Weightlessness in a Satellite

Newton's second law, $F=ma$, applies to any object with a net force F producing an acceleration a. Consider a passenger standing on a weighing machine inside a lift (an inertial-frame analysis): regardless of whether the lift is at rest, moving at constant velocity, or accelerating, the passenger experiences exactly two real forces -- gravity, $mg$, acting vertically downward, and the normal reaction force N from the lift floor (which is what the weighing machine actually reads), acting vertically upward.

Case I -- zero acceleration (lift at rest, or moving up/down at constant velocity): the net force is zero, so $mg=N$, and the passenger feels their normal weight.

Case II -- net upward acceleration $a_u$ (the lift just starting to move up, or about to stop while moving down): the upward force must exceed the downward one, giving $N-mg=ma_u$, so $N=mg+ma_u>mg$ -- the passenger feels HEAVIER, and this is not merely a subjective sensation: the weighing machine genuinely records a larger reading.

Case III(a) -- net downward acceleration $a_d$ (the lift just starting to move down, or about to stop while moving up): now $mg-N=ma_d$, so $N=mg-ma_d<mg$ -- the passenger feels LIGHTER, again a real, measurable effect, not an illusion.

Case III(b) -- free fall (the extreme case where $a_d=g$, as if the lift's cables were cut): then $N=mg-mg=0$ -- the weighing machine reads exactly zero, and the passenger experiences TOTAL weightlessness, since there is no normal-reaction force at all being exerted by the floor. …