Question

Why do astronauts “float” in space? Explain this fully, along with what it has to do with centripetal acceleration.

Answer 1

The space station orbits around the Earth at a height of around 400 km from the surface. At that heigh the gravity is still around 9.8 m/s². But the astronauts inside the space station experience "zero gravity" because of the space station's orbital motion.

The orbital motion of the space station in a circular path creates a centripetal force in the space station's frame which is equal to

where v is the orbital speed of the space station and r is the distance of the space station from the center of the earth and m is the mass of the astronaut inside the space station. This centripetal force acts radially outwards(away from the earth) on the astronaut.

The astronaut also experiences a gravitational force due to earth and this force acts towards the earth

Since these 2 forces act in opposite direction, their magnitude is such that they cancel out

And hence the net force on the astronaut is zero. This is the reason why the astronauts feel "zero gravity" in the space station and "float" in space.