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Why do astronauts age more slowly?
Short answer
Barely measurably, and biologically not at all. According to relativity, the clock of a fast-flying crew runs slightly slower, while at higher altitude it runs slightly faster; the net result, after months in orbit, is fractions of a second. The body, on the other hand, tends to age faster there, not slower.

Two effects pulling in opposite directions
According to special relativity, a moving clock runs slow compared to one at rest, and a space station moves very fast. According to general relativity, on the other hand, a clock runs faster the weaker the gravitational field at its location; in orbit, Earth's pull is somewhat weaker than at ground level. Both effects are real and are corrected for daily in satellite navigation. In low orbits, the velocity component dominates, so the crew's clock falls minimally behind.
The difference is minuscule
"Aging more slowly" sounds like years, but it's a matter of fractions of a second. Even after many months in space, the time difference compared to those who stayed on Earth is so small that it can only be detected with atomic clocks; no one notices it in everyday life. The effect would only become perceptible at speeds close to the speed of light or near extremely compact objects like neutron stars. Current spaceflight is far from both scenarios.
The body actually tends to age faster
From a biological standpoint, spaceflight is no fountain of youth. Bones and muscles weaken, the immune system reacts abnormally, fluid shifts toward the head are linked to vision changes, and outside the protective atmosphere the radiation dose rises markedly. Many of these changes reverse after return, others only partially. If astronauts look especially fit after long missions, that's due to selection, training, and medical care, not relativity.
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