Journey to the Center of the Earth

[mrtwister]

In the late 1600’s Robert Hook wrote to Isaac Newton suggesting that if a tunnel were drilled straight from London to Rome a “gravity train” could travel the distance with no engine. It would “fall” halfway because of gravity, and coast the rest of the way on momentum. Is there any merit to this idea?






noggintwisters.com: math and science puzzles to make you think.

[Janus]

As long as you could eliminate all friction, it would work. In real life, you would have to compensate for friction losses.

[freeztar]

Originally Posted by Janus

As long as you could eliminate all friction, it would work. In real life, you would have to compensate for friction losses.

Enter maglev?

[Janus]

Originally Posted by freeztar

Enter maglev?

That, and you would have to evacuate the tunnel of air. But even that wouldn't eliminate all friction. You'd still end up giving the train a tiny push at the begining to make up for what's left.

[Thunderbird]

I have a similar question. I would like to build an elevator to space by drilling a hole into the earth.

If you would tunnel into the earth say half way to the core located on the equator, {Impossible I know} but theoretically, then lower a vehicle say 4-5 thousand feet into the hole. utilizing electromagnetic rail gun technology, accelerate the vehicle to an escape velocity.

My question is this, would the hyper-deep tunnel in the earth create a low gravity corridor extending up into space over the hole, allowing the vehicle to coast upward easer than it would if the hole was not there.

[CraigD]

Originally Posted by mrtwister

In the late 1600’s Robert Hook wrote to Isaac Newton suggesting that if a tunnel were drilled straight from London to Rome a “gravity train” could travel the distance with no engine. It would “fall” halfway because of gravity, and coast the rest of the way on momentum. Is there any merit to this idea?

In a word, yes – though practical applications are likely limited.

This question, as an exercise in mathematical physics, is a moderately famous one know as ”the hole problem”. The main interesting result you can derive from it is that if you connect any two points at the same altitude with a straight track, whether on opposite sides of the Earth, or just a few meters away, the time it takes for a frictionless car to coast between the two points is the same: about 5080 s (42:20 on a stopwatch).

The engineering challenges of actually doing such a thing make it pretty impractical. Folk with the technology to drill indestructible, airtight tunnels through the Earth, are not too likely, IMHO, to worry about saving energy getting from point A to point B, and likely to consider 42 minutes an inconveniently long time. If such a thing is ever done on Earth, my guess is that it will be a small demo model done just to show off super engineering technology and educate kids – a sci/tech museum piece.

In “Gravity-powered Inductrack on the moon?”, I speculated that there might be some practical application for such a system in the near (this century) future for cargo hauling on the moon, where there’s already a pretty good vacuum, and likely to be value in a transport system that's nearly a “free ride”.

[mrtwister]

Yeah you guys have probably already guessed it, there are a few problems with this, first, the tunnel would have to pass through the earth’s molten core. But even if the tunnel were drilled on the moon where the core is cold, friction would slow the train along the way, and before it reached the other end of the tunnel, it would fall back, sliding to and fro in the darkness. But if you smoothed it out and coated it in teflon it would be a pretty good way to travel.




Noggintwisters.com: math and science puzzles to make you think.

[CraigD]

Originally Posted by mrtwister

Yeah you guys have probably already guessed it, there are a few problems with this, first, the tunnel would have to pass through the earth’s molten core. But even if the tunnel were drilled on the moon where the core is cold,

An important consideration is that such transit systems don’t have to be all underground - above ground, supported by trestles and naturally occurring terrain is OK – nor must the point-to-same-altitude-point be straight, only have a “dip” and either end. The transit time will be longer if the line is not straight, but this might not be a significant issue.

Another is the use of magnetic levitation, which can actually be easier and less expensive to build than ordinary roads, tracks, or guideways. If the maglev track material can be made superconducting – not outside of the realm of practical feasibility in lunar conditions - the system can in actuality be nearly frictionless.