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 $c^2$.

 

[RosutoTakeshi]

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 $c^2$.

Right, information on neutron stars is available, but energy density related to the chain you wanted me to figure out... I can't seem to find

 

[PeterDonis]

energy density related to the chain you wanted me to figure out... I can't seem to find.

You don't need to find anything. You have all the information you need to calculate what I asked for.

You calculated a tensile strength in MPa for the chain. MPa (megapascals) is the same as MJ/m^3 (megajoules per cubic meter) in SI units, i.e., pressure and energy density have the same units. So your calculated tensile strength equates to an energy density. By the rule I gave before, to avoid violating the limits imposed by relativity, the tensile strength equated to an energy density must be less than 1/3 the energy density of the material that has that tensile strength. So the energy density of the chain has to be at least 3 times the tensile strength you calculated. How does that compare with the energy density of a neutron star?

 

[DaveC426913]

If the neutronium chain is strong enough to withstand that acceleration, can we also assume the mass (the neutron star itself) is rigid enough to be accelerated that quickly? Or will it get ... cut in half?

 

[PeterDonis]

If the neutronium chain is strong enough to withstand that acceleration, can we also assume the mass (the neutron star itself) is rigid enough to be accelerated that quickly?

I have not made any assumptions about rigidity of the neutron star or the chain in what I've said in this thread. The calculations I have described do not tell you any details about how the shape of either one changes during the acceleration. They are just simple calculations of what could be viewed as reasonable average values.

Or will it get ... cut in half?

I have assumed that it wouldn't. However, that assumption might be rendered implausible if it turns out that the energy density of the chain is substantially higher than the energy density of a neutron star (that's meant to be a hint ). That's not a matter of rigidity so much as hardness or sharpness--is the chain effectively "sharp" enough to cut into the neutron star instead of just transmitting a force to it? Obviously the narrower the chain, the more likely this is to happen; but I have not discussed how that might be estimated beyond the rough heuristic I just gave.

 

[RosutoTakeshi]

MPa (megapascals) is the same as MJ/m^3 (megajoules per cubic meter) in SI units, i.e., pressure and energy density have the same units. So your calculated tensile strength equates to an energy density.

So...

1.21e33 Mpa = 1.21e33 MJ/m^3

So the energy density of the chain has to be at least 3 times the tensile strength you calculated

1.21e33 * 3 = 3.63e33 MJ/m^3

How does that compare with the energy density of a neutron star?

Well I'm still trying to figure that one out. Haven't found anything that offers a straight answer. As of now, I need to find its Electric and Magnetic field in order to see. I'll keep looking

 

[RosutoTakeshi]

Well I'm still trying to figure that one out. Haven't found anything that offers a straight answer. As of now, I need to find its Electric and Magnetic field in order to see. I'll keep looking

Scratch that. I think I'm looking at it the wrong way

 

[PeterDonis]

I think I'm looking at it the wrong way

Yes, you are. EM fields do not provide any significant amount of energy density to a neutron star. All you need is the mass density, as I pointed out in post #35.

 

[some bloke]

It's probably a safe bet that the chains are simply required to be strong enough to accelerate the mass of the star, and that there may be some sort of cradle or dampening field or some other scifi handwavium to prevent the start from getting cut in half - after all, the chains are used to move stars, not to cut them!

So essentially Superman would also need to be strong enough to move said star in the same manner to be equally as strong as the chain, right?

There is also the physical properties to consider - tensile strength is one aspect, but brittleness is another - I can snap a hardened steel file in half over my knee, but I couldn't pull one so hard that it snap like a christmas cracker! If the chains are specifically designed with tensile strength in mind, and were not expected to have to be malleable, then they may be easier to break through a concerted effort to break them than they are when being used for their designed purpose.

 

[essenmein]

Not entirely sure how a rope would even "hold" a ball of plasma, its not particularly erm "solid".

Let alone plasma that is in fact a raging ball of nuclear fire.

 

[PeterDonis]

Not entirely sure how a rope would even "hold" a ball of plasma, its not particularly erm "solid".

Let alone plasma that is in fact a raging ball of nuclear fire.

This was already pointed out in post #23. The discussion has more or less shifted to an alternative scenario where the object to be pulled is a neutron star of the same mass as our Sun.

 

[some bloke]

I feel we're getting caught up on the wrong part of this issue. The issue is the strength of chains used to haul a mass (which we assume to be that of the sun) in space. I don't know the equations, but I would expect that you would be looking at the minimal forces needed to overcome inertia in order to move the star - I doubt that this is going to be about making that star move quickly (after all, they will have to stop it somewhere too!).

The logistics of moving a star don't factor into how strong superman would have to be to break these chains.

 

[DaveC426913]

I would expect that you would be looking at the minimal forces needed to overcome inertia in order to move the star

You still have two things to factor:
how strong Superman is, and how much thrust he can produce in flight.

With insufficient flight power, all he's doing is hauling himself toward the star.

 

[PeterDonis]

I feel we're getting caught up on the wrong part of this issue. The issue is the strength of chains used to haul a mass (which we assume to be that of the sun) in space.

If you think we haven't discussed what you say the issue is, I think you haven't read the thread. The strength of the chain is exactly what we've been discussing.

I don't know the equations

A number of formulas have already been given in the thread.

 

[jackwhirl]

You still have two things to factor:
how strong Superman is, and how much thrust he can produce in flight.

With insufficient flight power, all he's doing is hauling himself toward the star.

Superman, in flight, can accelerate himself to speeds greater than the speed of light. His flight thrust is infinite. Maybe more than infinite? If infinite thrust is required to reach 1c, how much gets you to 1.1c? ...That's meaningless, isn't it?

 

[PeterDonis]

That's meaningless, isn't it?

As far as trying to analyze using the laws of physics, yes.