A Mission to the Earth’s Core

Published in the December-2003 issue of Analog Science Fiction & Fact Magazine ^ | 06/22/2003 | by John G. Cramer

[Oberon]

I'm interested to see the proof, and I've got an open mind on this one at this point.

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.

[Lekker 1]

actual number was probably supposed to be 10^8, or 10 to the 8th power kilograms. Make it 100 million kilos of iron.

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.

[chipengineer]

I seem to remember proving the zero g inside a hollow sphere in HS calculus.

[Not a 60s Hippy]

Looks to me like they would just be drilling a hole for another volcano.

Nothing mentioned about the internal pressure.

[Fredgoblu]

with a mass of about 108 kilograms, the amount of iron in a sphere about 30 meters in diameter.

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.

[Lekker 1]

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.

[Tarpaulin]

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

[Lonesome in Massachussets]

BTW, it would only be zero-G inside a hollow sphere at the exact center.

Nope everywhere inside. Freshman problem in Resnick and Halliday, 1968 edition.

[Little Ray]

A sphere of iron 30m across masses 108 kg? I think not. Dunno the specific gravity of iron, but 10800 metric tons is more like it....

Weird idea, but a crummy article.

[bruin66]

to do a 38 minute in-vacuum free-fall through the Earth’s interior gravitational field to the other side of the planet...

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...

[familyop]

"...a 30 meter BALL of melted iron is gonna weigh MUCH MORE."

Yes. Stevenson’s "modest proposal" is probably some kind of left/liberal satire. Iron at any weight would not even be a candidate for any kind of deep earth shot. A very hard rock would be better.

The most likely object to go to the center of the earth would be a very large meteor traveling toward it from way out in space at a very high rate of speed.

And we know what other kinds of effects that would be likely to have.

[Oberon]

Okay...imagine that you're inside a big hollow sphere, floating. Now imagine an invisible cone with its point three inches behind your belly button at the center of your mass. Its far end describes a circle on the wall of the sphere, and the cone represents the gravitational pull of the sphere's wall on your body.

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.

[Graycliff]

No kidding

I've worked on wells on the west coast that had 450+degrees at 3500ft, flow lines were so hot they had to be insulated from contact.

Some of the wells in this area have down hole pressures in excess of 6000psi. I can only imagine what the pressures would be at those depths.

[HuntsvilleTxVeteran]

We could revive the MOHOLE project.
It only got about 1,000 feet before funding was cut off because of project directors feuding.

[Fredgoblu]

actual number was probably supposed to be 10^8, or 10 to the 8th power kilograms. Make it 100 million kilos of iron.

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?

[shaggy eel]

,,, basalt futures: trade short.

[familyop]

LOL!

[UCANSEE2]

Let's see.... I'll have to get out my infinite tape measure.

[Tarpaulin]

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.

[PISANO]

What 'earthly' reason could there be for this type of incursion to the center of our planet?