36,260 mph
At least that is the highest velocity change ever given to a space craft by a rocket. I am not counting gravitational assist from a close pass with Jupiter or anything like that.
I say that and not 150,000 because most of the 150,000 in the above answer was not provided by our rocket power. And it is a speed with respect to the Sun, which means you could add the 66,000 MPH of Earth's orbit to the space shuttle's 17,500 MPH to get 83,500 MPH for anything in Earth orbit. If you want to do that, you can also add the millions of MPH at which the Sun is orbiting the galaxy.
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