specific_scope": "The focus is on calculating the perceived travel time for an astronaut moving towards Earth at 0.99999987 times the speed of light, considering the relativistic effects on time.", "goal": "Determine the time experienced by the astronaut during the journey to Earth, given their speed and the principles of time dilation."}, "summary": "This problem explores the concept of time dilation in the context of special relativity, where an astronaut travels at a speed very close to the speed of light. The task is to calculate how long the journey to Earth will feel for the astronaut, given their speed of 0.99999987 times the speed of light. The goal is to find the perceived travel time, which is approximately 81 years, despite the long duration from an external observer's perspective."}