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How fast do astronauts travel in space?
Short answer
It depends on the orbit. Astronauts on the International Space Station travel at about 7.7 km/s, close to 28,000 km/h, circling Earth roughly every 90 minutes. On a trip to the Moon the departure speed was around 10.8 km/s, and the Apollo capsules re-entered the atmosphere at about 11 km/s.

Orbital altitude sets the speed
An object in orbit doesn't choose its speed: altitude dictates it. To stay at 400 km above Earth's surface, where the International Space Station flies, it must move at about 7.7 km/s, nearly 28,000 km/h. Slower, the trajectory curves too sharply and the vehicle re-enters; faster, the orbit rises. At that speed the station completes one trip around the planet every ninety minutes, and its crew sees sixteen sunrises and sixteen sunsets each day.
The higher the orbit, the slower the travel: a geostationary satellite, at 35,786 km, covers its circle at about 3.1 km/s and takes exactly one day to go around.
Leaving Earth orbit costs more
To leave Earth's vicinity requires much higher speeds. Apollo crews began their trajectory toward the Moon at about 10.8 km/s, close to escape velocity, and from there Earth's gravity slowed them down over the three-day trip. The return reversed the process: the capsule reached the upper atmosphere at about 11 km/s, the highest speed ever reached by human beings.
Speed that goes unnoticed
None of this is felt on board. With no air to produce noise or turbulence, and no nearby reference points, the sensation of movement disappears completely; only the parade of the Earth's landscape beneath the observation cupola gives away the motion. What does matter is relative speed: a docking with the station is carried out with differences of just a few centimeters per second, even though both vehicles share that 28,000 km/h relative to the ground.
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