How fast do astronauts travel in space?

What keeps a spacecraft up is not height but pace. At station altitude the vehicle is still deep inside Earth's gravity well; it stays up because it moves sideways fast enough that the curve of its fall matches the curve of the planet beneath it. NASA quotes about 28,000 km/h (17,500 mph), close to 5 miles per second, which works out at one orbit every 90 minutes and sixteen sunrises a day. The figure is not a choice. Slow down and the orbit decays into the atmosphere; speed up and it climbs to a higher, slower one.

The number rises as soon as a crew leaves that regime. Escaping Earth's pull altogether takes around 11.2 km/s, roughly 40,000 km/h, and Apollo crews were accelerated to close to that value by the Saturn V's third stage before coasting towards the Moon, losing speed the whole way out. Coming home, every bit of that energy had to be shed again into the atmosphere, which is why lunar-return capsules needed a far deeper heat shield than anything dropping back from low orbit.

Speed by itself produces no sensation; acceleration does. Once the engines shut down, crew and vehicle share an identical free-fall trajectory, so nothing presses anyone into a seat and there is no way to distinguish 28,000 km/h from standing still except by looking out of a window. Relative speeds are what matter operationally: a visiting cargo ship closes the last few metres at walking pace, because both vehicles are already travelling at almost exactly the same enormous velocity.