What is the relationship between the density of the solar nebula and its free-fall time?
Answer
Higher density leads to a faster collapse due to the inverse relationship
The free-fall time represents the theoretical duration required for a cloud to collapse to a central point if no other forces, such as rotation or magnetic fields, oppose it. This duration is inversely proportional to the square root of the cloud density. As the nebula begins to collapse, its density increases, which leads to a corresponding decrease in the free-fall time. Consequently, the collapse process gains momentum over time. This accelerating nature of the collapse allows a diffuse cloud to transform into a dense stellar core within a relatively brief astronomical timeframe.
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