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Re: Journey to the centre of the earth
Posted:
Jul 20, 1996 2:48 AM


In article <1996Jul12.181655.516@schbbs.mot.com>, Bob Morris x2357 <morris@phx.sectel.geg.mot.com> wrote: >In article rms@newton.cc.rl.ac.uk, "M.Warren." <mdw95@mailbox.cc.rl.ac.uk> () writes: > >> >You're about to be dropped into a tunnel that's been prepared in the earth. >> >This tunnel has been accurately designed so that you will not collide >> >with it on either side, but will emerge... >> >> I presume that it doesnt matter..In the same way that it doesnt matter >> for an aeroplane?...anyone know the physics involved? I think its because >> when you are dropped you are already moving at the earths rotation..as >> you fall there is nothing to 'slow' you down relative to the earths >> rotation. therefore the hole would be perfectly straight and pass thru >> the centre of the earth. put it another way...you are infact in a >> geosynchronous orbit..(below ground..but same thing). this is just me >> trying to work it out...it may well all be guff...anyone know? >> Mikw. > >I disagree. At the surface you are travelling at X miles per hour >which translates to Y radians per hour, the same as the surface >itself. As you go down, you continue to travel at X miles per hour, >but the earth continues to travel at Y radians per hour. The >relationship between X and Y (at the equator) is X=Y*distance from >center/radius of earth, so as you go deeper, the earth's speed in miles >per hour decreases and you hit the wall of the tunnel. Something >similar happens away from the equator, but I have to go to a meeting >now, so bye. > > >Bob Morris >morris@phx.sectel.mot.com >bazerko@aztec.asu.edu >
As the one who originally posted this question, >> >You're about to be dropped into a tunnel that's been prepared in the earth. >> >This tunnel has been accurately designed so that you will not collide >> >with it on either side, but will emerge...
I just wanted to say that I have a *hunch* what the correct path would be. First, what's the proper name for a cycloid made by one circle *inside* a larger circle? Well, my hunch is that the path would *be* one of those inner cycloids. Now, if the radius of the inner circle is exactly 1/2 the radius of the outer circle, wouldn't the inner cycloid in this case be a straight line through the outer circle? And that would be path of an object dropped from a nonspinning earth or from either of the poles. Well, for an object dropped from the equator, you'd probably have to reduce the radius and then go ahead and trace the inner cycloid to get the path of the tunnel. And perhaps my other question about being dropped from some latitude would have *that* path completely in the plane of the great circle route having the initial latitude being the farthest point from the equator, and having the radius of the tracing circle being somewhere between the smallest value, which would be the case with a drop from the equator, and 1/2 the radius of the earth, which would be the case for a drop from one of the poles. Does this hunch make sense? Am I way off? Can anybody out there actually do the math? ;)
 Jim Waters <jwaters@az.com>



