Re: damien's tunnels

Date: Mon Oct 15 2001 - 11:06:39 MDT

In a message dated 15/10/01 03:49:43 GMT Daylight Time,

> Assume you are at a party where nerds gather and someone proposes
> a tunnel drilled diametrically thru the earth, and asks you to assume
> away all traces of an atmosphere and any asphericity of the earth.
> She asks if a particle dropped into the tunnel will arrive before or
> after another particle in a treetop orbit, assuming the tunnelling particle
> is dropped just as the orbiting particle goes by; that is will the particle
> that falls thru the earth take more or less than 42 minutes.
> The other nerds know the answer is about 42 minutes. They are
> wrong of course, for you now know that the correct answer, which I
> finally got off my lazy ass and calculated, is 37 minutes. The reason
> it takes less than 42 minutes is that the earth has a definite density
> gradient, so that the core is much denser than the crust and mantle.
> If you wish to appear astute before the other nerds, you might go
> on to observe that a particle thru the center can be arranged to
> take longer or shorter than the minimal orbit particle, but in order
> to make it take the same time, the sphere needs to be of uniform
> density. Once can arrange for the particle thru the center to take
> longer than the orbitting particle by having a hollow sphere for
> instance.
> Regarding Damien Broderick's train on a straight frictionless track
> on a non-diametric chord thru the earth, the train will arrive at its
> destination, regardless of where, in slightly less than 42 minutes. spike

       Remind me not to come to one of your parties. :o) and if you come to
one of mine, I suggest that you never mention anything remotely more
inteligent than "CHUG CHUG CHUG....".


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