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The question is moot because I don't think the shuttle can break orbit. However, in an effort to give you some usefull answer, it took about 3 days for the Apollo missions to reach the moon, and the Sun is about 400 times further than the moon. I would suggest that the speed they were traveling to the moon it would take years. There is no reason to suppose that any craft carrying human cargo would be limited to the speeds we used on the voyages to the moon. Typical estimates for getting to Mars (about half as far from the Earth as it the EArth is from the sun) are about 6 months. That would suggest we could get to the sun in just a year. But I think the sun is an easier target to hit because of its huge gravity that pullls you in as you get closer. So as my final answer I am going to say it would be on the order of months, between 6 and 18 months depending on what orbit you were trying to achieve.

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Q: How long would it take to get to the sun in the fastest space shuttle?
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