IIRC, The escape velocity from an orbit is the orbital velocity multiplied by 1.414 (the square root of 2). So, if you are in orbit, traveling at 17,000 mph, the escape velocity will be just over 24,000 mph.
Fascinating stuff. I was researching for a story on Apollo 8 a while back and I thought it was pretty neat that the crew never left earth orbit. They went fast enough to make a long loop away from the planet, and by the time they reached the moon’s orbit, they had slowed down to somewhere around the speed of a bullet.
Considering all the calculations that it would take to send astronauts out to a specific point where they will be intercepted by the moon’s gravity, along a course so specific so they can map a certain section of the moon, then blast off again to a point where they will re-enter the atmosphere at a precise angle (so as not to bounce off and be lost forever, or burn up) and splash down right next to an aircraft carrier is beyond spectacular.
Keep in mind that their computers were extraordinarily primitive (the smart phones in our pocket are around 1,000,000 times more powerful), the earth was rotating, the moon was rotating around the earth, and both were traveling tens of thousands of miles per hour. And we were going somewhere where no humans had ever gone before.