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Question

This is not particularly book related, but I m just curious wether the sun can engulf the earth during the red giant stage of its death

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Solution

No, the Earth will not be able to support life if the Sun becomes a giant star. Giant stars have large radii as their name implies. When the Sun becomes a giant star, it may become so large as to engulf Earth, in which case the planet will be destroyed. Even if this does not happen, the sun will expand so far out that the temperatures on Earth will become extremely high so that all oceans will evaporate away, and there will be no water left on Earth. So, no life which depends on water will be able to survive.

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