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How long does it take a space shuttle to reach the Moon?

Short answer

It never reached it and never could: the space shuttle was a low Earth orbit vehicle, designed for altitudes between 185 and 643 kilometers (115 to 400 statute miles). The Moon is 384,400 kilometers (238,855 miles) away on average, a scale completely beyond its reach.

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A vehicle built for low Earth orbit

The space shuttle was never a lunar vehicle. It was designed to reach orbits between roughly 185 and 643 kilometers in altitude (115 to 400 statute miles), the range where satellites are deployed, scientific instruments are repaired, and a station is assembled. To stay there it flew at about 17,321 mph, and its missions were usually planned to last between five and sixteen days; the longest of all, STS-80 in November 1996, ran 17.5 days. None of those figures belongs to the problem of getting to the Moon.

The real scale of a lunar trip

The Moon orbits at an average distance of 384,400 kilometers (238,855 miles) from Earth. Reaching it isn't about climbing higher, it's about accelerating enough to leave Earth orbit, which requires a trans-lunar injection stage the shuttle neither carried nor could have carried in its payload bay. Its heat shield wasn't designed for a reentry at the speed of a return from the Moon either, far higher than a return from low Earth orbit.

How long it takes for vehicles that actually can

For reference, crewed Apollo flights took several days to get there, with the fastest, Apollo 8, doing it in just under three days. That's the timescale of a crewed lunar trip, and no version of the shuttle was ever capable of attempting it. The question, then, has no numerical answer: the vehicle lacked the thrust needed to climb out of Earth's gravity well, not the time.

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