Why do astronauts float in space?

Why do astronauts float in space?

Astronauts float not because there is no gravity, but because they are in continuous free fall. At the International Space Station's altitude of about $400$ km gravity is still almost $90\%$ as strong as on the ground; the station and everyone inside simply fall around Earth together, so nothing pushes on anyone.

Is there gravity on the space station?

Yes. Gravity weakens with the square of distance from Earth's centre, but it never reaches zero. At height $h$ above the surface, with Earth's radius $R \approx 6371$ km:

So why do they float?

Weight, as we feel it, is not gravity itself but the contact force that stops us falling: the floor pushing up on your feet. In free fall that force disappears. Astronaut and station accelerate toward Earth at exactly the same rate, so the astronaut and the floor never press on each other. It is the same feeling as being in an elevator whose cable has snapped, or at the top of a roller-coaster drop.

Aircraft can reproduce it briefly: on a parabolic flight the plane follows a free-fall arc and passengers float for about $20$ seconds.

Why doesn't the ISS fall to the ground?

It does fall, but it also moves sideways very fast. Imagine firing a cannonball horizontally from a tall mountain: faster shots land farther away, and at a great enough speed the ground curves away beneath the ball as quickly as the ball drops. It never lands, and that is an orbit. For a circular orbit of radius $r$ the required speed and the period are:

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