How Strong Does Superman Need to Be to Pull Our Sun?

[RosutoTakeshi]

[Moderator's note: Unnecessary introductory statement deleted.]

There's a comic where Superman breaks out/shatters chains that were designed to haul stars across the galaxy
- Let's say these chains were made to pull (our) sun
What tensile strength would a chain need to help pull our sun without breaking? And if I'm not asking the right questions, please let me know what other information you need to solve this

 

[phinds]

What tensile strength would a chain need to help pull our sun without breaking?

Forgetting the absurdity of the scenario, it is an incomplete problem statement. Do you understand what's missing?

 

[RosutoTakeshi]

Forgetting the absurdity of the scenario, it is an incomplete problem statement. Do you understand what's missing?

I do not know what's missing. Enlighten me

 

[256bits]

I do not know what's missing. Enlighten me

Do you need a half inch diameter rope to pull a bus, or a 10 inch thick rope?

 

[phinds]

Do you need a half inch diameter rope to pull a bus, or a 10 inch thick rope?

And that would still leave something missing. Think classical mechanics 101.

EDIT: ah, wait. I see now. I was thinking of how fast you accelerate it but that is NOT really the question.

 

[256bits]

And that would still leave something missing. Think classical mechanics 101.

It is a hint to help figure out what is missing.

 

[RosutoTakeshi]

Do you need a half inch diameter rope to pull a bus, or a 10 inch thick rope?

Ah, I see what you mean. Not really sure for this one though. Diameter doesn't look that big compared to his arm

 

[phinds]

It is a hint to help figure out what is missing.

Yes. I edited my post before your post appeared.

 

[RosutoTakeshi]

I'm just randomly guessing here, but, is the force of the pull needed as well?

 

[phinds]

Ah, I see what you mean. Not really sure for this one though. Diameter doesn't look that big compared to his arm

Irrelevant. The question is not about THAT chain because it is already stated to be unbreakable (absurd because that implies infinite tensile strength). You are asking about a breakable chain, else the question doesn't even make sense.

 

[RosutoTakeshi]

Irrelevant. The question is not about THAT chain because it is already stated to be unbreakable (absurd because that implies infinite tensile strength). You are asking about a breakable chain, else the question doesn't even make sense.

Don't mind the unbreakable statement, it's just hyperbole

 

[phinds]

Don't mind the unbreakable statement, it's just hyperbole

Exactly what I just said, as regards your question.

 

[256bits]

And that would still leave something missing. Think classical mechanics 101.

EDIT: ah, wait. I see now. I was thinking of how fast you accelerate it but that is NOT really the question.

OK , Now you got me..

 

[RosutoTakeshi]

Exactly what I just said, as regards your question.

Right, so I just need the diameter of said chain? Let's assume it's 4 inches. What's my next step?

 

[phinds]

OK , Now you got me..

Well, if you wanted to get it moving from zero to a zillion miles and hour in 6 seconds (relative to its starting position), you'd need a different tensile strength than if you wanted to just barely move it. Minimum tensile strength in this situation means just barely getting the sun moving before the chain breaks. He HAS to be asking about minimum tensile strength, else the question would have no answer.

 

[RosutoTakeshi]

Well, if you wanted to get it moving from zero to a zillion miles and hour in 6 seconds (relative to its starting position), you'd need a different tensile strength than if you wanted to just barely move it. Minimum tensile strength in this situation means just barely getting the sun moving before the chain breaks. He HAS to be asking about minimum tensile strength, else the question would have no answer.

yes, minimum tensile strength.
And let's assume it's moving from 0 to 184,410 miles per second in 1 minute

Thanks by the way. At first I didn't know what's needed to continue

 

[RosutoTakeshi]

So a 4 inch diameter chain, wrapped around our sun. Being pulled, moving the sun, going from 0 to 184,410 miles per second in 1 minute

How tough would that chain need to be?

 

[phinds]

So a 4 inch diameter chain, wrapped around our sun. Being pulled, moving the sun, going from 0 to 184,410 miles per second in 1 minute

No, with that question you are NOT trying for minimum tensile strength but some specific tensile strength greater than the minimum. Reread post #15

 

[RosutoTakeshi]

No, with that question you are NOT trying for minimum tensile strength but some specific tensile strength greater than the minimum. Reread post #15

Oh ok I understand what you were saying now

 

[phinds]

So a 4 inch diameter chain, wrapped around our sun. Being pulled, moving the sun, going from 0 to 184,410 miles per second in 1 minute

How tough would that chain need to be?

Another point to be made here is that you are specifying zero to almost the speed of light in 1 minute. That would require something ENORMOUSLY beyond the maximum possible tensile strength (the point where molecular bonds can't hold).

 

[RosutoTakeshi]

Another point to be made here is that you are specifying zero to almost the speed of light in 1 minute. That would require something ENORMOUSLY beyond the maximum possible tensile strength (the point where molecular bonds can't hold).

Right, it's not realistically possibleI know. Good thing this is the science fiction section of this website

Is there a formula(s) I can use to help figure this out?

 

[phinds]

How would I find out the tensile strength needed for a chain to pull our star from 0 to 184,410 miles per second in one minute?

Another way to view this question is that it is exactly equivalent to: "if the laws of physics no longer apply, what do those laws say about <insert statement of your choice>.

 

[PeterDonis]

What tensile strength would a chain need to help pull our sun without breaking?

You can't pull our Sun. It's not solid and will not move as a single coherent object if a force is applied to it.

The best you can do is to do the computation for some hypothetical object with the mass of our Sun that will move as a single coherent object when subjected to the large acceleration required by your specifications. See below.

let's assume it's moving from 0 to 184,410 miles per second in 1 minute

This is 0 to 0.98995 c in 60 seconds, which works out to an acceleration of 504,727 g. (You should be able to verify this computation.)

Is there a formula(s) I can use to help figure this out?

Once you have the acceleration, you know the force required to impose that acceleration on an object with the mass of the Sun. Then you can just use standard formulas for the breaking strength of a cable to find what tensile strength would be required for a cable of your given cross sectional area to sustain that force.

 

[PeterDonis]

Another way to view this question is that it is exactly equivalent to: "if the laws of physics no longer apply, what do those laws say about <insert statement of your choice>.

This response is not quite justified. There is a valid objection to be made about trying to pull our actual Sun with a cable (which I made in my post in response to the OP just now), but there is also a valid calculation that can be made within the known laws of physics for a hypothetical object with the mass of our Sun subjected to the specified acceleration (which I described in my post in response to the OP just now).

The result of that calculation (which I'll let the OP discover for himself) does not actually give a tensile strength that violates the known laws of physics--it still implies a sound speed in the material that is less than the speed of light. (You actually don't have to do the full calculation I described to see this--you can combine the acceleration I gave with the known diameter of the Sun to check that my statement is correct. Can you see how?)

 

[PeterDonis]

All thread participants, please note, some inappropriate posts have been deleted. Please be civil to other posters. Thanks!

 

[RosutoTakeshi]

All thread participants, please note, some inappropriate posts have been deleted. Please be civil to other posters. Thanks!

Thanks. (You've) been helpful, and I appreciate that

 

[phinds]

This response is not quite justified. There is a valid objection to be made about trying to pull our actual Sun with a cable (which I made in my post in response to the OP just now), but there is also a valid calculation that can be made within the known laws of physics for a hypothetical object with the mass of our Sun subjected to the specified acceleration

Fair enough. I was being quite literal minded about pulling the sun and here's a response I had typed in when the thread got closed (temporarily).

If this was not quantifiable from the get go, then say (that)

No, I did not say, nor did I imply, that. It IS calculable if you have all the information, although not having made the necessary assumptions about the material of the chain nor done the calculation, I don't know that the answer would be less than the maximum possible tensile strength without making the diameter of the chain a large number of miles.

I think the way to approach it would be to assume that you want to push the limit of the maximum possible tensile strength and then from that figure out how big a chain you would need. This does ignore the issue with pulling the sun as opposed to something more reasonable.

------------------------

@PeterDonis, if I understand it correctly, there IS a maximum tensile strength beyond which no material can have molecular bonds strong enough to maintain it. Is that correct?

 

[PeterDonis]

if I understand it correctly, there IS a maximum tensile strength beyond which no material can have molecular bonds strong enough to maintain it. Is that correct?

Relativity does impose a limit on the tensile strength of materials. This limit is most easily thought of as requiring the speed of sound in the material to be less than the speed of light.

Thinking of it in terms of molecular bonds being broken is not really the right way to think of it because, first, molecular bonds are many, many orders of magnitude weaker than the maximum limit I just described, and second, not all substances are made of molecules or even atoms. Consider white dwarf or neutron star matter, for example.

 

[RosutoTakeshi]

You can't pull our Sun. It's not solid and will not move as a single coherent object if a force is applied to it.

The best you can do is to do the computation for some hypothetical object with the mass of our Sun that will move as a single coherent object when subjected to the large acceleration required by your specifications. See below.
This is 0 to 0.98995 c in 60 seconds, which works out to an acceleration of 504,727 g. (You should be able to verify this computation.)
Once you have the acceleration, you know the force required to impose that acceleration on an object with the mass of the Sun. Then you can just use standard formulas for the breaking strength of a cable to find what tensile strength would be required for a cable of your given cross sectional area to sustain that force.

Yeah I'm trying to figure it out right now. Currently working on it. I'll comment what I (think) is correct in a bit

 

[PeterDonis]

This does ignore the issue with pulling the sun as opposed to something more reasonable.

One way to modify the scenario to make this somewhat more reasonable would be to imagine pulling a neutron star with the mass of the Sun, using a chain made of neutronium.

 

[PeterDonis]

The result of that calculation (which I'll let the OP discover for himself) does not actually give a tensile strength that violates the known laws of physics--it still implies a sound speed in the material that is less than the speed of light.

Actually, I should clarify this. A better way of stating the limit on tensile strength for this problem is that the tensile strength in pressure units, or equivalently energy density units (which are the usual units for tensile strength) must be less than $1/3$ of the energy density of the material. This allows one to explore a range of parameters for the chain, balancing the energy density against the cross sectional area (basically, the smaller you want the cross sectional area to be, the greater the energy density has to be to stay within the limit, since smaller cross sectional area means larger tensile strength required for a given force).

Given the above, there is a range of parameters for the chain that allow a tensile strength that does not violate the known laws of physics. But those parameters are pretty extreme.

 

[RosutoTakeshi]

Once you have the acceleration, you know the force required to impose that acceleration on an object with the mass of the Sun. Then you can just use standard formulas for the breaking strength of a cable to find what tensile strength would be required for a cable of your given cross sectional area to sustain that force.

Alright let me take a shot at this. I need to figure out the tensile strength of a cable (4in. in diameter) pulling an object with the mass of our sun (1.989e30kg) going from 0 to 0.99c in 1 minute

Acceleration:
a = (v-u)/t
a = (296344604m/s - 0m/s) / 60s
a = 296344604 / 60
a = 4,939,076 m/s^2

Force:
F = ma
F = 1.989e30 * 4939076m/s^2
F = 9.82e36 N

Cross Sectional Area (Cylinder):
πr^2
3.14(2in^2)
3.14 * 4
12.56in^2
Conversion to mm2:
8103mm^2

Ultimate Tensile Stress:
T = F/A
T = 9.82e36/8103mm^2
T = 1.21e33 Mpa

... I was struggling all night too. How does it look?

 

[PeterDonis]

How does it look?

The general form of your calculations looks fine. Now you should calculate what the minimum energy density of the chain material would need to be in order to meet the condition that the tensile strength must be less than 1/3 of the energy density. How does this energy density compare to, for example, the energy density of a neutron star?

 

[RosutoTakeshi]

The general form of your calculations looks fine. Now you should calculate what the minimum energy density of the chain material would need to be in order to meet the condition that the tensile strength must be less than 1/3 of the energy density. How does this energy density compare to, for example, the energy density of a neutron star?

I haven't been able to find anything relatable. All information on energy density is regarding electric fields, magnetic fields and electromagnetic waves

 

[PeterDonis]

I haven't been able to find anything relatable.

There are plenty of places online that will tell you the mass density of a neutron star. The energy density is just the mass density times $c^2$.