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Does the particles involved in a star's final core collapse travel faster than the speed of light?

I've read that the final core collapse of a star happens within less than a second. It seems to me that the outer layers of particles would have to go faster than the speed of light for this to occur so quickly. Is this actually true? Have I misread? Miscalculated? Or else, how can it occur so quickly?

The 'core' of the star is much smaller than the whole star. At the time of the final core collapse of a star, the core itself is only about the size of Earth, and it contracts to something approximately sixteen kilometers across (diameter). So if the star core has a radius of about 6378 kilometers (Earth’s radius) when it begins to collapse, then it has to contract to something with a radius of about 8 kilometers. The outer particles thus have to travel 6370 kilometers in less than one second, but the speed of light is 300,000 kilometers per second, so they actually have plenty of time to collapse.

October 2008, Sarah Scoles (more by Sarah Scoles) (Like this Answer)

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