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How many times has Earth orbited the sun?
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With an age of 4.5 billion years one could expect 4.5 billion trips around the sun - but this is only valid if earth always stayed in it's current orbit. It is a good estimate, though, as the only event that could have resulted in a noticable change of orbit was probably the creation of the moon, which also belongs in the 4.5 billion years ago category.