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Because everything is in free fall, traveling at the same speed: the space station, the person & everything else.

Its the same thing as being in a falling elevator. The elevator is falling at the same speed as the person. If there was a scale in that falling elevator, the person would be weightless. Unlike the satellite which can fall around the earth for many, many years, the elevator ride to the basement will not last long.

It the same as being on an airplane that suddenly dives at the same acceleration as gravity (9.8m/s/s). You, the plane, and everything in the plane is falling at the same rate. If there was a scale there, you would weigh nothing, until the plane pulled out of its dive.

Knowing the acceleration of gravity on the moon, Mars etc..., can be recreated in such a plane. They only need to dive at such an acceleration that it cancels the right amount of Earth's gravity. So the Moon's gravity is 1/6th that of Earth, or, things fall at 1.6m/s/s. So the plane would only dive to remove 8.2m/s/s of Earth's gravity, leaving 1.6m/s/s. The same can be done for simulating Mars' gravity, etc.... This allows Moon walkers to practice walking techniques while wearing their spacesuits.

Its almost the same as being in a roller coaster going down a big hill. The cart, seat and you are all falling at the same speed, you feel ~weightless (briefly).

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Q: Why a person in satellite feels weightless?
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