Posted on 02/10/2005 10:59:13 AM PST by vannrox
Adventure stories involving the exploration of the interior of Planet Earth have a long and distinguished history in science fiction. Jules Verne’s Journey to the Center of the Earth (1864) was perhaps the first such tale. Despite the title, the story involves explorers following the instructions of a 17th century runic message on a trip that descends into the crater of an Icelandic volcano and into a long tunnel connecting to a vast cave containing a conveniently phosphorescent ceiling, an ocean, islands, dinosaurs, and mastodons, all in the interior of the Earth some miles beneath the surface.
Now, however, there’s some new writing about the exploration of the Earth’s core, but this time it’s not fiction, but a serious scientific proposal. David Stevenson, a Professor of Planetary Science at CalTech, has proposed mounting an ambitious NASA-style mission to the Earth’s core. He describes his “modest proposal” (in the Swiftian sense) in a paper recently published in the journal Nature. Since Stevenson has not yet mastered the use of the twistor effect, however, he has to do things the hard way. He cannot be accused of thinking small. He proposes to use a multi-megaton nuclear weapon and one hour’s worth of the net iron production of the Earth’s iron smelter facilities (~108 kg). In this column I want to describe this proposal.. Stevenson is faced with the basic problem is how to get through all the rock between the surface and the core. Anyone who has ever dug a post-hole recognizes the problem. Something like Abner Perry’s mole machine that took Perry and David Innes to Pellucidar couldn’t really do the job. We now have well engineered digging machines for tunneling, and they can’t go down more than a few thousand meters. Deep well-drilling techniques are not much better. The deepest drill hole, dug in the Kola Peninsula in Russia, goes down only 12 km. So Stevenson has proposed a more radical approach: melt your way through the rock. It takes about a mega-joule of energy to melt each cubic meter or rock, assuming that the rock is already hot enough to be near its melting point. Therefore, melting a tunnel that is 3 square-meters across and 6,380 km long, all the way to the Earth’s center, would use an energy of about 2 ´ 1013 joules. That sounds like a lot of energy, but consider that a large nuclear power plant produces about 8 ´ 1013 joules per day, so we are in the right energy ballpark. The challenge is to find a vehicle that can withstand the heat and pressure of the Earth’s interior while making the trip. Stevenson would start the process by finding a suitable fissure in the Earth’s crust, setting off a multi-megaton underground nuclear explosion to widen the fissure to a sizable crack, and then dumping in an instrumented blob of liquid iron (melting point 1535 C) with a mass of about 108 kilograms, the amount of iron in a sphere about 30 meters in diameter. The blob would then assume an elongated shape that would fill a part of the crack and cause the crack to propagate downward under the pull of gravity, melting the path in front, with liquid magma flowing around the outside of the iron mass and sealing the path behind. As the iron blob moved downward, despite the high pressure from below, it would achieve a fairly high velocity. Assuming that the iron elongates to melt a path about 1 meter across, its downward speed would be about 30 meters per second. At that speed it could reach the Earth’s core in about two and a half days. Today’s microprocessors are made of silicon (melting point 1410 C) and can’t operate at high temperatures. The instrumentation package would either have to be locally insulated and cooled or would require a presently unknown microprocessor technology. Further, getting the measurement information from the probe to the Earth’s surface is very difficult. There could be no trailing wires, no light beams, no radio waves, so Stevenson proposes to use acoustic signals with a radiated power of about 10 watts for the duration of the mission. The frequency of the acoustic waves is limited at the high end by absorption in the rock, and at the low end by seismic noise and the rate of information transfer. Stevenson proposes a signal frequency around 100 Hz for sending signals to a surface detector similar to the LIGO gravity-wave detector, but coupled to rather than insulated from the Earth’s vibrations. This, he estimates, should allow the transfer of 10 megabytes or so of information during the duration of the mission. The power supply for the mission is also a challenging problem. Conventional batteries and fuel cells do not tolerate high temperatures any better than microprocessors. The thermo-electric nuclear isotope power generation used in some spacecraft would not work because the molten-iron environment is already hotter than the decaying radioactive isotope. Stevenson proposes to use a Stirling-cycle engine to tap into a part of the energy flow that occurs as the iron melts its way to the core, using the temperature difference between the molten iron and the cooler surrounding rock. To me, that sounds difficult, and I also foresee a problem with the generator that the Stirling engine drives, since most magnetic materials, on which standard generators depend, lost most of their magnetic properties in a high temperature environment. Writing the environmental impact should also be interesting. The proposal for crack-creation process wilt a nuclear explosion is probably in collision with various international treaties and is sure to raise the ire of anti-nuclear activists. And it would probably be necessary to set very low probabilities that the project would not produce a new active volcano at the launch site or generate massive earthquakes as it moved downward. I doubt that either of these scenarios is likely, but “proving’ that with our present understanding of geology is a formidable problem. That’s a lot of money, but as I see it the proposal would do more for society than the current administration's tax break for millionaires, and it costs a lot less. In any case, the first steps would not be implementation, but research into all the technical issues that the proposal raises. This research should begin. It may be a long time until we can probe the Earth’s core, but we should make a start.
Following Verne’s lead and doing considerably more violence to geology, paleontology, and physics, Edgar Rice Burroughs wrote seven novels beginning with At the Earth’s Core (1922) that were set in Pellucidar, a “land” occupying the inner surface of a vast spherical hole in the Earth’s hollow interior. Pellucidar had a sizable ocean and more land area than Earth’s outer surface, had its own internal sun and moon, and was populated by mastodons, dinosaurs, and an intelligent but rather nasty reptilian species called the Mahars. Burroughs’ various protagonists (including Tarzan) traveled to Pellucidar in a variety of ways, including a mechanical mole machine, arctic pirate expeditions, and a vacuum-filled magnesium dirigible.
Unfortunately, Burroughs got the physics of hollow planets completely wrong. The Mahars, dinosaurs, and explorers would not be pulled to the inner surface of Pellucidar by inside-out gravity. As Isaac Newton first proved, because of the inverse-square law the pull of gravity anywhere in the cavity in a thick massive hollow sphere is zero, because the gravity pulls from below and above any point exactly cancel. Potential inhabitants of Pellucidar would find themselves floating around in free fall.
Not immune to the pull of the Earth’s interior, I also once wrote an almost-published piece about the exploration of the Earth’s core. Near the end of the original manuscript of my first hard SF novel Twistor there is a long scene in which my protagonists David and Vickie, with some help from Boeing Aerospace, build a special “inner-space craft” vehicle that uses gravity and the twistor effect (a “rotational” interchange of normal matter and shadow matter) to do a 38 minute in-vacuum free-fall through the Earth’s interior gravitational field to the other side of the planet, sampling snippets of the Earth’s interior all along the trajectory to the center and back and exploring for the first time the “inner space” of our world.
Unfortunately my editor, in his wisdom, decided to halt the narrative at an earlier point and removed this scene from the published version of Twistor, so few people have actually read my inner space adventure.
Stevenson’s “vehicle” is a large blob of molten iron. Iron is very heavy, with a density of 7.87 grams per cubic centimeter, as compared to a density of about 2 g/cm3 for rock. Therefore, a large blob of sufficiently hot molten iron would tend to produce a “China Syndrome”, melting its way through the Earth’s crust, losing thermal energy but gaining gravitational energy as it went. Planetologists believe that the iron at the Earth’s core got there in just that way, melting its way through the crust of the primordial planet until it reached the core.
The problem with this scheme, of course, is that a blob of molten iron that is subjected to the very high pressures in the Earth’s interior does not provide a very good mode of travel. Thus, the “passenger” would have to be neutral buoyancy micro-miniaturized robotic instrumentation that would relay measurements from the core to the surface of the Earth. How to accomplish that is also a challenging problem.
There also may be other problems with the scheme. If the propagating crack containing the blob splits, it may also split the iron mass into two blobs, which may not individually be massive enough to continue propagating to the Earth’s core. Also, the envisioned communication link is one way. As NASA-watchers know, space probes work best when there is two-way communication, permitting course alterations and program alterations to deal with unforeseen problems. Further, the Earth’s gravity pull downward diminishes linearly as the probe moves downward, and I see nothing in Stevenson’s calculations that takes this into account. Presumably there is some critical depth at which the iron blob would stall because the pull of gravity is insufficient to move it further or provide more gravitational energy.
How much would the project cost? Stevenson’s proposal has no budget attached, and his a bit cagy about the cost. He points out that the cumulative cost of unmanned space exploration has been more that $10 billion, and that the exploration of the Earth’s interior should deserve “a comparable or lower amount”. My guess is that the price tag would be several billion dollars.
Sorry...I wouldn't still have that paper. It wasn't a breakthrough or anything, but a normal exercise from a math prof (Charles Oering of Virginia Tech). The assignment sprung out of a discussion of Newton, who proved it long before I did.
Well luckily, a little less than 50% of the people in this country don't seem to care if the numbers make sense as long as the point seems valid.
I seem to remember proving the zero g inside a hollow sphere in HS calculus.
Looks to me like they would just be drilling a hole for another volcano.
Nothing mentioned about the internal pressure.
WTF ? a 30 meter BALL of melted iron is gonna weigh MUCH MORE.
I caught the same thing. Heck, I stand under two meters high, and I weighed in at ~96kg this morning. I still float in water, so I think it's safe to assume I'm less dense than molten iron.
Methinks the author missed a few zeros.
Exactly. I remember calculating how long it would take for an object to freefall to the center of the Earth through a very deep hole. You only consider the size of the sphere "under" you as you go...the rest cancels out. So gravity tapers off to zero as you reach the center.
You say you did a proof, so I believe it. Its the "exactly balanced" part I'm having trouble with. It just seems counterintuitive.
But then, I occasionally shove my block shaped head into a round hole as well. :^)
Thanks
Nope everywhere inside. Freshman problem in Resnick and Halliday, 1968 edition.
If I remember right, if a hole were bored all the way through the center of the Earth and an object of sufficient tolerance to temperature, etc,were dropped in the hole, it would have a period of oscillation of 84 minutes. BTW that is also the period of a satellite at the surface of the (smooth) Earth. In addition, a pendulum of infinite length, with its mass swinging at the surface of the Earth, would have a period of 84 minutes. You're welcome...
You're at the center of the sphere, though, so something is keeping you from falling [splat!] against the wall of the sphere you're facing. You look over your shoulder, and check it out...there's another invisible cone behind you, pointing in the exact opposite direction from the one in front of you. The pull of the second cone exactly counteracts the pull of the second one.
Okay. Now imagine that using sheer force of personality, you propel yourself forward through space toward the wall in front of you. The angle of the apex of the cone doesn't change. What hapens to the circle described by the far end of the cone on the wall ahead of you? It gets smaller. Feeling uneasy, you look over your shoulder at the back wall of the sphere...sure enough, the circle behind you has got bigger.
As you approach one wall, the circle behind you gets bigger and bigger, and the one in front of you gets smaller and smaller. The gravitational pull toward the far wall increases with the square of the distance from you to it...but the amount of far wall exerting that pull decreases with the square of the distance as you approach it.
The reverse thing is happening behind you...as you get farther away from the back wall, the gravity becomes weaker with the square of the distance, but the amount of wall exerting the pull is increasing at the same rate.
All other gravity inside the sphere...up and down, left and right...is balanced. You can construct these conceptual cones for any position inside the sphere. So, voila! Zero G regardless of position.
Well luckily, a little less than 50% of the people in this country don't seem to care if the numbers make sense as long as the point seems valid.
Love that tongue-in-cheek stab at the left. You beat me to the punch on the real number...and you are right:
--30m ball of iron is 1.41 x 10^10 cc
--Density of iron at 20C is 7.874, but molten iron is in the range of 7.01 to 7.15 g/cc at 1550C.
--Using 7.1 g/cc, the molten ball is 10^11 g or 10^8 kg.
What's a few zeros between science fiction writers?!?! The real questions:
1. Does this stand a rat's chance in hell of...well...making it to hell?
2. The follow up...how in the world would this "instrumented" blob of iron be distinguishable from the molten material that's down there now?
3. Just how does this solve the looming Social Security crisis...or...what's the point?
LOL!
Let's see.... I'll have to get out my infinite tape measure.
That's somewhat what I said at #23.
I guess I was putting too much "weight" on the gravitational factor and not paying enough attention the the inverse square law.
I was thinking that if you were standing on the interior surface, the small amount of force from the material under your feet would be overwhelmed by a larger force from the massive amount of material over your head.
Thanks for your insights. This has been interesting.
What 'earthly' reason could there be for this type of incursion to the center of our planet?
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