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If humans were to muster all their weapons together would it be possible to move Earth's orbit? If we were able to manage it, how far and fast would it travel? Most likely it would kill all inhabitants of Earth and these weapons are of the current technology.

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    $\begingroup$ Seriously scale error here. $\endgroup$ – JDługosz Jul 7 '16 at 19:25
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The world contains about 15,000 nuclear weapons. The largest nuclear test by the US was around 25 megatonnes of TNT in yield, so let's assume that our average yield is about 20 megatonnes. A megatonne of TNT has a yield of 4.2 petajoules when converted to standard units, or $4.2 \times 10^{15}$ joules. Multiplying all of this together, we get a total energy for all of our nuclear weapons of:

$4.2 \times 10^{15} \times 20 \times 15,000 = 1.26e \times 10^{21}$ joules of energy.

This is enough energy to do a lot of damage to the Earth, but it's still more than two orders of magnitude less energy than the asteroid that killed the dinosaurs, and even that amount of energy is far less than the amount of energy it would take to significantly change the orbit of the Earth. As a rough estimate, we can say that the amount of energy required to significantly change the orbit of the Earth must be of a comparable magnitude to the amount of orbital kinetic energy the Earth already has. The Earth has about $10^{33}$ joules of kinetic energy, which is greater than the energy of all of our nuclear weapons by around 12 orders of magnitude.

If we assume that, for small changes in distance relative to total orbital radius, orbital radius varies roughly linearly with energy, this yields a total change of orbital radius for the Earth of about a 10th of a meter if we could detonate all of the nuclear bombs we have in such a manner as to dump all of their energy into moving the Earth. We might change the orbit of the Earth by a little bit, but probably not by enough to measure with the most accurate instruments we've created.

For reference, radiation pressure from the sun probably moves the Earth by about this much every day. Pressure from particles from the solar wind move the Earth by about this much every year.

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Yes, theoretically.

But not by any amount that could be measured. The mass of earth and the orbital velocity around the sun is so huge that any conceivable weapon would give it such a tiny nudge you would never notice.

Remember that to change the orbit you need to launch something away at escape velocity. Firing a gun into the air won't do it, you need to be launching projectiles at 11.2km/s and then somehow stopping the air from slowing them down.

Now compare the mass of that projectile to the mass of the earth and you see the problem.

Even something like an enormous explosion that splits the planet in two (which we couldn't generate anyway) won't change the orbit unless substantial amounts of the planet are launched at a speed above escape velocity. The two halves of the planet would just continue in the same orbit rotating around each other and either join back together or form into a binary.

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Think of it another way. Instead of trying to directly move the Earth, with our current weapons could we nudge an asteroid into a near earth "miss" that would gravitationally drag Earth a little bit?

Probably, but it would require a lot of careful preparation and the margin of error would be minute. Then we would be potentially increasing the number of big things with an orbit that crosses the Earth (assuming the big rock will circle back around to pass by the Earth again), never a wise decision. Ideally there is one already out there we could slightly adjust for our purpose.

Plus it would be a LONG process as any asteroid we could move with our current weapons/rockets wouldn't be very large, so the drag it could place on the Earth would be very small. We would have to repeatedly nudge the asteroid, pass after pass, to keep the Earth moving in the desired direction (away from the expanding sun, presumably). "Weapons" (like nuclear explosives) probably aren't the best things for this, but anything with the power to shift an asteroids orbit can be considered a weapon (be it nuclear thrust, a laser, or mass driver coilgun).

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I'm going to go ahead and assume that by "dislodge earth's orbit" you mean "escape the gravity of the sun." Correct me if I am incorrect, of course.

To answer your question: Unfortunately, no, we can't even hope to do that, even if we waive the survival of life as a requirement.

In order to effectively break from orbit around the sun, we have to reach what is called Escape Velocity. This is the minimum speed at which an object must be travelling in order for that object not to be slowed and reversed by the gravity of the body it is trying to escape. Think of throwing a ball into the air. The faster you throw it, the farther up it travels before falling back to the ground. If you throw it fast enough, it will never return. This speed is escape velocity.

The Solar Escape Velocity is 42.1 km/s. That's fast. The Earth actually already moves at about 30 km/s though, so if we wanted to eject the Earth from her Solar Orbit, we need an effective Delta-V of 12.1 km/s. Let's do some quick math to see how much energy will be needed to achieve that change in velocity.

Kinetic Energy is calculated with the formula E = (1/2)mv^2 where m is the mass of the object and v is its velocity. The mass of the earth is 5.972x10^24 kg. The velocity of the earth, as I stated, is 30,000 m/s. Inserting those into the equation yields a kinetic energy of 2.6874x10^33 Joules. This is the current kinetic energy of the Earth.

To find out how much energy we will need, we need to calculate the hypothetical kinetic energy of the earth at escape velocity, then subtract the current energy to get the difference. Running the numbers using solar escape velocity gives a kinetic energy of 5.2924x10^33 Joules. That's something like double the current energy of the earth. To be exact, we'll need to increase the earth's kinetic energy by 2.605x10^33 Joules.

So how much energy IS 2.605x10^33 Joules? If we write out that number in a more familiar way, it looks like this: 2,675,000,000,000,000,000,000,000,000,000,000 J. To be honest, there is really no way the human mind can grasp that sort of number. The entire energy consumption of human civilization of the Earth is something like 10^19 J in one year. The Estimated reserves of energy bound in oil is 10^22 J. Magnitude ~9 Earthquakes put out similar energy. The meteor strike that "killed" the Dinosaurs released about 10x that amount. Here's the thing about this sort of estimation, though. 10^23 might seem only slightly less than 10^33, but in reality each single increase in the exponent increases the number by 10 times. 10^33 is 10 BILLION times greater than 10^23.

Going back to the Earthquake example, a magnitude 9 Earthquake is horribly intense, and it's not even close to enough energy. An estimated magnitude 12 is what was caused during the above mentioned meteor strike in the Yucatan, and even THAT is way too small. The level of energy we would need to break the Earth free from the sun would register as a magnitude 19 on the Richter Scale. This is literally Earth Shattering. So even if humanity DID possess enough energy to achieve this goal (we don't), then attempting it would literally destroy the earth.

But that's all assuming we wanted to do it all at once. Obviously we don't launch rockets using one giant bomb, we distribute the energy flow over the course of the launch. Let's assume we mounted a massive rocket engine on one side of the Earth, and lit it off with the hope of launching the Earth away from the sun after a long burn. If we limited the energy output of the rocket to something reasonable (let's say ~5x10^16 Watts, which would feel like a constant magnitude 8 earthquake) then the rocket would burn for a billion years before the Earth had enough velocity to escape the sun's gravity.

So unfortunately, I can't really say that moving the Earth is a viable option. Her mass is just Too Damn High!

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How much would you want to move the orbit for it to be considered significant?

Back in October 2013, the Juno probe stole some of Earth's momentum as it flew by in a gravity assist, altering it's orbit. The amount was infinitesimally small, but still measurable to a degree.

Given that you talk about weapons, the method would be different from a gravity assist, but the change would be there all the same. However, the effects would be completely unnoticeable compared to the effects of the weapons themselves, which would wipe out life before you could even notice the orbit had changed.

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protected by L.Dutch - Reinstate Monica May 17 at 11:03

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