Slowing a Rogue Iron Asteroid: Can it Survive 900 Gees of De-Acceleration?

[chasrob]

Story line I'm working on: an iron asteroid--huge, 20 km in diameter--is zipping along in its orbit in the asteroid belt. It's solid Ni-Fe, same composition as an iron meteorite, only gigantic. I need to have its velocity slowed down.

900 gees of de-acceleration for 10 seconds. Can this mass survive without breaking up? It is solid iron, after all.

Thanks for any input. Guesses too.

 

[Simon Bridge]

Back of envelope ... the trick is to convert the figures into the energy it has to lose somehow.

Iron has a density 7874kg/m³
assuming a rough spherical symmetry, and solid iron, the asteroid will have mass about 3.2x10¹⁶kg

decelerating that at 900g (8820ms^-2) for 10 secs would dump the order of 10²⁶J

Now we need to compare that with something:

1kT of TNT is 4181J - so that would be about 10¹⁶ megatonnes of TNT.
iirc the total megatonnage of the US nuclear stockpile in 2007 was about 2000MT - a mere firecracker by comparison!

What do you think it's chances of survival?


Note. if that 10sec deceleration brought the asteroid to rest, then it's initial orbital speed was of order 1000kmps ... which is very fast. The orbit speed at 1AU is about 40kmps and it gets slower the farther out you go.

 

[D H]

You've left out two important parts, how and why.

How:
This is going to require an immense amount of power. You're operating on the lottawatts scale (100 yottawatts). That's on the upper edge of a Type II civilization. Certainly such a civilization could accelerate a rubble pile asteroid of that mass at 900 g. Apply the magical force uniformly across the asteroid, use a magical force field to hold the asteroid together, or reinforce the asteroid with magical unobtainium rods. No problem! An iron-nickel asteroid would be a piece of cake compared to a rubble pile.

Note the words "magic" and "unobtainium". A Type II civilization would be magic by our standards because "any sufficiently advanced technology is indistinguishable from magic."

Why:
Why are you doing this? 900 gees for 10 seconds is a Δv of 88 km/s. You are sending the asteroid out of the solar system, and rather quickly at that. Why? Wouldn't it be better to mine it?

 

[jedishrfu]

there was talk of painting an asteroid with some reflective paint so that the sun's rays could more effective change its course. Not sure if that may help your story. It won't be a fast deceleration but rather would push it out further.

 

[D H]

there was talk of painting an asteroid with some reflective paint so that the sun's rays could more effective change its course. Not sure if that may help your story. It won't be a fast deceleration but rather would push it out further.

That won't help his story. You're talking about the Yarkovsky effect. This is exceedingly small, ten orders of magnitude or more too small compared to 900 g.

 

[Simon Bridge]

continuing...
melting point of iron is about 1800K, specific heat (solid) about 450J/kgK
If we start the iron at 0K, then the energy to melt the entire asteroid is: 452*1800*3.2e16=2.6e22J ... so it is conceivable that the process could liquify the entire thing if the energy is not drawn away somehow.

Latent heat of vaporization is 6090kJ/kg, so we can work out how much of the asteroid could be vaporized.

These calculations are pretty straight forward ...

Note - for a rubble asteroid, the gravitational binding energy would be given by $U=3GM^2/5r$ - which would be the energy to disperse the asteroid to the edge of the Universe. Just for comparison.

Phil Plait does this sort of calc routinely...
http://www.badastronomy.com/bad/tv/doomsday.html

 

[chasrob]

Quick post--I apologize; in the OP I said the asteroid was in orbit... the situation is that it has a velocity of ~100km/s and the "slowing down maneuver" results in an planet-friendly orbiting speed of 10-11 klicks per second.

I noticed the error before I posted and meant to change it but... too many distractions (firecrackers) going off in the meantime?

 

[mfb]

Why do you need to slow it down within 10 seconds?

While the energy needed for acceleration (the same as deceleration, and it is easier to work in the frame of the asteroid) is enormous, the heating of the asteroid is a different question - if most of the energy goes into uniform motion, it can survive the process. The speed of sound in iron is several km/s - if you slow it with a surface force, the asteroid needs ~4 seconds until you can slow it uniformly. Within that timescale, the front moved (assuming 900g) by 18km compared to the back. That is not reasonable - the acceleration is sufficient to give a shock-wave in the asteroid, and will heat it extremely.

If you leave more time for the acceleration, things look better: With 1000 seconds, the acceleration to get the same velocity change is just 9g. The initial compression of the asteroid is of the order of 1%, and more than 99% of the time you can slow it down uniformly.

Magnetic fields could apply a force on the whole volume, so higher accelerations might be possible.

 

[chasrob]

You've left out two important parts, how and why.

How:
This is going to require an immense amount of power. You're operating on the lottawatts scale (100 yottawatts). That's on the upper edge of a Type II civilization. Certainly such a civilization could accelerate a rubble pile asteroid of that mass at 900 g. Apply the magical force uniformly across the asteroid, use a magical force field to hold the asteroid together, or reinforce the asteroid with magical unobtainium rods. No problem! An iron-nickel asteroid would be a piece of cake compared to a rubble pile.

Note the words "magic" and "unobtainium". A Type II civilization would be magic by our standards because "any sufficiently advanced technology is indistinguishable from magic."

Why:
Why are you doing this? 900 gees for 10 seconds is a Δv of 88 km/s. You are sending the asteroid out of the solar system, and rather quickly at that. Why? Wouldn't it be better to mine it?

Yep, good points. It's a Kardashev nightmare!

The "civilization/entity" in my story has this problem: the 'roid can be slowed, the biggatons of energy are there, but there are no magic fields to hold the chunk together. At least I'm working from that premise currently. The coupling of that energy to the metal mountain, didn't think of that... might involve some more magic.

As to the Why--I had a brain fart and left out some stuff in the OP.

Mining it would definitely be better, and is a part of the story.

 

[D H]

I was off by an order of magnitude in my first post. I misread diameter as radius.

Mining it would definitely be better, and is a part of the story.

The energy required is on the order of 10²⁶ joules. A 20 km diameter iron-nickel asteroid is not going to be worth that kind of energy expenditure. So what's the point of this exercise? Certainly a civilization of that scale would be smart enough to know that the most economical thing to do is to ignore the asteroid. That changes if it's on a collision course with a planet or something else worthwhile, but then the strategy would be to deflect rather than stop.

What is the source of this super-civilization's energy? Have they found that MWI is not only the correct interpretation of QM, but also that it is exploitable? For example, open a gateway to some pre-inflationary universe and tap that huge amount of energy. In a sci fi world, that's easy. It's just words in a row. If that's the case, instead of opening a gateway to transfer energy and use this energy to stop the asteroid, why don't they just open a gateway and transfer momentum to/from some other universe? Get rid of the energy middle man.

 

[chasrob]

The energy required is on the order of 10²⁶ joules. A 20 km diameter iron-nickel asteroid is not going to be worth that kind of energy expenditure. So what's the point of this exercise? Certainly a civilization of that scale would be smart enough to know that the most economical thing to do is to ignore the asteroid. That changes if it's on a collision course with a planet or something else worthwhile, but then the strategy would be to deflect rather than stop.

Absolutely. But an advanced civilization is not involved in the plot, and the cost of the energy expenditure is nil.

I'm not trying to be cryptic here, I am just trying to determine the effect of the forces on a real asteroid and maybe tweak the story to fit. How much magic and technobabble will be involved, IOW?

...What is the source of this super-civilization's energy?

Hawking radiation at trans-Planckian energy densities. The hilarious thing is that's what I actually plan to use in the narrative. Sci-fi, right?

I'm not trying to be a wise acre, its just that you-all are tired of hearing crackpot theories.

Have they found that MWI is not only the correct interpretation of QM, but also that it is exploitable? For example, open a gateway to some pre-inflationary universe and tap that huge amount of energy. In a sci fi world, that's easy. It's just words in a row. If that's the case, instead of opening a gateway to transfer energy and use this energy to stop the asteroid, why don't they just open a gateway and transfer momentum to/from some other universe? Get rid of the energy middle man.

Awesome ideas, as the kids say.

MWI?

 

[chasrob]

continuing...
melting point of iron is about 1800K, specific heat (solid) about 450J/kgK
If we start the iron at 0K, then the energy to melt the entire asteroid is: 452*1800*3.2e16=2.6e22J ... so it is conceivable that the process could liquify the entire thing if the energy is not drawn away somehow.

Latent heat of vaporization is 6090kJ/kg, so we can work out how much of the asteroid could be vaporized.

These calculations are pretty straight forward ...

Note - for a rubble asteroid, the gravitational binding energy would be given by $U=3GM^2/5r$ - which would be the energy to disperse the asteroid to the edge of the Universe. Just for comparison.

Phil Plait does this sort of calc routinely...
http://www.badastronomy.com/bad/tv/doomsday.html

I didn't think of the heat involved, urk. I had inertia and tensile strength of iron, only, on my mind--why I mentioned guesses in the OP. I thought that if the asteroid didn't hit anything, no kinetic energy would be released.

So, you're saying slowing the sucker down would be like a slo-mo, 10 second collision,or something like that? Would part of that energy be in heating the metal chunk and part be tearing it apart? Since turning it to rubble would be so energy intensive, most of the KE would be used to heat it?

 

[chasrob]

Why do you need to slow it down within 10 seconds?

While the energy needed for acceleration (the same as deceleration, and it is easier to work in the frame of the asteroid) is enormous, the heating of the asteroid is a different question - if most of the energy goes into uniform motion, it can survive the process. The speed of sound in iron is several km/s - if you slow it with a surface force, the asteroid needs ~4 seconds until you can slow it uniformly. Within that timescale, the front moved (assuming 900g) by 18km compared to the back. That is not reasonable - the acceleration is sufficient to give a shock-wave in the asteroid, and will heat it extremely.

If you leave more time for the acceleration, things look better: With 1000 seconds, the acceleration to get the same velocity change is just 9g. The initial compression of the asteroid is of the order of 1%, and more than 99% of the time you can slow it down uniformly.

Magnetic fields could apply a force on the whole volume, so higher accelerations might be possible.

Exactly what I was looking for. Yes, slow the de-acceleration time scale.

But that surface force you speak of to slow it down, must that be applied over all the surface; half the surface? I was thinking of a force applied to a small area (~0.001 m²). That would surely cause, at least, local melting and possible fracture of the asteroid?

 

[D H]

Exactly what I was looking for. Yes, slow the de-acceleration time scale.

But that surface force you speak of to slow it down, must that be applied over all the surface; half the surface? I was thinking of a force applied to a small area (~0.001 m²). That would surely cause, at least, local melting and possible fracture of the asteroid?

At 900 g, that wouldn't stop the asteroid. It would punch a hole straight through it.

That's assuming your that your 0.001 m² device was made of ultra-strong unobtainium, Not your run-of-the-mill ordinary unobtainium, mind you. This needs to be a nearly unobtainable type of unobtainium. If your device was made of ordinary matter it would crumple into junk the instant power was supplied.

0.001 m²? Do. Some. Math. That's a pressure of 3×10²⁶ pascal, or 10 million times the pressure at the very center of the Sun.

 

[chasrob]

I was referring to the 9g scenario of mfb.

 

[D H]

You've reduced the acceleration, and hence the force, and hence the pressure by a factor of 100. So now you're just 100,000 times the pressure at the very center of the Sun. It still won't work.

 

[Ryan_m_b]

Is there a reason you want the asteroid slowed down so quickly? Why not have a scenario where a massive solar sail is attached to it and using power beamed from solar collectors near the sun it is slowed down over a period of years? That's a fantastic engineering challenge but not a magic one.

 

[Simon Bridge]

I didn't think of the heat involved, urk. I had inertia and tensile strength of iron, only, on my mind--why I mentioned guesses in the OP. I thought that if the asteroid didn't hit anything, no kinetic energy would be released.

When you slow the asteroid down, you must turn it's kinetic energy into something. The calculation was what would happen if all the kinetic energy turned into heat - distributed evenly over the entire asteroid.

If it does not go into heat - where does it go?
This is where the "how" question comes in.

So, you're saying slowing the sucker down would be like a slo-mo, 10 second collision,or something like that? Would part of that energy be in heating the metal chunk and part be tearing it apart? Since turning it to rubble would be so energy intensive, most of the KE would be used to heat it?

It does not matter how slow the deceleration is, if the energy stays with the asteroid. If the acceleraton is very slow, you may be able to radiate the heat away as fast as it is generated. You can use Stephan's law to work out the energy lost through radiation from the iron when it is merely red hot (say) and that tells you the deceleration rate... if you really want.

It is the "how" that governs things here though ...

The energy for "tearing it apart" depends on the "how" as well ... you could melt the entire thing and still have a big wobbly liquid iron thing in one bit, or you could vaporize it and have a big cloud of gas or vapor ... these things are held together by gravity and some sort of weak electrostatic attraction(?) a la Van der Waals (the gas woud probably have enough KE to escape the weak gravity of the aggregate - vapor droplets would cool to ball-bearings quite fast I suspect). To totally destroy it you want to overcome the gravitational binding energy. That would also work if you just carved bits off and chucked them away.

I still think you have to answer the how and why questions - what is the point of doing this in the first place and how do you plan on removing the kinetic energy?

Hawking radiation at trans-Planckian energy densities.

... i.e. you are slowing it by hitting it with a lot of subatomic particles? This will make a lot of heat - you have to fire them head on and they are going to lose KE as well... so, off the top of my head, roughly double the prev figures?

As previously observed though, such an energy beam would just punch a hole right through the asteroid. Set it to a wide dispersion instead? Perhaps use the beam to carve the asteroid into manageable chunks and a railgun to decelerate them?

I think you should be getting an idea of just how much technobabble is involved.
If the idea is to catch the asteroid BTW, you need only reduce it's kinetic energy to below it's binding energy with the Sun. Then they've got it, maybe in a long period ellipse, and they can use long-term strategies to slow it further.

 

[D H]

The calculation was what would happen if all the kinetic energy turned into heat - distributed evenly over the entire asteroid.

That is not a valid computation, Simon. You are violating conservation of momentum. Moreover, the asteroid is not an isolated system. Momentum (and hence energy) is transferred to the external environment. The asteroid's total energy is not a conserved quantity.

 

[mfb]

Hmm... some other ideas:

Detect it early enough - we have unlimited energy, so I assume large space telescopes are not an issue.
Hit it with some mass (railgun installed somewhere? another asteroid?) to modify its path to come very close to the sun - something like 5 million km (I did not check the Roche limit to see if it breaks apart, but I think for iron this should be fine). This gives a perihelion speed of 197km/s, and you just have to reduce it by 27km/s to 170km/s to catch the asteroid - you reduced the necessary velocity change by a factor of 4. While the asteroid is close to its perihelion, it receives ~5*10¹⁴W of solar radiation, and it spends ~25000s in this distance, so it just gets 10^¹⁹J of solar radiation - about 1J/g, low enough to neglect it. The required deceleration is roughly .1g.

If you can install something on the asteroid to eject a lot of material with a velocity of 1000km/s (purely science fiction here), you "just" need 2.5% of the asteroid mass and heat just depends on the efficiency of those objects. The required energy is incredible.
Heated to 1000K, the asteroid emits 71TW of thermal power (in the best case - a perfect blackbody). If we hit the asteroid with particles at a relative velocity of 100km/s and assume perfect heat conduction, we can shoot with 14 tons/s (twice the rate of trash production in the US, thank you WolframAlpha), giving a deceleration of 1.4µm/s². To slow it by 100km/s, we need just 22000 years! Heating it to 2000K does not help much, it reduces the time to 1400 years.
If we coat the surface with a good thermal insulation and add a layer of tungsten, it could be possible to go up to ~4000K for a while, but then we still need nearly 100 years (and no thermal insulation will resist that temperature for 100 years).
A lower velocity reduces the heat to deceleration ratio, but then the first material will increase the momentum of the asteroid. You quickly get the nasty rocket equation, where the material of the asteroid increases exponentially. Certainly not a useful way to slow it down.
Bombarding the asteroid with anything is not reasonable as main method to slow it down.Jupiter could help, but only if the asteroid has been slowed down significantly before (like ~50km/s?). Then, Jupiter can reduce the velocity by several km/s in a fly-by.

 

[Simon Bridge]

That is not a valid computation, Simon. You are violating conservation of momentum. Moreover, the asteroid is not an isolated system. Momentum (and hence energy) is transferred to the external environment. The asteroid's total energy is not a conserved quantity.

Yes exactly!
The computation itself is valid, but the assumptions (total energy of asteroid conserved[1]) do not hold - so it's results could not be used as per post #12. That's not what it was for.

It is important for people reading the calculation to realize that I intended it only as a comparison for the energies involved. I have not even touched on conservation of momentum ... I couldn't really because, at the time, OP had not gone into detail about "how" the asteroid was to lose all that energy.

Readers should understand that I am not writing a thesis here.

They should also realize that I am not the only person providing answers here - so I don't have to be complete all the time. Education is a process not a result - it will usually take a few posts to get a complete answer out.

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

[1] I had suspected earlier that OP was not thinking about what happens to the kinetic energy that gets lost ... the comment: "I thought that if the asteroid didn't hit anything, no kinetic energy would be released" in post #12 would seem to bear out that suspicion. I suppose I could have just asked first...

 

[chasrob]

It seems that my story as it stands is intractable.

But I'm somewhat confused. Are you saying that, e.g., if I hooked up 50 million Saturn V's (or one giant equivalent) and slowed the asteroid down by ~90 km/s, the asteroid itself would heat up, because its difference in KE?

 

[mfb]

No. If you can install giant mass drivers on the planet, you can slow it down without (necessary) heating. In an ideal world, where the rocket engines of those Saturn V do not heat up, you get the same, if the rocket is pointing downwards (so the exhaust leaves the asteroid). Saturn V won't help, however - they can change their own velocity by ~15km/s, and they need to be staged for that. There is no way to slow down additional mass (and we have a lot of mass) by 100km/s with chemical combustion.

 

[Simon Bridge]

I concur - that's why the "how" is so important ;)
You'd get some heating from the engines, but you are basically chucking mass away as your method of slowing.
The energy kinda leaves with the mass, so it doesn't hang around heating stuff up.

OTOH: if you directed a particle beam at the oncoming asteroid as your "how"...