Did you hear about the discovery of this new exo-planet around Alpha Centauri?! Just a little larger than Earth, it’s the smallest world we’ve found to date. It’s pretty close to its parent star though, with a year lasting just over 3 days and a surface temperatures forecast at 1200 Celsius!
It got me thinking though. Might there be another solution to your puzzle? Suppose the planet were tidally locked (always the same side facing) with its parent star. Could the parent star be massive enough to pull any surface dwellers upwards to the same degree that the planet’s gravity pulls them downwards?
Or perhaps such a massive star would cause the planet to orbit so quickly that the centrifugal force experienced on the planets surface would be so great that you’d be crushed into the ground (on the day-side) or thrown off into space (on the night-side)
Question 1: Is it possible to experience weightlessness on a tidally-locked planet as a result of the Sun pulling you up?
Question 2: Is it possible to experience weightlessness on a tidally-locked planet as a result of a super-tight, super fast planetary orbit that flings inhabitants off into space?