Re: A Hole through Earth?


Steven Gray wrote:
> "Henry Lemington-Wholeflavors" <cwocwocwo@xxxxxxxxxxx> wrote in
> news:1126207658.092759.65370@xxxxxxxxxxxxxxxxxxxxxxxxxxxx:
>
> >
> > Gareth Evans wrote:
> >> I don't have great knowledge of physics, but I'd be interested for
> >> answers to this question.
> >>
> >> If there were a big hole from one surface of the globe through the
> >> center to the other side of the globe, (pretending there is no hot
> >> core). If one would jump down it from one side, would they fall
> >> through the other side, then fall back again and end up hovering in
> >> the middle? Would the air density increase so much that the person
> >> would end up being squashed?
> >>
> >> This was quite a random thought!!!!
> >
> > They would fall down to the Earth's centre and past it, but not reach
> > the surface on the opposite side because of air resistance, then fall
> > back "up", but even less far, and continue doing this until they became
> > eventually at rest in the Earth's centre.
> >
> > With regards to pressure, bare in mind that the gravitational fields of
> > the Earth's material further out than you are, exactly cancels. You
> > only have to consider gravity arising from the material from where you
> > are now, down to the centre, and the same distance beyond.
>
> True, but the force of gravity doesn't suddenly disappear when you get below
> the surface.

Of course it doesn't, and I didn't say it did. I said the force of
gravity depends just upon the material below you i.e. you can consider
each point inside to be on the surface of another sphere with radius of
(R - r) where R is the Earth's radius and r is the distance you've
travelled into the Earth.

Assuming uniform density, this gives the gravitational force a (R - r)
dependence.

It decreases linearly from the surface value to zero at the center. To
get
> the pressure, you'd have to integrate the weight of a 5000 mile column of air, with
> that linearly increasing force of gravity, from the center to the surface, and add in
> the effect of the pressure already at the surface. It's complicated, of course, by
> the compressibility of the air.

Sure. Another complication would be differential densities of the Earth
itself.
Density of surface material averages at about 3000 kg/m^3 whereas the
average for the whole Earth is 5515 kg/m^3.

> I haven't done the calculation, but it may well be substantial. The pressure that we
> have at the surface results from a column of air only about 100 miles high, in a
> field that decreases as 1/r^2 as you go up.

It would be a nice calculation do to. I might try it.

--
http://cherenkov-radiation.blogspot.com/

.

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