# Journey Through the Center of the

# Earth ... and the Moon

## By Eric M. Jones

LET’S START AT THE TOP and work our way down: This charming 1913 plan from “Popular Mechanics” to bore a tunnel to the center of the Earth for picnics and frolicking in weightlessness was at least a semi-serious, if entirely bonkers proposition. But it was typical of the great hope around the turn of the last century ... before the “war to end all wars.” Access was to be by two long spiral train tracks hugging the walls of a very deep well. It was understood that the center
of the Earth is a zero gravity playground ... if you don’t mind the heat (which they knew nothing about) ... but it’s a *dry* heat.

We are getting ahead of ourselves. Back to Great-Grandma’s Zero-G playground. How long would it take a picnic watermelon to reach bottom if it were dropped from the top of the well (ignoring all kinds of things)? We won’t do the calculation, but the answer is about 21 minutes. At the center of the Earth, it would be going exactly at orbital velocity. Now, what is remarkable about this watermelon is that it would pass clear through the Earth to appear at the other end in 42 minutes, and falls back to where it started in 84 minutes.

Eighty-four minutes? I hear you say, “That’s the same time it took to orbit the Earth when Yogi Bear knocked over the satellite launching rocket that orbited the Earth at ground level before returning to Jellystone Park!” (Giant parenthetical remark—The minimum Earth-grazing-orbit satellite time is about 84 minutes ... Furthermore, the calculation of the tunnel through the center of the Earth involves the messy fact that the acceleration due to gravity changes because it is calculated *only* using the distance to the center, and all the Earth above it at an instant in time doesn’t count—this lengthens the transit time. Most calculations are done using a simple homogenous Earth. But this equation needs to be modified to account for the change in density as the watermelon approaches the center, which is thought to be a large lump of iron—this shortens the time. These two modifications to the theory pretty much cancel. Most calculations are done using a simple homogenous Earth. This should really be no surprise, since the energy is all there really is and the simple harmonic equations yields 84 minutes round trip. We also ignore the Earth’s rotation, air resistance and atmospheric pressure and that the center is many thousands of degrees hot.)

The new movie “Total Recall” (2012) features a through-the-Earth sort of gravity railroad to ferry workers to and from the oppressive slum and the worksite, where they make robots their oppressors use to keep the workers oppressed.

But what is the shape of the tunnel? You might be surprised to learn that given some hand-waving calculations assuming a homogenous planet, a “gravity train” track that depends only on the freefall ride should be hypocycloidal. Because, as it turns out, this results in the minimum travel time. A curious “semi-proof” of this is that the shortest-time train tunnel from one side of the Earth to the other is obviously a straight line. And so is a hypocycloid with a generating circle equal to the radius of the Earth. This will handily win most bar bets, even from some pretty sober people, (Another parenthetical remark: Johann Bernoulli—brother of “Bernoulli Principle” Daniel Bernoulli—published this in the late 17th century and called it a brachistochrone—meaning “shortest time.” Huygens did something similar, but both based their work on cycloids rolling on straight lines, not inside circles. The beginning and end of any hypocycloidal track is straight up and down, so the initial acceleration (g) is maximum.)

But if such a railroad were to be built, the engineers would calculate the minimum cost, not the minimum time. The minimum cost is just how they build it now ... on the surface with an occasional bridge or tunnel.

We aren’t likely to bore a hole through the Earth, but we *could* bore through the center of an astronomical body like the Moon that has a relatively cool interior—830°C, far below the melting point of structural metals likely to be used. As a bonus, we could use the heat to power the gigantic railgun we’ll build into the tunnel.

Railgun? What would we do with such a thing? If the tunnel went through the equator, a railgun could shoot a package to Mars twice-a-month, with a transit time (including deceleration to Mars orbit, of about 50 days; less than one-tenth the time of other schemes. The railgun would provide six G’s acceleration for 344 seconds. Tough for humans (although within the realm of possibility), but easy for freight.

And how would such a thing be accomplished? By a pair of LTBMs: Lunar Tunnel Boring Machines. The lunar vacuum, low gravity, and low spin allows some very creative engineering solutions.

Furthermore, as the tunnel goes deeper, the need for spacesuits decreases, so that by a depth of 300 km, *no* spacesuits would be needed because atmospheric pressure would be close to Earth-normal.

Now here’s how an engineer’s mind works:

- It currently costs roughly $1 million to put a kilogram of equipment or people on Mars.
- You want to plan sending 10 million kilograms to Mars over ten years.
- That’s $10 Trillion.
- It currently costs $100,000 per kilogram to put men and equipment on the Moon.
- A pair of lunar TBMs, and shipping them to the Moon, would cost maybe $400 billion.
- Boring the hole and finishing the tunnel and railgun, $250 billion tops.
- Thereafter, launching to Mars would cost $5,000 per kilogram, perhaps in perpetuity.
- So the cost of putting 10 million kilograms on Mars would be $700 billion vs. $10 trillion. A bargain ... and you’d still have the lunar railgun.

The rest of the plan is just lines on paper. Piece of cake.

*Eric M. Jones is an engineer, designer and entrepreneur, currently working
in his internet business PerihelionDesign, designing, building and
selling products and materials for people in the experimental aircraft
community. Most of his working career was spent designing advanced medical
devices. In his spare time ... okay he has no spare time.*