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How powerful would a series of explosions have to be to significantly change a planet's axial tilt?

In my universe they have highly energy efficient crystals, not only do they store energy but they also produce it, somewhat like quartz. These crystals also potentiate the power of any energetic reaction released close by to astonishing levels whilst containing effectual destruction to a smallish area. If they are set off in a town, maybe the town's perimeter will be totally destroyed, razed, but its periphery will suffer "only" from radiation.

So my question is: would such a series of explosions, carefully planned and set, be able to affect the axial tilt of a planet?

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    $\begingroup$ Verne did the calculation for Earth in his Topsy Turvy $\endgroup$ – L.Dutch Nov 3 '17 at 15:10
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    $\begingroup$ @L.Dutch thanks, heading off to project Gutenberg ;) $\endgroup$ – shieldedtulip Nov 3 '17 at 15:21
  • $\begingroup$ @shieldedtulip when come back post answer! $\endgroup$ – Robert Columbia Nov 3 '17 at 15:28
  • $\begingroup$ Was also (sort of) the plot of THE CORE (2003), maybe as a reference of what NOT to do. LOL $\endgroup$ – wetcircuit Nov 3 '17 at 17:25
  • $\begingroup$ @wetcircuit, but on that film they had to reset the earth's core, not what I want to happen LOL I don't want to stop the core spinning, I want to change the tilt... if at all possible. Topsy Turvy is half read, more or less, but I need to get on with nanowrimo ;) $\endgroup$ – shieldedtulip Nov 3 '17 at 17:50
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An absolutely fascinating article was written by NASA about the magnitude 9 Sumatra Earthquake. That earthquake was so powerful that it...

  • Sped up the Earth's rotation.

  • Changed the Earth's shape.

  • Changed the Earth's axial tilt.

It's worth noting that the changes were, of course, miniscule. (The axial tilt changed by single centimeters.) But it did it. So, let's examine that earthquake. In the article, Dr. Benjamin Fong Chao said...

Any worldly event that involves the movement of mass affects the Earth's rotation, from seasonal weather down to driving a car.

The earthquake released energy equivalent to 1.8 trillion Kg of explosives. Converting that to a more practical measure, it's the equivalent of a 2,000 megaton nuclear explosion.

And to put that into perspective, the Tsar Bomba nuclear test explosion of the Soviet RDS-220 hydrogen bomb was ONLY 50 megatons. It had a 100% destructive blast radius of 35Km (22 miles). That's the radius, not the diameter. The earthquake was 40X more powerful (think, "100% destruction of the entire United States coast-to-coast." Chant it with me, children! "From sea to shining sea!").

But the earthquake wasn't a surface explosion. It was directly moving the mass of the earth. A surface explosion has "less to push against."

Newton's third law is not our friend when it comes to your question. Atmosphere represents very little in terms of what you can push against, which means a chunk of the energy needed to shift the earth's axis is lost to the springy mattress of atmosphere. I'm not even going to try to be accurate. Let's just assume you need at least 10X the surface explosion to do to the Earth what the earthquake did — not that I actually need more boom for a more dramatic conclusion....

But, now we're talking about a blast radius that would totally destroy the entire western hemisphere and a fair chunk of the eastern hemisphere. This is an important point that I'll conclude with. Call it "foreshadowing."

However, we are NOT doing something that's inside the earth and capable of affecting (at least not easily) it's rotation ... and rotation is what you need to shift the axial tilt. A surface explosion can push against the surface perpendicular to the earth's center, but it can't roll the planet over. You need to be inside to do that. You can move it in its orbit (push it closer or futher away from the sun, change its elliptic angle, or make the year longer or shorter), but you can't turn it upside down (which would be cool, by the way, if nobody got hurt in the process... which is the problem, donchaknow).


CONCLUSION

No, not really. You can't substantially change the axial tilt of the earth with a surface explosion.

But, if you could, the explosion needed would quite literally bring 100% destruction to a hemisphere. The resulting impact on the planet would certainly kill every living thing. So, even if you could shape the charge to give you the inclination needed to roll the planet... you wouldn't have a habitable planet left to brag about. And what are you bragging about? Having rolled the earth a few centimeters!

And I haven't even talked about what this explosion might do to the mantle.... That's an entire thesis by itself.

BIG EDIT: I've been thinking about this answer, and maybe... MAYBE... if you set this big mother hubbard of an explosion off against a large enough escarpment — not a mountain, not even a mountain range — but a big escarpment like Africa's Great Rift Valley... maybe you could get enough rotational push (assuming the escarpment is along the correct axis, which the Great Rift Valley isn't), maybe enough push to roll the planet.

So, maybe it is possible... but you still don't have a viable planet and you've still only rolled it a few centimeters. So the practical answer must remain "no."

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  • $\begingroup$ I read a similar one about the Japan quake. Had forgotten it. But it doesn't say that other things can't change the tilt so I'd have posted the question anyway. $\endgroup$ – shieldedtulip Nov 4 '17 at 1:18
  • $\begingroup$ Yeah. It's all a question of scale. Most people don't realize how unimagninably enormous the amount of energy released in an earthquake is. We're lucky as a species that all but a fraction of that energy is absorbed by the earth itself. $\endgroup$ – JBH Nov 4 '17 at 1:22
  • $\begingroup$ It's not luck, it's God. :) $\endgroup$ – shieldedtulip Nov 4 '17 at 1:37
  • $\begingroup$ What about "mad scientist bombs" buried in the crust? $\endgroup$ – RonJohn Feb 17 '18 at 0:03
  • $\begingroup$ @RonJohn, as I mention in the answer, the problems are (a) having something to push against that will rotate, not push, the planet and (b) not completely destroying the planet's habitability in the process. You can always handwave some Clarkean magic, but the science says it can't be done. $\endgroup$ – JBH Feb 17 '18 at 3:35
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To change the axial tilt you need to turn the angular momentum vector $\pmb{L}$ by supplying an angular impulse $\pmb{\alpha}$. So if you want to change the tilt by an angle $\theta$ the required impulse is $\pmb{\alpha}=\sin(\theta)\pmb{N}+(\cos(\theta)-1)\pmb{L}$ where $\pmb{N}$ is a normal vector to $\pmb{L}$ of the same length. The magnitude of the impulse is $||\pmb{\alpha}||=\sqrt{2}\sqrt{1 -\cos(\theta)}||\pmb{L}||.$ So the impulse will be of roughly the same order of magnitude as the angular momentum.

The angular momentum of Earth is $\pmb{L}=\pmb{I}\cdot \omega$ where the angular velocity $\omega=2\pi/T=7.2722\cdot 10^{-5}$ radians per second and the moment of inertia (assuming uniformity and sphericalness) $\pmb{I}=(2/5)Mr^2\approx 9.6928\cdot 10^{37}$, so $||\pmb{L}||\approx 7.0488\cdot 10^{33}$ Joule-seconds.

That means that to move it ten degrees, you need $0.1743||\pmb{L}||\approx 1.2287\cdot 10^{33}$ Joule-seconds. If we assume a second-long explosion to do it, that implies a roughly equal energy. This is more than the gravitational binding energy of the Earth ($10^{32}$ J), so it is likely that that kind of wrench will just splatter the planet. If we suppose it takes a day, then we are talking about slightly less than the Moon's kinetic energy and slightly above the impact that made the Caloris basin on Mercury. That crater is 1,500 km across.

In short, magical crystals (or crystal explosives) that can change the axial tilt of a planet can also definitely make it an uninhabitable ball of lava.

Now, if the crystals do weird things with momentum maybe they could turn the planet without splatting it. But now you have crystals that can also turn mountain ranges around; while crude as a melee weapon they do a lot of damage if you just leave them on top of your enemy and his kingdom.

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  • $\begingroup$ What if there were a series of "small" explosions which cause earthquakes on fault lines? (I'm thinking of the Sumatran earthquake that caused a minute change in axial tilt.) $\endgroup$ – RonJohn Feb 17 '18 at 17:33
  • $\begingroup$ Small explosions cause small changes. You would need enough of them to add up to a big change, and then you are talking about the same or more energy needed for doing it in one go. $\endgroup$ – Anders Sandberg Feb 18 '18 at 10:52
  • $\begingroup$ Very true. But nothing in the Question about doing it all at once. A Summatran-style earthquake every hour for a few million years... :) $\endgroup$ – RonJohn Feb 18 '18 at 13:30
  • $\begingroup$ Note that I did upvote your answer... $\endgroup$ – RonJohn Feb 18 '18 at 13:31
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No, for a number of reasons.

  • the required energy is several orders of magnitudes greater than that supplied by quantities of antimatter sufficient to blow the planet apart.
  • applying the force to the crust will rip said crust from the "liquid" mantle beneath, which would not follow immediately the change of direction.
  • unless performed in very, very long times, the planet would "wobble" and the ecosphere would be utterly destroyed in the shattering of the crust.
  • you don't need simply "energy" to change the momentum of a rotating body - you need to apply force, and this requires mass expulsion. The more and the faster, the better. It goes in the other direction too: you can do it with mass impulsion. But we're again talking of energies sufficient to shatter the planet and revert it to its molten state. Then, after enough million years to cool down, you'll have a planet again, with its axis tilted.

But...

  • If you used high-energy explosions or any other suitable means to throw carefully balanced mountain-sized projectiles at c-fractional, at a suitable angle (e.g. drilling a well at an angle so that the explosion does not push straight towards the center of the Earth)
  • allowing enough time for atmospheric turbulence to subside and extra energy dumped all the way to the stratosphere to cool off,
  • for a very long time (probably million of years; you might be able to do it in a few hundred thousand, but I'd need to run the calculations)

...then yes, you could nudge the planetary axis any which way and still have a planet at the end of the day. But you're never going to do it with Verne's canon qu'on braque.

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No

The astronomical properties of a planet such as earth would not be alterable in the way you describe. To change the axial tilt you would be fighting the angular momentum of the whole planet as the earth is “spin stabilised” and angular momentum is conserved. Any force capable of changing the axial tilt significantly would have to employ such enormous energies that the entirety of the crust would probably be melted due to frictional forces

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Yes.

If you create a powerful enough explosion that can jettison away enough mass at great enough velocities, you could alter the planet's axial tilt. Although, you'd probably alter a little more than the planet's tilt in the process ...

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