--- Eugene Salamin <gene_salamin@yahoo.com> wrote:
--- Henry Baker <hbaker1@pipeline.com> wrote:
According to Newton, the weight near the center of the earth is near zero, because most of the mass is around you in equal & opposite directions.
You raise an interesting question, which I think may have been asked in my physics class when I was an undergraduate:
If one drilled a Verne-like well all the way to the center of the Earth, what would the air pressure there be (assuming that the insulated walls of the well withstood the pressure of the rock/magma/iron/etc.), assuming that the temperature at the bottom was reasonable -- room temperature.
The air would be mostly liquid, so let's just fill the hole with water. Assuming incompressibility, the pressure is
P = rho g h / 2
= (1000 kg/m^3) (10 m/s^2) (6.4*10^6 m) / 2
= 32 GPa = 3,200,000 atm.
Whoops, that should be 320,000 atm.
Taking account of compressibility, there's more water in the hole, so the pressure is higher.
The division by 2 accounts for the parabolic shape of the gravitational potential, assuming uniform Earth density.
Gene
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