Q.Why do astronauts in an orbiting satellite have a feeling of weightlessness?

[!TLDR] A satellite is in continuous free fall, with gravity supplying only the centripetal force, so there is no normal-reaction force -- exactly the free-fall (zero apparent weight) case. [!ANSWER] Zero apparent weight because gravity …

Apparent weight -- what is actually FELT and what a weighing scale records -- comes from the normal reaction force N exerted by a support, not directly from gravity itself. Analysing a lift shows that N equals $mg$ when there is no relative acceleration, exceeds $mg$ under upward acceleration, falls below $mg$ under downward acceleration, and drops to EXACTLY ZERO in the special case of free fall, where the downward acceleration equals g exactly (as if the lift's cable were cut). In this free-fall case there is genuinely no normal-reaction force at all, since nothing is pressing the body against any support; both the body and its 'support' are accelerating downward at the identical rate g, so there is nothing to press against. …

Connect the free-fall case of the lift analysis (net downward acceleration = g gives zero apparent weight) to a satellite's orbital motion, where gravity alon …

Incorrectly claiming there is 'no gravity' in orbit -- gravity is very much present and acting (it is what keeps the satellite orbiting); weightlessness is abou …