Weight is defined as the force of gravity. Strictly, then the only way one can be weightless is to be so far from any massive object, like a planet or star, that the gravitational field is zero! No human has achieved this state. In a satellite the gravitational field is about 80% as large as it is on Earth’s surface, so the force of gravity on an astronaut in the satellite is not much smaller than it is on the astronaut on Earth.

How do you measure weight? If you stand on a scale, the scale measures the upward force of the scale on your feet. According to Newton’s Third Law, that force is equal to the downward force of your feet on the scale. (Actually, there is a slight difference because of the rotation of Earth.) If you stand on a scale in an elevator, you’ll see that your “weight” changes as the elevator accelerates. When it is going up and increases its speed, the scale will record a larger weight. The same will happen when you are going down and come to a stop. When it slows while going up or speeds up while going down the scale will show a smaller weight. Newton’s Second Law can explain these changes using the fact that a net force is needed to accelerate you along with the elevator. (Note that you don’t really need a scale to sense these accelerations. You can feel them in your stomach!)

What would happen if the cable holding the elevator would break? You and the elevator would both be in free-fall, accelerating at g. There would be no weight shown on the scale. You and the elevator would both be in the state of “apparent weightlessness.” We’ll meet this term again when we explore the motion of satellites. The apparent weightlessness of astronauts will be explained there.