How long to journey through the center of the earth?

[Saltee]

Ok- a while ago I saw a documentary that I wish I would have paid more attention to and now I can't remember the important part relating to this question. Here it is- If we were to drill a hole from one side of the earth to the other that ran through the center, and (ignoring the heat at the core) I jumped in, how long would it take for me to reach the other side of the world? Thanks for the help in this one, everybody!

[neufer]

Ok- a while ago I saw a documentary that I wish I would have paid more attention to and now I can't remember the important part relating to this question. Here it is- If we were to drill a hole from one side of the earth to the other that ran through the center, and (ignoring the heat at the core) I jumped in, how long would it take for me to reach the other side of the world? Thanks for the help in this one, everybody!

42 minutes...the same as it would take you through an evacuated frictionless tunnel from any point on earth to any other point on earth (ignoring rotation). The round trip of 84 minutes is the same as the orbital period of an earth satellite at zero altitude (neglecting friction).
---------------------------------------------------------------
"Rule Forty-two. All persons more than a mile high to
leave the court . . . It's the oldest rule in the book".

In _Phantasmagoria_ Lewis Carroll gives his age as 42.
---------------------------------------------------------------

<<Hitch Hiker's Guide to the Galaxy: "the Answer to
the Ultimate Question of Life, the Universe, and Everything"
was determined by the computer 'Deep Thought' to be Forty-two.

In The Restaurant at the End of the Universe it was found that
'the Question to the Ultimate Answer' was 'What do you get
if you multiply six by nine?' In base 13 as it happens '42',
so a simple programming error might account for the anomaly!

The original title page of Alice's Adventures in Wonderland
boasted it contained 42 illustrations (changed to 50).

Another Carrollian Rule 42, that of the Naval Code, according to the
Preface to The Hunting of the Snark, states: "No-one shall speak to
the Man at the Helm, and the Man at the Helm shall speak to no-one".
The first Fit of that poem mentions that the Baker, destined to be
victim of the Boojum, "had forty-two boxes all carefully packed, with
his name painted clearly on each ... all left behind on the beach",
and "he had seven coats on when he came, with three pairs of boots
but had wholly forgotten his name" in other words
he was clearly "all at sixes and sevens".

In the second part of Carroll's later work Sylvie and Bruno, the German
professor describes a railway system in which the trains move under
gravity: "Each railway is in a long tunnel, perfectly straight: so of
course the middle of it is nearer the centre of the globe than the two
ends: so every train runs halfway downhill, and that gives it force
enough to run the other half uphill" (what is this if not an example of
Science Fiction worthy of Verne?). I am informed (reliably?) that such
a grav(it)y train would make all its trips in 42 minutes, the same time
it would take an object to fall through the centre of the earth,
the time constant regardless of the tunnel's length.>>

[BMAONE23]

Really though you wouldn't be able to reach the other side as gravity would pull you to the center then pull you back to the center as you passed that point. You could only make it half way. Momentum might take you 2/3 of the way through before gravity stopped you.

[Saltee]

42 minutes? Thank you everybody! Today me and a buddy were discussing this and while I could remember that the number of minutes was less than 100, my friend thought it would take much longer- citing something about terminal velocity and whatnot. Physics was never my thing, though, and any math beyond simple algebra makes me look like a rockbanging caveman. Thanks!

[Chris Peterson]

Really though you wouldn't be able to reach the other side as gravity would pull you to the center then pull you back to the center as you passed that point. You could only make it half way. Momentum might take you 2/3 of the way through before gravity stopped you.

The reasons this wouldn't work in practice have nothing to do with gravity. The problem is air resistance (actually, it's even worse because the air would be a liquid before you got too deep into the hole). But if your hole had a vacuum in it, you'd jump in one side and come to a brief stop exactly at the surface on the other side, and this would repeat forever. You wouldn't decay towards the center.

[neufer]

if your hole had a vacuum in it, you'd jump in one side and come to a brief stop exactly at the surface on the other side, and this would repeat forever.

Actually, for a clean fall, you would be well advised to dig a hypocycloid like series of tunnels that miss the center of the earth and ends you up exactly 10.5º west of the surface point on the other side since that is how much the earth rotates in 42 minutes:

[rstevenson]

Or you could dig your hole from pole to pole to avoid the rock rash you'd get from the rotation. (That would be the rotational pole, not the magnetic pole.)

Rob

[neufer]

Or you could dig your hole from pole to pole to avoid the rock rash you'd get from the rotation.
(That would be the rotational pole, not the magnetic pole.)

Or from any point on earth to its mirror image point
in the opposite (North <=> South) hemisphere.

(E.g., Perth, Australia <=> Central China)

Although:
1) train rails resisting sideways gravity can also resist coriolis forces.
2) Hypocycloid tunnels will generally be faster than straight tunnels.

<<In Lewis Carroll's later work Sylvie and Bruno, the German
professor describes a railway system in which the trains move under
gravity: "Each railway is in a long tunnel, perfectly straight: so of
course the middle of it is nearer the centre of the globe than the two
ends: so every train runs halfway downhill, and that gives it force
enough to run the other half uphill." Such a train would make
all its trips in 42 minutes, the same time it would take
an object to fall through the centre of the earth,
the time constant regardless of the tunnel's length.>>

[aristarchusinexile]

if your hole had a vacuum in it, you'd jump in one side and come to a brief stop exactly at the surface on the other side, and this would repeat forever.

Forever is a long time. How can what you describe happen without mass expending energy? It seems to be energy would have to be created to reach the 'forever' mark .. especially remember that a true vacuum seems to be impossible, that a true vacuum creates energy.

[bystander]

Forever is a long time. How can what you describe happen without mass expending energy? It seems to be energy would have to be created to reach the 'forever' mark .. especially remember that a true vacuum seems to be impossible, that a true vacuum creates energy.

What Chris is describing is a no loss system driven only by gravity, providing a perpetual motion machine. But no loss systems don't exist, and neither does perpetual motion. It has nothing to do with mass expending energy or vacuums creating energy.

[neufer]

Forever is a long time. How can what you describe happen without mass expending energy? It seems to be energy would have to be created to reach the 'forever' mark .. especially remember that a true vacuum seems to be impossible, that a true vacuum creates energy.

What Chris is describing is a no loss system driven only by gravity, providing a perpetual motion machine. But no loss systems don't exist, and neither does perpetual motion. It has nothing to do with mass expending energy or vacuums creating energy.

To compensate for any energy losses take along a rifle as a "kick back" propulsion devise.

When should you fire your rifle to have maximum "kick back" effect
(Does it even matter when you fire?)

[Chris Peterson]

if your hole had a vacuum in it, you'd jump in one side and come to a brief stop exactly at the surface on the other side, and this would repeat forever.

Forever is a long time. How can what you describe happen without mass expending energy? It seems to be energy would have to be created to reach the 'forever' mark .. especially remember that a true vacuum seems to be impossible, that a true vacuum creates energy.

Well, I assumed that the typical Physics 101 assumptions about no air resistance, ideal conditions, etc would be recognized in my comment. Obviously, no such conditions exist in reality, although you can get arbitrarily close. Whether a "perfect vacuum" as it is currently understood (that is, with virtual particles going in and out of existence) actually produces resistance is an interesting question, and I don't know the answer. But the simple fact that you are a moving mass as you pass back and forth in your tunnel means you must be radiating gravity waves, and thus losing some energy.

Still, I expect you could set up realistic conditions that would keep you in motion for billions of years, which is close enough to forever for most cases! <g>

[Chris Peterson]

What Chris is describing is a no loss system driven only by gravity, providing a perpetual motion machine. But no loss systems don't exist, and neither does perpetual motion. It has nothing to do with mass expending energy or vacuums creating energy.

Nevertheless, you can come arbitrarily close to a no loss system, and perpetual motion doesn't violate any laws of physics. Of course, as the term is usually used it means a device that runs forever even as you extract energy from it, or more generally, a device that outputs more energy than it consumes. That clearly does violate some very basic laws of the Universe.

[makc]

I always knew that 42 was special number.

[neufer]

What Chris is describing is a no loss system driven only by gravity, providing a perpetual motion machine. But no loss systems don't exist, and neither does perpetual motion. It has nothing to do with mass expending energy or vacuums creating energy.

Nevertheless, you can come arbitrarily close to a no loss system, and perpetual motion doesn't violate any laws of physics. Of course, as the term is usually used it means a device that runs forever even as you extract energy from it, or more generally, a device that outputs more energy than it consumes. That clearly does violate some very basic laws of the Universe.

Click to play embedded YouTube video.

[Ann]

I am probably not allowed to post this, because it is in Swedish, but I'll do it anyway. This is a Swedish song, called "Den makalösa manicken" (The Amazing Contraption), and this contraption is a perpetual motion machine (evighetsmaskin). I think the song is funny, and I like the sound of it, so here it is. A bemused oberver asks the professor about the strange thing the professor has built of cogwheels, cones, bicycle pumps, bicycle generators, propellers and what not. The professor explains that his machine can't exactly do anything except produce enough electricity to keep itself going forever.

http://www.youtube.com/watch?v=azikQ6qA ... ure=search

Ann

[orin stepanek]

When you stop and think about it; the universe seems to be in perpetual motion.

[Beyond]

When you stop and think about it; the universe seems to be in perpetual motion.

Orin, that's because we are so small in it. If we were bigger and saw it from the outside, we would probably say that at the least, it needs a bath

[orin stepanek]

When you stop and think about it; the universe seems to be in perpetual motion.

Orin, that's because we are so small in it. If we were bigger and saw it from the outside, we would probably say that at the least, it needs a bath

Sorry; somehow I miss the gist of that reply!

[neufer]

When you stop and think about it; the universe seems to be in perpetual motion.

When you stop and think about it; Matt Harding seems to be in perpetual motion.

But TRUE perpetual motion requires that entropy does NOT increase.

[Beyond]

When you stop and think about it; the universe seems to be in perpetual motion.

Orin, that's because we are so small in it. If we were bigger and saw it from the outside, we would probably say that at the least, it needs a bath

Sorry; somehow I miss the gist of that reply!

The "gist" of the reply is that IF we were big enough to be able to observe the Universe from the outside - instead of the inside where we now are, the Universe would most likely appear brownish from all the dust and maybe some other stuff, and so look like its dirty and in need of a bath.

[bystander]

and that relates to perpetual motion how ???

[orin stepanek]

and that relates to perpetual motion how ???

Thanks bystander; That is what I was asking.

[Beyond]

and that relates to perpetual motion how ???

Well, perhaps the constant conversion of energy to matter to energy would have something to do with trying to have perpetual motion, if it were possible to have perpetual motion the way the Universe is now. And if the Universe was cleaned up of all the dust and stuff that comes from all the conversion of energy to matter to energy that is going on(given a bath), perhaps it would be "clean" enough to obtain a brief period of perpetual motion, but then it would not have enough matter(dust and stuff) to convert to enough energy, to actually obtain perpetual motion, even if it could. But even if it could, it can't. It just does not have the oomph that it once had as it is aging and going the way of all things. But hold on - the Universe is getting older -- but it is also getting faster at the same time that it is getting older. That is just as improbable as pepetual motion is as long as there is friction. So when we see the impossible happening on such a large scale; then other impossibilites seem more probable, like perpetual motion.

[Chris Peterson]

... to obtain a brief period of perpetual motion...

There's something very wrong with that concept...