How powerful would nuclear blast on the Earth's surface have to be in order nudge it slightly from its orbit?

Odd you should post this as it brings to mind this film: The Day the Earth Caught Fire (1961) where exactly this happened.
Admittedly I would imagine it would have to be multiple blasts rather than one as the power involved would be massive.

This is one for Monkey Boy to work out.

A few things to consider
1) The mass of the earth-5.98 × 1024 kg

2) The momentum of the earth in its orbit

3) The conservation of momentum- For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision. That is, the momentum lost by object 1 is equal to the momentum gained by object 2.

Do the math :)

You haven't defined "significat amount" but let's assume you mean an amount that would be detectable (a change in the length of year of a second or 2)

Very incredibly powerful. We've had huge meteors crash into the earth with little to no change in the orbital.

For a nuke (or any explosive), you have to remember that the blast actually does nothing to move the earth. The only thing that would make the Earth move would be the ejection of particles and radiation out into space.

I have no idea how much that would be but I would imaging it would be a small fraction (20%? 5%?) of the mass of the bomb and a very very very tiny tiny tiny fraction of the mass of the Earth. By conservation of momentum, that would be not much movement of the earth. Our current nuclear tests/bombs have done squat to change the earth's period.

You could look at it as being an Earth-rocket. The more you spew out one way, the more it accelerates in the other way.

You're not going to do anything without a bomb a significant fraction of the mass of the earth, that's fairly beyond us at this stage.

I know this isn't the best answer but I hope it starts to satiate your curiosity.

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Originally Posted by Capuchin

You havent defined "significat amount" but let's assume you mean an amount that would be detectable (a change in the length of year of a second or 2)

Very incredibly powerful. We've had huge meteors crash into the earth with little to no change in the orbital.

For a nuke (or any explosive), you have to remember that the blast actually does nothing to move the earth. The only thing that would make the Earth move would be the ejection of particles and radiation out into space.

I have no idea how much that would be but I would imaging it would be a small fraction (20%? 5%?) of the mass of the bomb and a very very very tiny tiny tiny fraction of the mass of the Earth. By conservation of momentum, that would be not much movement of the earth. Our current nuclear tests/bombs have done squat to change the earth's period.

You could look at it as being an Earth-rocket. The more you spew out one way, the more it accelerates in the other way.

You're not going to do anything without a bomb a significant fraction of the mass of the earth, that's fairly beyond us at this stage.

I know this isnt the best answer but I hope it starts to satiate your curiosity.

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I was under the impression that since every action there is an opposite one the force of the blast pushing against, or downward would make the Earth react without the debris having to be cast into outer space. Why do you say that the Earth reacts to the push only if the debris is thrown into outer space? What cancels out the push of the blast if the debris isn't thown into outer space?

If you view the earth and the blast as a single system (which they are) then how does it move without anything escaping?

A nuke is similar to an earthquake in what it does to the earth... earthquakes certainly don't move the earth out of orbit.. nukes have the added complication of the particles and radiation going off into space thing, but the change would be tiny when compared to, say, the radiation and solar wind from the sun hitting the earth.

*agree with capuchin*

For the earth to change momentum in direction D by magnitude M the nuclear blast would have to propel mass with a momentum M in the direction -D.

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Originally Posted by Capuchin

if you view the earth and the blast as a single system (which they are) then how does it move without anything escaping?

A nuke is similar to an earthquake in what it does to the earth... earthquakes certainly don't move the earth out of orbit.. nukes have the added complication of the particles and radiation going off into space thing, but the change would be tiny when compared to, say, the radiation and solar wind from the sun hitting the earth.

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Remember that Sci Fi program, "Space 1999", I think it was called, where they had stockpiled nuclear armaments on the moon and they exploded and sent the moon out of its orbit. Is that scientifically accurate?

Moonbase Alpha's Space: 1999 Page

Well, the mass of the moon is 1/80 that of the earth, the escape velocity is about 5 times less. So it's certainly EASIER to move. However I think the moon would be more likely to disintegrate from internal forces before it is shunted far enough out of orbit. You'd need a WHOLE LOAD of nukes.

Escape velocity is
The moon orbits at about 380000km from the earth and the mass of the earth is about 6*10^24kg and G is 6.67*10^-11, therefore, the moon's escape velocity is about 2.1*10^9 km/s
the moon's mass is 7.36*10^22 kg

So the energy required to accelerate the moon to this speed is given by and that's 1.62e47 joules. (needed to convert velocity to m/s since joules is kg (m/s)^2)

1 kiloton = 4.186*10^12 joules so you'll require the energy of 3.87*10^31 megatons of nuclear weapons

I couldn't find a good number for the total size of all of the world's nuclear weapons but it seems to be somewhere in the 8000 to 20000 megaton range. This is obviously far short of the required amount needed and this doesn't even account for the fact that not all of each weapon's energy would go in the right direction.

My head hurts! Lol!

Asterisk, I think you might need to take relativistic effects into account if you're accelerating the moon to a speed faster than the speed of light ;)

Agreed! Hadn't noticed that minor detail. I don't think that I did anything wrong so that's just another proof that an explosion will not be able to send the moon off into space.

More force is exerted on it by the sun's radiation than anythign we could ever push it with.

I swear to God my waking thought this morning was;

"Well what if the Earth was like a big balloon, and I undid the end - would it go flying all around the galaxy making a farting noise as it deflated?"

What the hell have you done to me!

That's your own problem mate :z

Fair play! Lol!

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Originally Posted by iAMfromHuntersBar

I swear to God my waking thought this morning was;

"Well what if the Earth was like a big balloon, and I undid the end - would it go flying all around the galaxy making a farting noise as it deflated?"

What the hell have you done to me!?

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Sounds like a personal problem to me! :)