Would the delay cause the box to move?

[nemesiswes]

Hi, a friend and I were talking and a question came up about a delayed force.

It goes like this:
This is hypothetical obviously.
You have the sun and the Earth pulling on each other because of gravity. (The force of the pull between them does not matter, it just has to be equal.)
The sun and the Earth are bolted down inside a gigantic solar system sized box, lol. So if one moves the other moves because they are both bolted to the box.
I attached a visual to help see what I mean.

The space between them inside the this box is 150 Million KM. Now the interesting part, the sun will at some point disappear (or shut off its gravity I guess, lol, doesn't really matter). The time taken for the sun to shut off its gravity or disappear is 1 minute. I assume that it would take a total of 8.3 minutes before the force pulling the Earth and thus making the net overall force on this box since they are bolted to it, becomes unequal. When the force does arrive and stop pulling the earth, since there was a 7.3 minute (sun took 1 minute to shut off) window where the sun was not there gravitationally to be pulled on from the Earth and the Earth was still feeling that pull from the sun even though it was not there gravitationally again, would that cause the box to move? Would that delay cause the Earth to experience the force and thus cause a overall net force on the box causing it to move?

I don't care how fast that force causes the box to move, just whether it ultimately will or not.

Every way my friend and I think about it, we think the answer is yes, weird but still a yes.

 

[Simon Bridge]

Not exactly - the delay to experience the sudden absence of the Sun means that the Earth+box keep doing what they were always doing. Though bits of the box will discover the absence of the Sun before the Earth does, and bits later, which should stress the box quite a bit (though probably not as much as the original setup - the tidal forces on the box must be huge! Or did you imagine the box is massless?)

You may want to think about this in terms of a Cavendish apparatus... where one mass is removed very quickly.

I'm wondering where this is coming from.

 

[nemesiswes]

The way we came about this question was because we watching this show and it mentioned that if the sun disappeared right now it would take like 8.3 minutes before the Earth would not only go dark but also stop orbiting the sun.

We eventually got to this question, lol. I kinda always imagined the box would be mass-less or at-least not interact at all gravitationally. It really is only there so any movement by the Earth would cause the sun to move as well (or what was once where the sun was) and obviously the box since they are both connected.

 

[Simon Bridge]

Well you didn't need it - Newton's 3rd law tells you that this happens anyway. That's what an orbit does... the Sun and the Earth orbit each other about their common center of mass.

The Cavendish experiment does something like this ... but in an attempt to measure G in Newtonian gravity. You set up two small masses and quickly remove the the big one and measure the effect on the little one. You have to do it carefully.

But you are interested in the delay ... a less magical experiment would involve separating two masses, originally quite far apart, very quickly. But you could just measure the gravity waves from a distant rotating but massive system like a pair of stars or something.

 

[nemesiswes]

Well the box was there specifically for when the sun disappears (or turns off). So the Earth which is still experiencing a pull towards the sun will also be causing the box to experience a pull toward the sun even though the sun is inside it turned off gravitationally. Thus the box and the sun and Earth will move in the direction from Earth to the sun.

 

[aerf]

It depends whether the sun can still interact gravitationally (be attracted) when the gravitational pull is turned off. If it can, as the sun 'sends' the gravitational pull at the last instant the Earth will send one too at the same instant which is of the same magnitude, causing there to be no net force on the box.

 

[nemesiswes]

No when the sun shuts off, it shuts off gravitationally (so it is basically as if the sun just disappears). Meaning it can no longer be effected by gravity in any way.

 

[Simon Bridge]

Ah so you are not thinking of the Earth in orbit - but more as two masses which would gravitate towards each other but for this box ... you remove the mechanical opposition (the walls keeping the masses apart because one end is no longer anchored) but keep the gravity? (you could imagine that whatever holds the Sun to the box stops working so now the box can slide past the Sun.)

Remaining mass suddenly starts accelerating since it now experiences an unbalanced force... which would clue the inhabitants of the remaining mass into the disappearance ahead of time ... which would be faster than light communication...

You'd be correct ... but that is because the model has too many idealizations: it's broken. What happens is the tension in the box walls does not dissipate right away. As far as the remaining mass is concerned, the box walls are still pushing back against it's weight.

It is quite common to find that common classical idealizations result in relativity violations. In this case it is the rigidity of the "box".

 

[nemesiswes]

but more as two masses which would gravitate towards each other but for this box ... you remove the mechanical opposition (the walls keeping the masses apart because one end is no longer anchored) but keep the gravity?

well actually the sun and Earth are at all times anchored to the box, just the sun shuts off gravitationally (meaning no interaction with gravity at all). No walls are removed. The box also doesn't interact with gravity either. Also the way I imagined it, the Earth and thus the box would not start to accelerate for at-least 8.3 minutes after the sun shuts off.

 

[256bits]

well actually the sun and Earth are at all times anchored to the box, just the sun shuts off gravitationally (meaning no interaction with gravity at all). No walls are removed. The box also doesn't interact with gravity either. Also the way I imagined it, the Earth and thus the box would not start to accelerate for at-least 8.3 minutes after the sun shuts off.

Why would there be acceleraton after 8.3 minutes? No force would then be acting upon the Earth after that time, so you should explain your reasoning.

But since it a thought experiment...
I see 2 choices for the box 1. it is rigid, or 2. it is springy(compressible ) . In one the Earth and sun begin to move right away. In the other the sun begins to move right away but the Earth only 8.3 minutes afterward. Do you see oscillations of movement occurring also?

 

[russ_watters]

well actually the sun and Earth are at all times anchored to the box, just the sun shuts off gravitationally (meaning no interaction with gravity at all). No walls are removed. The box also doesn't interact with gravity either. Also the way I imagined it, the Earth and thus the box would not start to accelerate for at-least 8.3 minutes after the sun shuts off.

So in your hypothetical box, the force the box is applying to separate the sun and Earth also disappeats instantly? What is this box made of?!

The outcome of a thought experiment that violates the laws of physics can be whatever you wish, depending on how you choose to write the laws of your fictional universe.

 

[nemesiswes]

Nevermind I don't think there would acceleration after the 8.3 minutes because like 256 bits said, there would no force acting on the Earth and thus the box afterwards. So does that mean there would be no movement of the box and thus the Earth and the sun? I am kinda of confused as to what would happen, lol.

 

[nemesiswes]

also why would the sun begin to move first and then the sun in your 2nd possibility Russ watters? Is it because of since the sun was being pulled toward the earth, the box was compressed and when the sun shut off, it uncompressed, moving away from the earth? Then what happens when that information that the sun is off reaches earth? Does the Earth uncompress in the same direction as the sun?

 

[A.T.]

You are basically asking: "What would the laws of physics predict, if the laws of physics were wrong?" The answer is: "Anything you wish." You cannot make mass disappear or switch off gravity.

 

[256bits]

You are basically asking: "What would the laws of physics predict, if the laws of physics were wrong?" The answer is: "Anything you wish." You cannot make mass disappear or switch off gravity.

So true. I consider some problems of this sort as answering the question 'what if' the universe was different and could it be different. sometimes fun too. But yeah, it can become bogged down very quickly. In this case, an exotic material for the box is envisioned that is non-gravitating and extremely super strong.
Maybe some sci-fi writer will use an exotic gravity drive by switching gravity on/off in the next race to the stars!

 

[nemesiswes]

well, I really am just trying to find out if the earth, sun and the box ultimatly move in one direction? I know every action causes a reaction and that should still hold up here. I imagine the reaction would have been the sun being pulled by Earth since the Earth is being pulled by the sun that was once there. However in this case the sun disappears and so no reaction can occur. The reaction is still there in a sense because the gravity wave which would have caused the reaction is still there, it just has nothing to pull and cause it. So would the box ultimatily move in one direction, if so which? I just have trouble thinking about it when compression and uncompression waves are included, lol. Every-way I think about it still, it would seem it would move toward the sun. The Earth is going to feel a force pulling it for 8.3 minutes until the absence of the sun reaches it. at the same time, the box is uncompressing in the direction of the sun right? I would assume the force of that uncompression would be equal to force of the compression. Meaning the box would feel a force pushing it in the direction of the sun for 8.3 minutes until it reaches earth.I know it's crazy and can never happen, but it's kinda interesting thinking about it.

 

[DaveC426913]

The presence of the box is obfuscating the principle. It's not that you can't have it in a thought experiment, it's just that it introduces so many irrelevant factors that must be considered, they will bog you down.

Changes in the gravitational pull of the sun will indeed take ~8 minutes before Earth feels them. The sun can't disappear but if it rapidly accelerated away far enough that its effect on Earth were dramatically reduced, then Earth would continue to orbit as normal for 8 minutes, after which its path would begin to straighten out along the tangent of its orbit.

It would be exactly like if you swung a pail of water on a string in a circle around you, then let the string go. The pail would travel in its circular path until the wave of released tension traveled the length of the string.

 

[nemesiswes]

Well that is why the box is there so any movement of the sun causes the Earth to move with it and vice versa. Since you couldn't make sun move away since that would cause the Earth to move aswell, you just turn off the sun or blow it up, just as long as it is no longer there gravitationly. Also the sun and the Earth are fixed in place inside the box.

 

[DaveC426913]

Well that is why the box is there so any movement of the sun causes the Earth to move with it and vice versa. Since you couldn't make sun move away since that would cause the Earth to move aswell, you just turn off the sun or blow it up, just as long as it is no longer there gravitationly. Also the sun and the Earth are fixed in place inside the box.

Okay, is the box closed? If so, then it is a closed system. The mass of the sun remains in the box. The box may shift, but will come to rest again with the centre of mass still inside the box (though not necessarily at the same place inside the box.)

 

[Waterfox]

Maybe another way to phrase the question would be that there is a space probe stationary 1 AU from the Sun firing its thrusters towards the Sun to stop it from falling towards it. All of a sudden the Sun disappears from the area (rapidly accelerates elsewhere or an anti-Sun annihilates with it and its mass-energy is quickly dispersed as photons) and around this time the space probe runs out of fuel (not sure if relativity of simultaneity will affect this). For the next ~8 minutes, will the probe accelerate towards where the sun once was until the "gravitational wave" meets it?

 

[nemesiswes]

Well the box is closed in the sense that the sun and the Earth stay in inside but it is open in that the gravity can extend past the box, just not interact with the box. To make it easier, it is just floating out in space far way from other objects. Also in response to Waterfox, I think the anwser is yes. It makes sense that it would be yes at-least