While in orbit, and to maintain orbit, the space shuttle goes about 17,500 miles per hour. The exact speed of the shuttle varies based on the orbital altitude which ranges from 190 to 330 miles above sea level. The altitude varies based on the purpose of the mission.
Also note that a rocket can go increasingly fast, as long as its fuel lasts. No mission ever tried to get the shuttle up to its “top speed”, because that would simply have thrown it into a high Earth orbit where there wasn’t anything particularly useful to do.
The shuttle could not make a flight to the moon, because it would run out of fuel. But if we wanted to get to the moon in 6 hours, in different rocket we could — it’s just that it would cost an incredible fortune. Eventually a rocket continuously firing would come close to the speed of light, at which point it could go very little faster, because the speed of light is the maximum speed in the universe, except perhaps in very specialized conditions.
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