Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: DoctorBeaver on 23/10/2008 19:24:29

Just watching a program about gravity. Apparently if you dig a straight tunnel between any 2 points on the Earth's surface and let gravity pull you through it, the journey will always take 42 minutes. So, a tunnel from London to Beijing  42 minutes. London to LA  42 minutes.
I find that quite interesting. You probably won't. You'll think it's really boring and wonder why the hell that damned rodent posted such an ennuiinducing thread [:(]

If it's true at all, then I suspect you've missed some vital details...
London to anywhere?
Let's consider something imaginable.
London to Cambridge?
London Kings' Cross to London Paddington?
All by gravity? I don't think so.
Edit to add:
After further thought, in a mathematicians dreamworld, maybe. I'm guessing you'd perform something approaching simpleharmonic motion in the frictionless tunnel, momentarily coming to rest at each end...?

Any 2 points on the Earth's surface that can be connected by a straight, subterranean tunnel.

The strange fact is the transit time of the 'Gravity train' depends only on the density of the planet it would be much the same on Mars or the Moon.
On a planet the size and density of the Sun it would take 55 minutes.
I was involved in a long discussion on this matter about two years ago
http://cr4.globalspec.com/blogentry/811/TheGravityTrain

Well, I don't much like long tunnels, especially not undersea tunnels! And they'd be so expensive. And the earth would be like a wormery with tunnels joining everywhere to everywhere else.
But your suggestion implies a frictionless transport mechanism  now for that I can see plenty more practical applications. [:)]

A frictionless mechanism is me after a few pints of Guinness and a hot curry! [:D]

Actually, the original post is in error. You could go from anywhere to anywhere using gravity but it would only be to the antipodes that would take '42 minutes'. For a journey between any other two points the time would be longer. The process involves the vertical component (i.e. towards the centre of the Earth) of the gravitational force. The nearer the points are then the smaller is this force. Despite the shorter journey length, taking into account the resulting acceleration and the velocity reached, the journey would take longer and longer, the shorter the tunnel.
The limit would be when they were very near, when the line joining them was almost horizontal  the force would be vanishingly small. Friction would dominate, however smooth you made the ride. There would be no movement.

In thought experiments we don't have such things as friction, long or short the journey would take 42 minutes

Sophie  I got the figure of 42 minutes from a program on Science Discovery about gravity. It was Alex Filipenko who said it.

I believe I've heard the same thing and that the figure of ~42 minutes for any two locations is correct. This all depends upon a purely gravitationally effected journey though  the longest journey, through the center of the Earth, gets the greatest acceleration whereas a shorter journey, which will be a chord, gets a proportionally lower acceleration, accounting for the similar journey times. I've got an idea it may depend upon the Earth being homogeneous though, which it isn't.

A frictionless mechanism is me after a few pints of Guinness and a hot curry! [:D]
I know the problem well & sympathise with you & your porcelain pan.

The time of a journey to the Antipodes and back is 84 minutes just the same as doing a ground level orbit.

I like undersea tunnels' Eurotunnel is the best way of getting to the mainland with your car but its so dammed expensive.

I like undersea tunnels' Eurotunnel is the best way of getting to the mainland with your car but its so dammed expensive.
Not if you buy a daytrip ticket each way, and don't use the return. I think that you should still be able to do this  we did it and it was €40 oneway....

I believe I've heard the same thing and that the figure of ~42 minutes for any two locations is correct. This all depends upon a purely gravitationally effected journey though  the longest journey, through the center of the Earth, gets the greatest acceleration whereas a shorter journey, which will be a chord, gets a proportionally lower acceleration, accounting for the similar journey times. I've got an idea it may depend upon the Earth being homogeneous though, which it isn't.
I did a quick calculation to check, and if you assume that the Earth is homogeneous you get a constant travel time between any two points. A nice writeup of the solution is given here: http://www.math.purdue.edu/~eremenko/dvi/gravsol.pdf

Well dang me. I just did the sums and the 'restoring force', which pulls you back to the lowest point does not include the actual distance from the centre. It is just equal (per kg) to (4/3)Gπρx, where x is the distance from the lowest point.
I stand corrected.