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It took the universe 13.8 billion years to cool down.
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The solar system was formed after the big bang (4.977 billion years), the stardust that was created at the bang began forming planet and stars. e.i The sun, moon, and earth.
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The moon was formed out of the debris created after a collision between a smaller proto-Earth and another planetoid.
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The earth cooled after 4.5 billion years.
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The end of the heavy bombardment occurred sometime between 4.5 to 3.8 billion years ago.