Gravity's tall box with a ball inside - scenario

Let's imagine we put a ball inside a box such that it doesn't touch its walls, and suddenly drop the box. Because the two objects fall at the same rate of acceleration, the ball will stay at the same distance from the walls of the box while on free fall. Correct?

Now, let's imagine the same scenario but with a really long box; one that extends from a few hundred meters off the surface of the Earth all the way to outer space where the force of gravity is much weaker. Let's imagine we put the ball inside the box, near the wall of the outer space side.

What would happen when we drop the box? The Earth surface side of the box will tend to fall at a much faster acceleration than the outer space side of the box. Will the outer space side of the box be pulled down by the Earth surface side causing the outer space side to fall faster than it normally would? Then, does that mean the ball would collide with the outer space side's wall?

Yes, in the situation you describe the ball will collide with the outer wall of the box.

This is an example of a tidal force. Suppose you are floating right in the centre of the box (specifically at its centre of mass), then you and the box will fall at the same speed so you'll appear to be hovering weightless at the centre of the box. Suppose you now release the ball slightly nearer the Earth than you are. Because gravity is slightly stronger at the ball's position it will start moving away from you towards the Earth and will eventually hit the side of the box nearest the Earth. Conversely, if you release the ball slightly farther from the Earth than you are the ball will start moving away from you in the direction away from the Earth and it will eventually hit the far side of the box.

On the other hand, if you hold the ball out sideways and release it at exactly the same distance from the Earth as you are, but displaced sideways, then when you release the ball it will start moving towards you.

As you and the balls fall towards the Earth the red balls will move away from you and the green balls will move towards you.

You might have heard that anything falling into a black hole gets spaghettified, i.e. stretched out into a long string. This is a result of the same tidal forces I've described above - just in a more extreme form.

• A few months ago I saw a YouTube video claiming that in the "tall box" scenario, the ball would still not hit the walls of the box. The claim was that the bottom side of the box fell faster than the top one, and at the same time the top one fell slower. This was due to the fact that gravity stretches out space and therefore the box with it. Is there any validity to this? I can't find the video now :-(
– user73879
Jul 27, 2015 at 18:02
• @YasmaniLlanes: The tidal forces on an object increase with the size of the object. So while I personally feel no tidal force from the Moon, the Earth feels enough force to create tides many metres in height. If you make the box big enough then tidal forces will pull it to bits. There's nothing mysterious about this - the tidal force on the box is no different to any mechanical force pulling the box apart. However, for the tidal force to be significant the box will have to be hundreds of miles long. Jul 27, 2015 at 18:42
• But assuming the box is strong enough to withstand tidal forces. Forget about tidal forces, air resistance, and what not. I'm just concerned with the nature of gravity.
– user73879
Jul 27, 2015 at 19:30
• @YasmaniLlanes: in that case the box will stay the same size and shape. Gravity is indeed due to curvature of spacetime, but there isn't some mysterious sense it which it deforms matter like this box. Gravity just exerts a mechanical force on the box, and the box size and shape only changes if that force causes the box to stretch. It's no different to you picking up the box and pulling on it. Jul 28, 2015 at 5:11