An astronaut is said to be "weightless" while inside a spacecraft in orbit above the Earth. This is not really true!
Any object that is traveling in a circular path (such as an astronaut in orbit) does so under the influence of a force acting at right angles to velocity: physicists call this force centripetal force (which means "center-seeking"). Centripetal force acts to change the direction of motion: it steers an object away from the straight-line path it would otherwise take (see my page on circular motion for more detailed information).
According to Isaac Newton's Universal Law of Gravitation, the attractive force between the Earth and any object is inversely proportional to the square of the distance between the center of the Earth and that object-- however, gravity has an infinite range and while it is weaker at an altitude of 200 miles it is by no means zero. In fact, an object in orbit has less weight than it would have at the Earth's surface but the weight cannot possibly be zero in orbit; otherwise there would be no centripetal force to keep an orbiting spacecraft from flying away from Earth in a straight line.
So where does the sensation of weightlessness come from? Rather than being an absence of weight, weightlessness is felt whenever a person is in a situation where their weight is unopposed. When you stand on the scale in your bathroom to weigh yourself, the scale provides an upward force on your feet to balance the downward pull of gravity on you, resulting in a net force of zero on your body (ie. equilibrium, you don't move). The scale doesn't actually read your weight: it reads normal force which the scale is providing upward on you. You can prove this by taking a bathroom scale into an elevator-- when the elevator is accelerating upward or downward, the reading on the scale changes relative to your usual weight and since gravity hasn't changed, it must be the changable upward force on your feet that is being shown on the scale! If the elevator were to fall freely down the elevator shaft (unpleasant thought), the scale would read zero and you would feel weightless. You get the exact same sensation for a brief instant when you are between strides while running, or when you are going over the top of a very fast roller coaster ride or ferris wheel at the amusement park.
So weightlessness is felt whenever a body is in free fall, such that the only force acting on the body is the force of gravity (the force of weight). Astronauts in orbit are actually in free-fall, in the same sense that a skydiver is-- only the forward motion is so fast that the curved Earth's surface gets out of the way preventing contact with the ground.
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