# Naked Science Forum

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

Title: How is it possible to travel from London to anywhere on Earth in 42 minutes?
Post 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 ennui-inducing thread  [:(]
Title: Re: How is it possible to travel from London to anywhere on Earth in 42 minutes?
Post by: techmind on 23/10/2008 19:36:58
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.

After further thought, in a mathematicians dream-world, maybe. I'm guessing you'd perform something approaching simple-harmonic motion in the frictionless tunnel, momentarily coming to rest at each end...?
Title: Re: How is it possible to travel from London to anywhere on Earth in 42 minutes?
Post by: DoctorBeaver on 23/10/2008 20:06:35
Any 2 points on the Earth's surface that can be connected by a straight, subterranean tunnel.
Title: Re: How is it possible to travel from London to anywhere on Earth in 42 minutes?
Post by: syhprum on 23/10/2008 20:14:40
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/The-Gravity-Train
Title: Re: How is it possible to travel from London to anywhere on Earth in 42 minutes?
Post by: techmind on 23/10/2008 22:44:48
Well, I don't much like long tunnels, especially not under-sea 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.  [:)]
Title: Re: How is it possible to travel from London to anywhere on Earth in 42 minutes?
Post by: DoctorBeaver on 23/10/2008 23:40:51
A frictionless mechanism is me after a few pints of Guinness and a hot curry!  [:D]
Title: Re: How is it possible to travel from London to anywhere on Earth in 42 minutes?
Post by: lyner on 24/10/2008 10:13:56
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.
Title: Re: How is it possible to travel from London to anywhere on Earth in 42 minutes?
Post by: syhprum on 24/10/2008 10:55:17
In thought experiments we don't have such things as friction, long or short the journey would take 42 minutes
Title: Re: How is it possible to travel from London to anywhere on Earth in 42 minutes?
Post by: DoctorBeaver on 24/10/2008 14:52:32
Sophie - I got the figure of 42 minutes from a program on Science Discovery about gravity. It was Alex Filipenko who said it.
Title: Re: How is it possible to travel from London to anywhere on Earth in 42 minutes?
Post by: LeeE on 24/10/2008 15:10:34
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.
Title: Re: How is it possible to travel from London to anywhere on Earth in 42 minutes?
Post by: Don_1 on 24/10/2008 16:20:59
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.
Title: Re: How is it possible to travel from London to anywhere on Earth in 42 minutes?
Post by: syhprum on 24/10/2008 18:19:17
The time of a journey to the Antipodes and back is 84 minutes just the same as doing a ground level orbit.
Title: Re: How is it possible to travel from London to anywhere on Earth in 42 minutes?
Post by: syhprum on 24/10/2008 18:22:41
I like undersea tunnels' Eurotunnel is the best way of getting to the mainland with your car but its so dammed expensive.
Title: Re: How is it possible to travel from London to anywhere on Earth in 42 minutes?
Post by: dentstudent on 24/10/2008 18:26:34
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 day-trip 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 one-way....
Title: Re: How is it possible to travel from London to anywhere on Earth in 42 minutes?
Post by: JP on 24/10/2008 20:30:44
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
Title: Re: How is it possible to travel from London to anywhere on Earth in 42 minutes?
Post by: lyner on 24/10/2008 20:33:58
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.