Apparent Weight and the Equivalence Principle

A bathroom scale cannot feel gravity. It can only feel you pressing down on it, and by Newton's third law, it pushes back up on you with a normal force N. That N is what the dial shows, and we call it apparent weight. Write Newton's second law for you standing on the scale, taking up as positive: N - mg = ma. Solve for N = m(g + a). When a = 0, N = mg, the scale matches true weight and everything feels normal. When the elevator accelerates upward, a is positive, N grows, and you feel heavier. When it accelerates downward, a is negative, N shrinks, and you feel lighter.

Push a downward to its extreme: if a = -g, the whole elevator is in free fall, N = 0, and the scale reads zero even though gravity is working exactly as hard as ever. This is the astronaut's situation. Orbit is not an escape from gravity — at a few hundred kilometers up, gravity is almost full strength. The astronaut and the station are both falling around Earth together, so the station never has to push on the astronaut, no normal force appears, and apparent weight vanishes while real weight does not.

This is the seed of the equivalence principle: a sealed lab accelerating through empty space at a feels exactly like a sealed lab sitting still in a gravitational field of strength a, with no local experiment able to tell them apart. That idea connects this topic forward to how gravitation is treated as a field (g as force per mass) rather than a mysterious action at a distance, setting up general relativity later and explaining why 'weightlessness' in orbit is really free fall, not zero gravity.