A hole through the Earth

Søren Krarup Olesen raptus at stofanet.dk
Mon Mar 22 18:59:33 CET 2004


Dear all,

I think I got a bit obsessed with the problem yesterday, so I decided to
calculate/simulate everything about it...once and for all.

Some nice results came out:

a) The yoyo-effect continues forever (disregarding air friction of
course), so effectively you end at the exact same spot on the opposite
side of the Earth. Not surprising when you think about it; the total
mechanical energy is of course a constant.

b) The yoyo-effect is (probably) a perfect cosine, which was both
surprising (to me) and a boring result actually. Theresa will explain
later :-)

c) The center of Earth is reached after 1233 seconds (i.e. 20 mins and
33 secs).

d) The velocity at the center of Earth is about 8134 m/s (i.e. 2260
km/h), quite speedy, but also the maximum speed you'll ever encounter on
such a journey.

Here are links to the documentation:

http://raptus.dk/center/center.cpp (the simulation program in C++)

http://raptus.dk/center/center.pdf (a PDF graph showing position vs.
time)

http://raptus.dk/center/center.ps (same as a PS file)

http://raptus.dk/center/data.txt (raw text data from the simulation)

http://raptus.dk/center/formulas.jpg (the initial formulas)

I am still a bit disappointed about the results...had hoped for more
funny behavious especially while reaching the midst of Earth,
but...nothing really happened... :-/

Søren




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