Thanks, samclem – and, hey, it’s my ignorance too. Anyway, here goes:
Bill –
Chuck Sheffield [that’s Dr. Charles Sheffield, former president of the American Astronautical Society – Jk] did all the hard work a long time ago. Using the assumptions of the people who wrote the “nuclear winter” papers, 1 megaton = 4.2e22 erg. 1 nuclear war = 25,000 megatons = 1e27 ergs. So you’re talking a thousand times that. Sort of like World War III fought every day for 3 years. (Sheffield “joked” in passing that this assumes all missiles are fired and they all work. As a Defense Department insider, he had reason to doubt that.)
But anyway it makes for a good metric here. Some comparatives:
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Available tidal energy (mainly the Moon braking the Earth) is a quarter of a Nuclear War per day. Course, we tap into hardly any of that. It goes into heat. Still, that adds up to your 10,000 gigaton bogey every 12 years.
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The blow-up of Thira, which wiped out Minoan civilization in 1470 BC, equaled 1 Nuclear War. (“fought” in this really small area.)
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Halley’s comet, about 10 km across, would impact with 170 million megatons, or 170,000 gigatons, or 7,000 Nuclear Wars. That’s an order of magnitude bigger than what you’re talking about. Sheffield told us to expect one of those events about once every billion years.
We can let Chuck out now. I’ll drive from here on.
Before the Solar System got cleaned up (mostly by bodies running into other bodies) this presumably happened a lot more often. We’ve probably taken at least half-a-dozen such wallops – including the one that ripped the moon out of the area that became the Pacific Ocean.
What would a ten thousand gigaton explosion feel like? Well, you can rest easy, relatively speaking – it would not bust the planet apart. I figured once (and maybe I sent you the numbers) that it would take total conversion of a cube of rock 11 kilometers on a side to shatter the Earth. (I think it’s pretty safe to say that no one will ever build a portable planetbuster!)
Still and all, a 10 K gigaton blast would for sure wreck the biosphere and maybe sterilize the planet. Maybe. But that assumes the energy is released in an instant. at the surface of the world.
The Earth is 40,000 km around. Surface area is 5,000,000 square km. Dividing, we get 2 megatons/square kilometer. We’d certainly feel that, if it came up all at once and was all expressed as mechanical shock. But I don’t think it would.
The tenth-of-a-second figure [for the final stage of black-hole evaporation – Jk] is irrelevant. Newton solved the differential equations of heat conduction a while back. And what he showed is thermal gradients tend to flatten out. Sharp wavefronts blur. Your backyard gets annual jolts of hot and cold, but there aren’t a steady series of thermal “rings” (like tree rings) sinking towards the center of the planet. Anybody who’s got a hand shovel can dig down to where the forefront is overtaken by the rearguard and the temperature is constant throughout the cycle. That’s why there’s permafrost in Tunguska.
It’s been a good 4 billion years and Earth is still leaking the heat of that 11-kilometer cube of rock-equivalent (the same energy it would take to blow the Earth to smithereens was, of course, released when it condensed from fragments). The Earth weighs six sextillion tons. Have to write that out to count the zeroes. 6,000,000,000,000,000,000,000 Six-times-ten-to-the-twenty-first tons. 6e24 kilograms. 6e27 grams.
One calorie heats one gram of water one degree C. Iron has a specific heat of 0.107, so 0.107 calories heat one gram of iron one degree C. … So 6.42e26 calories will heat the entire Earth one degree C.
One erg is 0.2388e-8 calories. 1e30 ergs is 2.388e21 calories.
The planet will warm 2.388e21/6.42e26 = 0.0000038 degrees C. Hold onto your hats, boys! Here it comes!
Well, that’s a pretty crude calculation. There’d be a lot more warming at the center. But even the rough numbers are enough to show that an energy release that’s beyond the imagination of us humans is just peanuts to a world.
The way to tell for sure is to compare it with the rate at which energy is released through radioactive decay. <http://www.public.iastate.edu/~astro.342/ps4.pdf> (Ah, the wonders of the Internet).
4e-8 ergs/gram/second x 6e27 grams =2.4e20 ergs/second = 7.573824e27 erg/year. This compares pretty well with world-wide energy release in earthquakes; 1e28 ergs/year (same source) – so figure 100 years of earthquake energy.
But how long would it take for this to trickle out? I’m no geophysicist, any more than your friend is, so take what follows with a grain or two of NaCl.
If the extra energy doesn’t induce a phase change in the core (it is under a couple gazillion atmospheres of pressure, after all), then all that happens is that the iron heats up a bit. Have to study a phase-diagram of Iron under those conditions (if one exists) to tell for sure. As an analogy, water at supercritical pressure will not flash into steam no matter how much heat you apply.
If the strain can’t be relieved by a radical volume change, the energy remains as heat and comes out real slow. (My old Thermo Prof used to describe adiabatic processes by telling us to think like the apparatus was “wrapped in a mile of rock wool”. Here, you’ve got 4000 miles.)
Scientists might notice the seismic waves. Sloshing in the core might move compass needles. The year might lengthen or shorten by a second or so…
John Q. Public might notice, too. But the headlines – assuming there were any – would more likely read “Insurers pay unexpected number of Earthquake and Volcano claims” than “Opportunities for investing in Arizona Ocean-front Real Estate,” much less “The End is Near!”. And it would pass entirely unnoticed if it took a millennium or two. I’d bet closer to a couple of million years.
Hope that helps,
Jack
