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How fast do astronauts travel to the moon?
Short answer
Speed changed constantly. Apollo 11 covered the 384,400 km to the Moon in just over four days from lift-off to touchdown. But the pace was never steady: the spacecraft was fastest in the minutes after leaving Earth orbit and slowest near the midpoint, where Earth's pull had almost stopped its climb.

A crossing measured in days, not in cruise speed
There is no cruising speed on the way to the Moon, because nothing is thrusting. A lunar spacecraft accelerates hard for a few minutes, then coasts for the rest of the journey, gaining and losing speed exactly as gravity dictates. Apollo 11 left the pad on 16 July 1969 and landed on 20 July, so the 384,400 km that separate Earth and Moon on average were crossed in a little over four days from lift-off to touchdown. No single speed describes any real moment of that trip.
Fast at the bottom of the hill, slow at the top
The profile is the interesting part. The burn out of Earth orbit, the translunar injection, is where the spacecraft is fastest; from then on it is climbing out of Earth's gravity well and losing speed the whole way, like a ball thrown upwards. Because Earth is far more massive than the Moon, the point where the two pulls balance lies much closer to the Moon, and by then the vehicle is crawling. Then it accelerates again, falling towards the Moon, and must brake into orbit or sail past.
The same arithmetic for the next crews
The return is the mirror image, and it ends with the only genuinely high speed of the trip: a capsule coming back from the Moon meets the atmosphere far faster than one returning from low Earth orbit, which is why lunar heat shields are a category of their own. Artemis crews fly the same arithmetic, with outbound legs counted in days rather than hours, and nothing on the drawing board changes it. A shorter trip is possible, but every hour saved is bought with propellant on departure and paid for again on arrival.
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