-3

enter image description here

The weak principle of equivalence says that freely falling towards the Earth is the same as being in space far away from any stars.

However, imagine that you are freely falling on a planet with $g=9\cdot 10^{99} m/s^2$ (due to the extremely large mass). Then how can it possibly be the same as being in space far from any stars? Because you would die due to the insanely large g-forces acting on your body.

Qmechanic
  • 201,751
Stallmp
  • 633
  • 7
    If you are freely falling there are no g-forces acting in your body. – mike stone Dec 25 '23 at 18:32
  • Explain? Because g force is essentially the acceleration on your body. Free falling means only the gravitational force is acting on you, so: ma = mg, so a = g = 9 * 10^99. Are you saying that you can't feel any acceleration unless there is some normal force acting on you? Your intestines are feeling normal force though however and you'd most likely die still. – Stallmp Dec 25 '23 at 21:16
  • If g is constant, you don't feel it when freefalling. But what's the radius of this "planet"? I bet the g at your feet is higher than the g at your head, so you'll get spaghettified by the tidal force. See https://physics.stackexchange.com/q/631414/123208 – PM 2Ring Dec 25 '23 at 21:21
  • How?? Because ma = mg so then a = g. How are you not feeling this acceleration, even if it stays constant? Let's ignore the effect of spaghettification – Stallmp Dec 25 '23 at 21:25
  • 1
    You can't feel it because every part of your body is being accelerated identically. – PM 2Ring Dec 25 '23 at 21:27
  • Interesting, this is a bit counterintuitive because there is an insanely large force acting on you, but somehow you don't feel the force but you can only feel changes in forces? Why is that? – Stallmp Dec 25 '23 at 21:29
  • Need to be careful about what you mean by acceleration - it has to be relative to something. If you are saying a = g, you are necessarily talking about a frame of an external inertial observer. This says nothing about what you "feel", just about how the observer perceives you. At any given point you may define your own inertial frame instantaneously in which the metric is flat locally and you feel no effect of gravity. This is truly what is meant by what you "feel". – Sidhaarth Kumar Dec 25 '23 at 21:34
  • Well acceleration relative to an inertial frame, any inertial frame will agree on the acceleration. Can you expand on what you mean by 'what you feel"? – Stallmp Dec 25 '23 at 21:40
  • If something (a floor say) is stopping accelerating at a the humungous $g$, you will certainly feel the floor flattening you, but no floor $=$ no flattening. – mike stone Dec 25 '23 at 22:56

1 Answers1

2

No matter what the actual value of g is, if g is constant, you won't feel it. In a real life situation you would eventually know you are falling towards the ground because g will not take the same value at all times during your fall.

user3011
  • 36