Shouldn't it be used for Hyperloop?

Sent from my iPhone

On Aug 6, 2017, at 6:05 PM, Steven A Smith 
<sasm...@swcp.com<mailto:sasm...@swcp.com>> wrote:


So... *IF* you could bore a perfectly straight hole thorugh the earth to your 
precise antipodal location (probably having to put one hell of a "well casing" 
in, probably of neutronium to withstand the temperatures and turbulences of the 
core?) what would the "orbit" of a falling body be?   Would a massive object 
(e.g.  metal sphere) simply fall to the center and then by it's momentum "rise" 
until it reached it's apogee somewhat short of the antipodal end of the casing, 
slowed somewhat by the atmosphere?

Is this a good problem for a second year differential calculus student?  Or 
might there be some simplifying assumptions that could be made?


My rough attempt to estimate the behaviour/trajectory: (spoiler?)

The "boundary conditions" suggest that upon dropping the mass, gravity and air 
density would be very close to what we have at or just above the surface and 
the mass would achieve terminal velocity (122mph for a sky-belly-flopper, a bit 
more for a true sky-diver, and probably somewhat higher for an iron or steel 
sphere, for instance) long before air density nor the value of gravity changed 
appreciably.

Near the core, the air density would approach zero (my assumption of a 
spherical earth and that the gravitational attraction of the mass "outside" the 
radius of the current location of the sphere summing to zero) it seems likely 
that terminal velocity would rise to some point, but it seems very difficult to 
estimate.

Other assumptions include that the diameter of the sphere is small enough 
compared to the borehole that there would be no significant amount of 
compression of the column of air in front of the sphere, if it were a "tight 
fit" I suspect the ball would compress the column of air under it until that 
pressure's exerted force exceeded that of gravitational pull and would 
eventually "bounce" long before it got near the core.

I also thought of coriolis forces, but then realized that the trajectory has 
only an R, no theta nor phi component, so in principle the sphere would not 
experience any coriolis force.  (nod to Nick's Swirlies)  On the other hand, 
since the sphere would nominally be in freefall, it's trajectory would be 
influenced by it's initial velocity (relative to the rotation of the earth), 
suggesting it would follow a spiral path toward the center of the  earth, 
suggesting that if we wanted a "bullet-train" that went straight through the 
earth, we would need to give it a *spiral* core?    Evacuating such a a tube 
would allow true orbital speeds.   The precision required to "drop" a 
bullet-train car "through* the earth seems excruciatingly difficult (as would 
be coming up with methods for the coring and the lining) seems 
insurmountable... but some form of magnetic levitation type "correction" along 
the way would seem possible if not easy.

I think tidal forces can safely be ignored?

I fondly remember when I first heard about the Freeman Dyson's "Dyson Sphere" 
and then Niven's _Ringworld_ and his followon _Integral Trees_ and Bob 
Forward's _Rocheworld_, realizing that there were alternative 
physics/engineering regimes not that far from our current experience, yet quite 
counter-intuitive to us.

'nuff for now,

 - Steve


On 8/6/17 5:30 PM, Gary Schiltz wrote:
That's really cool, Gillian. If you click on Santa Fe, you get a nice snarky 
response like one of the following for the Antipodes Location:

You`re alone and the water is so cold.
Incredible! There is no one around you, just fish.
You`re in the water and all you need is a boat.
Most likely the ocean. Watch out for sharks.

So, if you decide to tunnel straight through the center of the earth, you might 
want to try making a little course correction somewhere.

Fortunately for me, most of Ecuador's antipodes location is on the island of 
Sumatra, which happens to grow my favorite variety of coffee.

On Sun, Aug 6, 2017 at 11:28 AM, Gillian Densmore 
<gil.densm...@gmail.com<mailto:gil.densm...@gmail.com>> wrote:
https://www.antipodesmap.com/#about-antipodes

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============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
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FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove

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