High-energy impacts with Styrofoam

[Molyneux]

I am not entirely certain whether this thread should be in SLAM, but it seemed more appropriate than any of the other boards.

After a discussion of the science flaws of certain comic books elsewhere on the board, I became curious about the possible destructive potential of styrofoam - namely, just how much damage could a chunk of Styrofoam with roughly twice the volume of the Earth do?

Volume of Earth is roughly equivalent to 1.087x10^12 cubic kilometers.
Volume of Styrofoam (at least according to this website) is 100 kg/cubic meter, or 1.0*10^11 kg/cubic kilometer.

Using those figures, a styrofoam planetoid with volume twice that of Earth would have a mass of 1.087*10^23 kg.
Google thinks that the Earth's own mass is fifty-four times that, 5.9742 × 10^24 kilograms.

What I'm not sure about is how to calculate the actual effects of an impact between the two, at any speed. I'm assuming the effects would be fairly traumatic for any residents of the Earth, though.

[Steel]

I am not entirely certain whether this thread should be in SLAM, but it seemed more appropriate than any of the other boards.

After a discussion of the science flaws of certain comic books elsewhere on the board, I became curious about the possible destructive potential of styrofoam - namely, just how much damage could a chunk of Styrofoam with roughly twice the volume of the Earth do?

Volume of Earth is roughly equivalent to 1.087x10^12 cubic kilometers.
Volume of Styrofoam (at least according to this website) is 100 kg/cubic meter, or 1.0*10^11 kg/cubic kilometer.

Using those figures, a styrofoam planetoid with volume twice that of Earth would have a mass of 1.087*10^23 kg.
Google thinks that the Earth's own mass is fifty-four times that, 5.9742 × 10^24 kilograms.

What I'm not sure about is how to calculate the actual effects of an impact between the two, at any speed. I'm assuming the effects would be fairly traumatic for any residents of the Earth, though.

Certainly going to wipe out all life on earth, even at tiny speeds.

Lets consider the problem in the rest frame of the styrofoam blob, and assume after the collision the earth becomes comedically wedged in the blob.
Spoiler

The earth has mass m1 and the styrofoam has mass m2. The earth is moving at speed v1 in the direction of the blob. Afterwards the combined body (of mass m1+m2) is moving at speed v2.

So by conservation of momentum we have that:

m1*v1 = (m1+m2)*v2

so

v2 = m1*v1/(m1+m2)

Now if we consider the energy before

E_before = 0.5*m1*v1^2

E_after = 0.5*(m1+m2)*v2^2

and using the expression for v2 above

E_after = 0.5*(m1^2/(m1+m2))*v1^2

So If we take E_after/E_before

we get

E_after/E_before = m1/(m1+m2)

If as you have the mass of the earth is about 50 times the blob, then

E_after/E_before = 50/51,

so about 2% of the energy has been released in some form (ruining the blob and the earth).

So if we are talking about a collision between the earth moving at its orbital velocity hitting this blob, then the E_before is the kinetic energy of the earth which is about 2.7*10^33J

So we release about 10^31 Joules in the collision.

Even if the vast majority of that goes into deforming the blob, its still more than sufficient to ruin anyones day. Not to mention that we have some portion of the earth now lodged in the blob.

For bonus points you can see how much of the blob that energy release could melt, and hence how large an ocean of boiling styrofoam would be unleashed on the earth.

[Spectre_nz]

Wouldn’t a ball of styrofoam the size of a planet compress itself under gravity and leave you with a hydrocarbon crust over a dense carbon core? (diamond I assume)
Or are you ignoring that specifically for the amusement value of working out the lethality of a marshmallow planet?

[Molyneux]

Wouldn’t a ball of styrofoam the size of a planet compress itself under gravity and leave you with a hydrocarbon crust over a dense carbon core? (diamond I assume)
Or are you ignoring that specifically for the amusement value of working out the lethality of a marshmallow planet?

...I hadn't thought of that. The specific inspiration for the thread was from someone mentioning, in the past, the Incredible Hulk punching through an "asteroid" twice the size of the Earth.

Honestly, the the Earth wedging itself into a monstrous ball of foamed plastic is the weirdest mental image I've had in a long while.

[madd0ct0r]

Wouldn’t a ball of styrofoam the size of a planet compress itself under gravity and leave you with a hydrocarbon crust over a dense carbon core? (diamond I assume)
Or are you ignoring that specifically for the amusement value of working out the lethality of a marshmallow planet?

Would it though?

Gravity can coalesce gas clouds, but the styrofoam has a certain structural strength, and the only force acting on (before we crash the earth in) is the gravity due to the (low) material density.

In fact, given it's huge volume, when it is just about to collide with the earth, won't the value of 'g' on the nearside and farside of the sphere be substantially different?

So rather then crashing, you'd have the earth pulling chunks out and down towards us, being tugged sideways by the Earth's Spinning atmosphere, resulting in a fake Snowball Earth with a big chunk stuck on one side.

maybe

[Spectre_nz]

Well, if the mass in the OP is to be trusted, the object has a similar mass to the moon Callisto. Objects quite a lot less massive than that made of ice or rock pull themselves spherical over time. Unless I'm mistaken and they only manage it while they're molten.

Maybe I'm thinking about it wrong, but as I see it, the combination of vacuum and its own gravity would press out all the trapped gas and compact the object until it was more like a lump of polystyrene resin. And if it masses around the same as Callisto it's going to make a fucking mess of us.

But that aside;

Assuming the object wasn't compacted, what cartoon noise are you imagining associated with the impact?
I'm kinda going with that pie-in-the-face splat noise.

Edit; apparently the density of expanded polystyrene can range from 16 to 640 kg/m3, so that would make for a lot of potential difference if you're calculating it based on volume. non expanded polystyrene has a density around that of water; 1.03g/cm3

[Freefall]

The total mass of the thing is off by a factor of 2; looks like you forgot to double the Earth's volume in the calculation.

EDIT: I will also point out that the dialog in the comic just says "twice the size of Earth." Whether this is twice the volume or twice the radius, or diameter, is not specified, although given its aspherical shape, I suppose volume is probably the most likely (it's also the least extreme in an already ludicrous situation).

Anyone know what kind of pressure styrofoam collapses under? I figure it can't be too high, but I really have no idea (guess it also depends what you mean by "collapse," and I'm not sure how to qualify that further).

If we assume uniform density throughout (which is what was done to get the mass figure given), then it's obviously a pretty simple to figure its gravity at any given point

a = G (100 kg/m^3)*4/3*pi*r

Where the maximum r can be is about 8,000 km, and a would be 0.023 g.

At r = 1000 km, the surface gravity is only about 0.00285 g. Of course, there's 7,000 km of material but I'd have to get my mechanics book to look up the real equation to figure out what the psi would be from all that; the gravity will change dramatically over that distance so it can't be done with just algebra. Of course, that wouldn't even be entirely accurate because, as pointed out, all that material will also be structurally supporting itself, unlike a gas or liquid.

Okay, I'll admit I'm not entirely sure where I'm going with this. Seemed like it might help when I started.

BTW, even though it doesn't directly pertain the the question here, the object in the Hulk comic was definitely not spherical. (of course, it probably wasn't supposed to be made of styrofoam either).

[Molyneux]

The total mass of the thing is off by a factor of 2; looks like you forgot to double the Earth's volume in the calculation.

EDIT: I will also point out that the dialog in the comic just says "twice the size of Earth." Whether this is twice the volume or twice the radius, or diameter, is not specified, although given its aspherical shape, I suppose volume is probably the most likely (it's also the least extreme in an already ludicrous situation).

Anyone know what kind of pressure styrofoam collapses under? I figure it can't be too high, but I really have no idea (guess it also depends what you mean by "collapse," and I'm not sure how to qualify that further).

If we assume uniform density throughout (which is what was done to get the mass figure given), then it's obviously a pretty simple to figure its gravity at any given point

a = G (100 kg/m^3)*4/3*pi*r

Where the maximum r can be is about 8,000 km, and a would be 0.023 g.

At r = 1000 km, the surface gravity is only about 0.00285 g. Of course, there's 7,000 km of material but I'd have to get my mechanics book to look up the real equation to figure out what the psi would be from all that; the gravity will change dramatically over that distance so it can't be done with just algebra. Of course, that wouldn't even be entirely accurate because, as pointed out, all that material will also be structurally supporting itself, unlike a gas or liquid.

Okay, I'll admit I'm not entirely sure where I'm going with this. Seemed like it might help when I started.

BTW, even though it doesn't directly pertain the the question here, the object in the Hulk comic was definitely not spherical. (of course, it probably wasn't supposed to be made of styrofoam either).

Whoops. I just realized I also typed VOLUME of Styrofoam where I meant DENSITY...I did assume volume, since it appeared slightly less ludicrous than radius.

[aimlessgun]

If it fused itself to earth it would probably screw up our orbit pretty badly as well. There's no chance of it bouncing off is there?

[General Zod]

If it fused itself to earth it would probably screw up our orbit pretty badly as well. There's no chance of it bouncing off is there?

Doubtful. If anything I'd expect something like the Tunguska event, only significantly more powerful.

[Chardok]

If it fused itself to earth it would probably screw up our orbit pretty badly as well. There's no chance of it bouncing off is there?

Doubtful. If anything I'd expect something like the Tunguska event, only significantly more powerful.

You don't think adding that much mass to the earth wouldn't cause a drastic increase in its gravitational pull? I'm thinking it'd pull down the freaking moon, draw numerous passing asteroids into the gravity well and maybe even destabilize it's orbit enough for it to crash into the sun.

Then again, I don't know shit about orbital mechanics and can barely calculate my grocery bill, let alone all these formulas with weird symbols and suttf.

[General Zod]

If it fused itself to earth it would probably screw up our orbit pretty badly as well. There's no chance of it bouncing off is there?

Doubtful. If anything I'd expect something like the Tunguska event, only significantly more powerful.

You don't think adding that much mass to the earth wouldn't cause a drastic increase in its gravitational pull? I'm thinking it'd pull down the freaking moon, draw numerous passing asteroids into the gravity well and maybe even destabilize it's orbit enough for it to crash into the sun.

Then again, I don't know shit about orbital mechanics and can barely calculate my grocery bill, let alone all these formulas with weird symbols and suttf.

Doubtful that it would bounce off, I meant.

[Chardok]

errg! My bizzad.

[GrandMasterTerwynn]

If it fused itself to earth it would probably screw up our orbit pretty badly as well. There's no chance of it bouncing off is there?

No chance at all. A collision with an object of the mass specified would wholly melt the crust of the Earth and throw a huge spray of carbonaceous rock into orbit. This mass of rocks will condense into a ring system to envy Saturn's, and may even result in Earth gaining another moon, depending on the angle of impact.

And no, it would not disturb the Earth's orbit . . . it barely has 2% of Earth's mass. The collision that formed the Moon certainly didn't "screw up our orbit pretty badly," and the world that collided with the primordial Earth had around a third of Earth's mass.

[madd0ct0r]

Strength of expanded polystyrene (in psi) can be seen here: http://www.dot.state.ak.us/stwddes/rese ... 0v35n1.pdf (top of page three)

It's becoming increasingly common as a way to build road embankments across poor ground.
It also experiences massive creep at loads much lower then failure. If we build this ball of plastic, it may be necessary to crash the earth into reasonably quickly. say within a few days.

I used to have the data for SI units, but can't find them right now.

[aimlessgun]

If it fused itself to earth it would probably screw up our orbit pretty badly as well. There's no chance of it bouncing off is there?

No chance at all. A collision with an object of the mass specified would wholly melt the crust of the Earth and throw a huge spray of carbonaceous rock into orbit. This mass of rocks will condense into a ring system to envy Saturn's, and may even result in Earth gaining another moon, depending on the angle of impact.

And no, it would not disturb the Earth's orbit . . . it barely has 2% of Earth's mass. The collision that formed the Moon certainly didn't "screw up our orbit pretty badly," and the world that collided with the primordial Earth had around a third of Earth's mass.

Well, the mass is very low, but with the image of the Earth hilariously wedged into this huge styrofoam blob, the center of that mass is stuck pretty far out from the surface of the earth. But even then I suppose it just doesn't weigh that much...would it at least slow down earth's rotation appreciably?

[Freefall]

I decided to plug this thing into the planetary parameter calculator here, and it gave a planetary binding energy of only 2.34e29 J, so if Steel's figure is accurate, it looks like the thing itself would be mostly destroyed in a collision with earth.

[Steel]

I decided to plug this thing into the planetary parameter calculator here, and it gave a planetary binding energy of only 2.34e29 J, so if Steel's figure is accurate, it looks like the thing itself would be mostly destroyed in a collision with earth.

I'm pretty sure that for an object this light the chemical binding energy is going to be much greater. That is the energy you need to deliver to melt it/smash it apart due to chemical bonds dwarfs the GBE.

Consider styrofoam packing chips, those have approximately zero gravitaional binding energy as they're only a couple of cm across and weigh at most a gram (about 10^-15J if my back of envelope calculation is correct). But if you breathe on it it wont be vaporised, nor will that happen if you fire a bb gun at it.

[Freefall]

You're right, I do keep thinking of the thing more as a collection of styrofoam particles rather than a single styrofoam construct. And my earlier calculation indicates that the whole object has a surface gravity of only about 2.3% that of the earth, so even though its total mass is still relatively high, it seems like gravity might still not be that big a factor due to its size.

[Steel]

You're right, I do keep thinking of the thing more as a collection of styrofoam particles rather than a single styrofoam construct. And my earlier calculation indicates that the whole object has a surface gravity of only about 2.3% that of the earth, so even though its total mass is still relatively high, it seems like gravity might still not be that big a factor due to its size.

Yes, if it were just the remains of Thor's new tv packaging things would be a lot less devastating, although we'd still be in for an extinction level event and a scouring of the earth's surface.

In particular for the binding energies point, for an object of mass M and radius r, the GBE goes as M2/r (and so as mass goes as r3) the GBE will go as r5. The chemical binding energy of an object will just go as M, and so r3.

For large r we can see that GBE is going to be much more important, but then below a certain radius the chemical binding energy will be dominant as it doesn't drop off as fast.

In fact, a lower bound for the amount of energy this blob can release as a cloud of packaging bits is if we assume that there isnt a collision, but it just appears next to the earth and bits of it start to sprinkle down from a height of 100km. That will release approx 1MJ per kg, which when multiplied by 1-2% (or whatever fraction you deem is capable of striking the earth in this scenario) of the mass of the earth adds up to an awful lot.

[madd0ct0r]

is that the energy released as the chunk burns up on entering the atmosphere, or the total chemical energy in the chunk?

[CSJM]

Just for how long could a styrofoam planetoid survive in the Solar system, anyway? How much energy would it gather from the Sun? I don't think it'd be quite light enough to be noticeably pushed by the solar wind, but the heat itself would probably build up until the whole thing melts.

And for the impact itself, I suspect the whole planetoid would crack apart and get smothered all over the Earth's surface. It'd be quite the extinction event.

[Wyrm]

At twice the volume of Earth, the Styrofoam planet would still mass in at around 7.907433e22 kg. It's only one percent the mass of Earth, but that's still a shitload of mass, so it will last a while, even if it vaporizes steadily.

Also, a body that large is held together by its self-gravity and not molecular forces. It will flow as it collides with the Earth, and result in significant distortion in the Earth as well from the impact. It's not something you want to be under, at any rate.

is that the energy released as the chunk burns up on entering the atmosphere, or the total chemical energy in the chunk?

Gravitational potential energy, I think.