Answer
Astronauts do not need to be a certain distance from the earth in order to feel weightless.
Work Step by Step
To feel weightless, we do not need to be a certain distance from the earth. We can feel weightless whenever we are in free-fall and there is no normal force pushing against us. For example, when people jump out of airplanes, they feel weightless as they are in free-fall toward the ground.
Astronauts in orbit feel weightless because they are in free-fall. Orbital motion is a special case of free-fall, where an object is moving at just the right speed to keep the object moving around in orbit. That is, the gravitational force is equal to the required centripetal force to keep the object moving around in a circle.
Therefore, astronauts do not need to be a certain distance from the earth in order to feel weightless.
