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True; they are not "weightless". Every object has mass, and mass generates gravity. So a person (who has mass) near the Earth (which has mass) will have a weight that is dependent on the sum of the masses divided by the square of the distance between them. So astronauts in orbit are being affected by the gravity of the Earth, which is close, and by the Sun, which is farther away but is far more massive. To some tiny extent, all of us are also affected by the gravities of the Moon and other planets such as Venus, Mars and Jupiter, and even by the other stars - and other galaxies. But those are so far away that the effect is entirely negligible.

So why don't the astronauts FEEL the affects of gravity? Because they, and the ISS, are in "free fall"; they are falling toward the Earth. But because they are moving a bit over 18,000 miles per hour, the ISS and the astronauts keep MISSING the Earth! It's a delicate balance - falling AROUND the Earth, without ever hitting it.

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