What is wrong with my math, or are asteroids just that impossible to move.

[travis575757]

So i was bored, i wanted to find what affect it would have if the strongest nuclear bomb ever made (tsar bomb, now marshmallow) would have on an asteroids velocity. This is what i got.

stony meteorite is 4.5g/cm^3

4.5 tonnes a meter

asteroid size is 8km by 1km by 1km

8 billion cubic meters

3.6x10^10 metric tonnes

3.6x10^13 kilograms

velocity 20 km/s

Energy in joules = 1/2 * m in kg * v^2 in m/s

potential energy 12,000,000,000,000,000,000,000

7.2x10^21 joules or 7.2x10^12 giga joules <---- yeah these values got messed up some how, the difference in the end was about .1 m/s pretty much little to no difference

energy of 1 ton of tnt = 4.184 giga joules

marshmallow is 50 megaton

50000000*4.184 = 209,200,000 giga joules

marshmallow energy in giga joules - 209,200,000

potential energy of asteroid - energy of marshmallow

11999790800000000000000 = 0.5 * 6x10^13*v^2

23999581600000000000000 = 6x10^13*v^2

399993026.66666666666666666666667 = v^2

19999.82 m/s = v

So is this right???? Thats just crazy right? I don't get it someone fix this please.

Edit: why is it that the velocity ends up different when using the velocity made by the

---

tsar bombmashmallow and when subtracting ke from initial energy

Edit: okay what I was trying to say above is that why is it that u get 100 m/s change when finding the change in velocity on the object alone but only .20 m/s with energy of the asteroid minus energy of bomb

Edit: Okay im pretty sure the problem is that kinetic energy shouldn't be used to find velocity because it is logarithmic and not linear in relation ship. As velocity goes up energy going up decreases. So basically kinetic energy is like a end result (right?). This means that kerbart with all of his ragging with the mess i had in my maths (BECAUSE I DID IT IN NOTEPAD AND COPY AND PASTED IT) did it the right way. Find velocity made from energy on mass of object first, then subtract velocity. If i did that math and subtracted a energy in joules from a object going very fast the speed would decrease less in total then the same on a object going very slow

A.5kg at 5000m/s taking away 2 joules of energy

5kg *.5 *5000^2 = 62.5e6 -2 = 62499998

Sqrt(62499998*2/5) = 4999.99992 m/s

then

B. Sqrt(2*2/5)= .8944271 m/s = 4.999.11 m/s

When looking at this its a big difference. Could someone clear this up so i can make sure that B. is the correct way.

Also people failed to realize that i used the word math in my topic so to stop complaining about how a nuke isn't going to give 100% energy kinetically i replaced all parts with tsar bomb with marshmallow. Who likes my 50 megaton marshmallow?

Edited February 27, 2014 by travis575757

[Lohan2008]

Are you trying to deflecting tragectory ? Is asteroid on an eliptical orbit around sun ?? Is it being affected by gravity from other celestral objects ?

Newton's laws of motion needs to be factored in the maths.

The kinetic energy (energy of motion), of a moving object is linear with both its mass and the square of its velocity: Ek= 1/2 m*v^2 {wikipedia}

It would not be energy effecient to use a BIG explosion that expands into a sphere, you would be better to shape the detonation with a series of smaller blasts.

Edited February 25, 2014 by Lohan2008

[Spica]

As far as I can tell, this math is assuming that all of the explosive force is imparted perfectly efficiently into the kinetic energy of the asteroid, which is most certainly Impossible.

[LordOfTheOrbits]

Ummmm, what is asteroid orignal velocity ? Are you trying to deflecting tragectory ? is asteroid on an eliptical orbit around sun ??

I think these calculations tell how much change in velocity is produced and not the total velocity.

I'm not sure if these calculations are correct, but you probably are assuming that all of the energy of the bomb is converted directly to velocity change in the asteroid, but you probably aren't calculating that some energy goes into other directions and a lot of the energy also gets converted into heat and light.

[falofonos]

You may be able to get 30% or the tsar bomb's energy to counter the velocity of the asteroid. Probably more if you used fancy alloys to make a shaped nuclear charge.

Your objective seems to be to stop the asteroid by detonating the bomb in its path. To deflect the asteroid you could attach the bomb perpendicular to the direction of the rock's motion and detonate, your change in orbit would be significantly more useful from that that just trying to stop it dead.

The rock would also have to be a nickle iron solid mass for this to work, for a carbonaceous chondrite it's likely it would break up and disperse from the blast.

Edited February 25, 2014 by falofonos

[Kerbart]

Why all the hard to read 10^13 notation?

Why not just write 10¹³?

Unless you want people just to ignore the post and what you're writing because it looks messy, of course.

Now some back-of-the-envelop calculations.

You're saying that the Tsar Bomba released 50×10⁶ tons of TNT of energy, and that one ton represents 4.2×10⁹ joules of energy. Multiplied that gives us about 200×10¹⁵ or 2x10¹⁷ joules of energy. (If you're going to work with scientific notation, use it to your benefitâ€â€sofar I did not need a calculator).

Now, with kinetic energy being ½mv² we can say that v² = 4×10¹⁷ ÷ m, with m being 3.6×10¹³ kilograms. That leaves you with v² = 1.1×10⁴ and v rougly equal to 100m/s give or take. Of course that's from a starting point of zero velocity. Your argument is that the asteroid is moving at 20 km/s, but that only applies if the bomb (assuming we manage to convert all its energy to kinetic energy which is a GIGANTIC if) is not moving itself and meets the asteroid at 20 km/s. A more likely scenario would be to explode the bomb while it matches the velocity of the asteroid, in which case the energy would amount to a delta-V of 0.1 km/s which is quite impressive for such a massive body, but does nearly nothing in regards to 20 km/s.

[Camacha]

Why all the hard to read 10^13 notation?

Why not just write 10¹³?

Unless you want people just to ignore the post and what you're writing because it looks messy, of course.

If you ever did anything with math and computers, chances are it looks the same to you. It pretty much does to me.

[softweir]

It's a matter of personal preference: I've done most of my math using computers, but even so I find the superscript system for exponents much easier to read.

[falofonos]

http://en.wikipedia.org/wiki/Chelyabinsk_meteor

That one was only 20 meters across and approximately 12,000–13,000 metric tonnes.

Your test rock would likely exterminate all life on earth if it hit.

[Kerbart]

If you ever did anything with math and computers, chances are it looks the same to you. It pretty much does to me.

Probably longer than you did. However I also do design. I can assure you it does not look the same to me. Why stick to a crutch when you don't have to? Notepad doesn't do superscript, but the forum software here does. Is there any reason to stick to ugliness?

[Accelerando]

Probably longer than you did. However I also do design. I can assure you it does not look the same to me. Why stick to a crutch when you don't have to? Notepad doesn't do superscript, but the forum software here does. Is there any reason to stick to ugliness?

It's quicker, it's easier. It clearly caught your attention so it seems to have done its job fairly well.

[Streetwind]

Yeah, what's the point in arguing about the notation anyway? It changes absolutely nothing about the intent or the factual content of the original post. It's also a well known and established method to write exponents.

Sometimes it's good to remind ourselves that just because we're on the internet, we're not contractually required to find something to complain about in everything we read.

Edited February 26, 2014 by Streetwind

[Ralathon]

So is this right???? Thats just crazy right? I don't get it someone fix this please.

Nah, asteroids are just hard to move. It's essentially a mountain that moves several kilometers per second after all.

That said, your velocity change would be even smaller due to the inefficiencies that creep into the nuclear blast. You radiate at least half of it into space and lose a lot of energy heating the surface. Luckily you don't need to adjust the velocity of the asteroid that much. Even 0.01m/s is more than enough to make it miss the earth by a wide margin assuming you do it early enough.

[radonek]

So is this right???? Thats just crazy right? I don't get it someone fix this please.

Yes, the idea that you can move a mountain of iron and stone wheezing around at tens of kilometers per second with a nuke really is crazy. I am seriously surprised you got to any velocity change at all…

I remember when Armageddon movie got out (… of mental hospital :-) ) just about all scientists pointed out that idea of moving, much less destroying an asteroid with nukes is ineffective, implausible and stupid. Seriously proposed methods involved (relatively) small forces like solar sails, laser ablation, gravity a-tractors etc. working over extended period of time.

AFAIK the main thing is that atomics are effective in terms of packing lot of energy – thousands of them is still small price for such a task. Its hauling them all the way from bottom of The Well that is wastefull. If you could produce them localy (ie, asteroid you are moving is rich in fissible material) that spell a different story…

[Scotius]

Good way to redirect such Doomsday Rock (provided we spot it early enough) is to send a set of ion engines, bunch of solar panels and a tank full of xenon. Anchor it firmly and start blasting. After a year (or ten) its trajectory would move just enough to change armageddon into near miss.

[Kerbart]

It's quicker, it's easier. It clearly caught your attention so it seems to have done its job fairly well.

Quicker and easier is the standard now, instead of careful and better? Good to know.

[Kerbart]

Sometimes it's good to remind ourselves that just because we're on the internet, we're not contractualyl required to find something to complain about in everything we read.

THE POINT IS THAT IF YOU WANT PEOPLE TO HELP YOU ITS BENEIFCAP DO MAAAK E SUR E THAT THEUY CAN REDA IT EASILYU INSTEAD OF FEEDING HTME HART RRO TEAD TEXT THAT TAKES A LOT OF EFFORT TO DECIPHER IT IS ACTUALLY IN ONES OWN BENEFIT TO KOMMMUNICATGE CLEARRYL INSTAD OF DOING OTHER SMAKE THE WORK FOR THEM BUT APPARENTLHY THAT DOESNT' TMATTER AND YOU CAN JUST RELXHA AND TYPE WITHOUT CARING IF IT LOOKS OK OR IS EASY TO READ TO ME THAT IS NOT THE RIGHT WAY TO ASK PEOPLE TO BE KIND OENOGH TO ANSWE A QUESTION BUT OBVIOUSLY I AM WRONG THE GOOD THING IS THAT IT SIS GOING TO SAVE HME A LOT OF WORK BWNE TYPEING HERE THANKS YOU COFR POINTNG THAT OUT

Whoops I noticed I left my capslock on. Well it's easier and quicker to leave it this way.

[Red Iron Crown]

Your math looks good to me (and while I prefer proper superscripts I can read your notation just fine ). It really does take a tremendous amount of energy to change the velocity of something so massive moving so quickly.

The good news is, if you're just trying to deflect it from striking Earth and you can get the bomb to it when it's far enough away, only a very small change of velocity is required.

If, however, you're trying to capture it and put it into an orbit of your choosing, you're gonna have a bad time.

[Albert VDS]

Good way to redirect such Doomsday Rock (provided we spot it early enough) is to send a set of ion engines, bunch of solar panels and a tank full of xenon. Anchor it firmly and start blasting. After a year (or ten) its trajectory would move just enough to change armageddon into near miss.

That could only works if this rock is one solid object, if you can get all the engines aligned so that it doesn't spin out of control, if it's close enough to the Sun to use solar panels.

So all the odd shaped asteroids, the ex-comet asteroids, the asteroids which are a bunch of smaller asteroids clumped together, the asteroids with a center of mass every but in the center, etc. are not possible to have their orbits changed by such a setup.

[Red Iron Crown]

That could only works if this rock is one solid object, if you can get all the engines aligned so that it doesn't spin out of control, if it's close enough to the Sun to use solar panels.

So all the odd shaped asteroids, the ex-comet asteroids, the asteroids which are a bunch of smaller asteroids clumped together, the asteroids with a center of mass every but in the center, etc. are not possible to have their orbits changed by such a setup.

Odd shapes or center of mass not at center of the asteroid are no problem, as long as the thrusters' vectors pass through the center of mass it shouldn't spin and the thrust will be changing the asteroids vector usefully. I don't know why you consider ex-comet asteroids to be immovable, there's no reason I can think of why that should be so.

[Albert VDS]

Sure you could do that, but that's still not an easy thing to do with an asymmetrical object.

Also, what about objects which are already spinning?

Ex-comet asteroids are basically a powder held together, it's not a solid object.

[PakledHostage]

Odd shapes or center of mass not at center of the asteroid are no problem, as long as the thrusters' vectors pass through the center of mass it shouldn't spin and the thrust will be changing the asteroids vector usefully.

While I agree that nudging an asteroid sufficiently to avoid an impact is within the relm of possibility, given enough advanced warning, you have to assume that the object is already spinning at some rate. It is just as improbable that the object has exactly zero rotation as any other rotational speed. Any scheme that uses engines mounted to the surface of the object is going to have to account for the rotation. This is where gravity tractors and nuclear warheads detonated above the asteroid's surface have an advantage. And nuclear bombs have the additional advantage that they can be detonated on a flyby trajectory. This may save enough delta-V to make it possible to deliver the charge quickly using only existing rocket designs.

Edit: Ninja'd by AlbertVDS... I guess I should have refreshed before replying.

Edited February 26, 2014 by PakledHostage

[Red Iron Crown]

Well, for a spinning object, we would need to thrust in such a way to create torque around the CoM until the spin was cancelled. For irregularly shaped objects, a gimballed thruster could quickly determine the CoM by measuring how it affects spin.

The comet thing is a problem though. Maybe if the thrust was low enough it would hold together? Or if it crumbled into smaller parts on differing orbits, wouldn't that achieve most of what we're looking for?

[PakledHostage]

Well, for a spinning object, we would need to thrust in such a way to create torque around the CoM until the spin was cancelled. For irregularly shaped objects, a gimballed thruster could quickly determine the CoM by measuring how it affects spin.

I suspect that you'd find that the amount of energy required to stop the rotation would be comparable to the energy required to deflect it by a few fractions of a m/s... You could, of course, pulse your engines every time the asteroid was oriented the right way, but then they would have to be designed for literally thousands (if not millions) of restarts and it would take a lot longer.

[radonek]

Idea: how fast can asteroid rotate before breaking up? I guess its out of question for iron ones, but ice?