AW: AW: analytical solution to center of earth problem

Ole R. Nielsen oleroc at
Wed Mar 24 17:07:47 CET 2004

Cord wrote:
>Hole only to the center of the earth: duck would burn, then crash
>Hole all the way to the other side: duck would yoyo several times
>and finally stop at the center of the earth (quite burned up, of course)

If possible, let's put a stop to this roast duck theory.
First of all, the example from "The Duck Who Fell To Earth" describes
re-entry into Earths atmosphere from orbit. The apparent weightlessness
experienced in orbit is caused not by being removed from Earth's gravity but
from being in a permanent free fall around the Earth. This requires a
forward motion of about 8 km/second in the Space Shuttle orbit height of 100
km (relative to the distance of 6000 km from the center of the earth, it
does not change much with altitude).
This forward motion makes you - as delightfully and accurately described in
another work of fiction - fall, but just exactly miss the ground

It is also this speed which is converted to friction energy (heat) when a
body leaves orbit and enters the atmosphere, i.e. brakes down to the speed
of the surface under him, which is about 0.5 km/second at the equator. I
assume that the mass of the decelerating body is a determining factor for
the converted kinetic energy, and that a space shuttle of 100 tons produces
a lot more heat than a 50 pound duck - which on the other hand would be
equipped with lot less protection from the heat.

The cause of this braking effect which is used intentionally to match speeds
of the shuttle and the landing strip is of course is the increased air
density nearer to the Earth's surface, which in turn increases drag. In the
lower layers of the atmosphere drag will cause a falling human body to reach
a maximum speed (a.k.a. terminal velocity) of about 200 km/h, before the
pressure of the 'air cushion' under him stops further acceleration.
Only by increasing aerodynamic capability or adding an engine will higher
speed be possible to obtain.

Needless to say, you can go a lot faster than that on the ground in a sports
car, and you are perfectly cool. :-)

The interesting thing is that continuing this line of thought, it is clear
that falling below the surface of the earth increases air pressure and
thereby (slowly) reduces the speed with which you are falling. Incidentally
the atmosphere will at a certain depth become liquid and a question is if a
person inside a military grade pressure suit would even have to bring a
shovel to dig through a solid atmosphere a couple of thousand kilometers
under our feet? A regular hand-held shovel, naturally, since a steam shovel
probably wouldn't work...

Gentlemen, start your engineering!

-- Ole

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