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Author Topic: travel through any hole in 42 minutes.  (Read 7710 times)

paul.fr

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travel through any hole in 42 minutes.
« on: 15/08/2007 07:36:40 »
We have numerous topics about digging a tunnel through the earth from the UK to Australia and it's effects, gravity, etc.

Now i "know" that if we dug such a hole you would travel through it in 42 minutes, but if i dug another from london to Edinborough this would also have a travelling time of 42 minutes.

But why?


 

Offline dentstudent

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travel through any hole in 42 minutes.
« Reply #1 on: 15/08/2007 07:46:31 »
Here comes another speculative answer. It's to do with the distance traveled, terminal velocity and the effects of gravity. On the shorter London to Edinburgh run, you don't get so much speed up as you have gravity with you for a much shorter distance before it starts working against you at the halfway point. On the Aussie trip, this force is for longer so you gain much more speed, but of course you have much further to travel- I suspect that it has to do with the fact that gravity is a constant and that the earth is (almost) spherical, and that these are analogous with distance traveled into the earth.

Not too scientific - I remember perhaps Dave talking about this a month or two ago?
 

paul.fr

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travel through any hole in 42 minutes.
« Reply #2 on: 15/08/2007 07:56:11 »
Many thanks, Stuart. I can't say that i remember dave talking about this ??? Does this "42 minutes thing" have a proper name?
 

Offline dentstudent

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travel through any hole in 42 minutes.
« Reply #3 on: 15/08/2007 08:05:32 »
As you should know, 42 is the meaning of life, the universe and everything! ;)
 

Offline syhprum

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travel through any hole in 42 minutes.
« Reply #4 on: 15/08/2007 08:48:10 »
It is an interesting point that the transit time depends only on the density of the gravitating body thru which you construct the tunnel not its size, a transit thru the Sun would take only a little longer if somewhat hot.
« Last Edit: 15/08/2007 10:00:25 by syhprum »
 

Offline lightarrow

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travel through any hole in 42 minutes.
« Reply #5 on: 15/08/2007 21:55:01 »
Really very interesting.
 

Offline neilep

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travel through any hole in 42 minutes.
« Reply #6 on: 15/08/2007 22:09:30 »
Hang On !!..I watched a program last night about the earths core !...it started with a bloke jumping out of a plane taking a fantasy ride through a hole to the earths core....it took about 36 hours !! give or take an hour or two !! ...what's that all about then ?
 

Offline ukmicky

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travel through any hole in 42 minutes.
« Reply #7 on: 15/08/2007 22:19:50 »
 I saw that neil ,the things we watch :) Yeap 32 hours is what they reckon it would take to free fall the distance to the centre of the earth.
 

Offline neilep

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« Reply #8 on: 15/08/2007 22:50:58 »
Thanks Michael...Yep..the things we watch indeed :)...I can only assume that there must be some kind of accelerated process happening in Paul's model !..whereas our guy just free falls  at a standard rate !...I think !!
 

Offline syhprum

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travel through any hole in 42 minutes.
« Reply #9 on: 16/08/2007 05:56:01 »
For a more authoritative account take a look at http://en.wikipedia.org/wiki/Gravity_train.
The transit time to Australia and back is of course the same as using a ground level orbiting satellite.
I think the guy who fell from an aircraft must have been travelling at the freefall speed that you do in the atmosphere
 

paul.fr

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travel through any hole in 42 minutes.
« Reply #10 on: 16/08/2007 07:55:06 »
Stuart, i know what you are referring to. Do you know, i never watched that programme!

Syhprum, Many thanks...Gravity train, ofcourse now i remember. I think i actually gave that answer in another topic some time back. My memory is just awful, thanks for the tap on the head.
 

lyner

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travel through any hole in 42 minutes.
« Reply #11 on: 17/08/2007 10:55:05 »
A few problems here.
The basic thought experiment assumes a vacuum and that gives a return trip time of about 90 minutes. This is the same as for low earth orbit. The vacuum assumption  assumes no loss of energy by friction.
Quote
a program last night about the earths core !...it started with a bloke jumping out of a plane taking a fantasy ride through a hole to the earths core....it took about 36 hours !!

If you want to introduce an atmosphere into the experiment then you can't just talk about free falling through 'normal' air.  You have to bear in mind that the density of the air will double every 5.5km you go down, in the same way that it halves every 5.5km you go upwards (first approximation). After only 110km, the density would have doubled 20 times and this would leave you trying to fall through a very thick liquid. You would be crushed and the whole experiment becomes a bit of a nonsense.
Then there's the temperature problem. . .
Best to stay as simple as possible in thought experiments.
I fancy the idea of doing it through a large, non-rotating  (or you bash into the sides),   spherical  asteroid.  It would be an excellent end to an already interesting trip.

btw, as it only depends on the density, there must be millions of bits of  dust, all in low orbit round lumps of rock up there and all with about 90minute orbit times.
 

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travel through any hole in 42 minutes.
« Reply #11 on: 17/08/2007 10:55:05 »

 

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