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shropshire

If you fell through the Earth..

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I'll throw in one that starts from the southern hemisphere. I'd be smack in the middle of Spain! Just outside of someplace called San Martin de Valdeiglesias, west of Madrid.
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"Perhaps she saw before her a lifetime of walking on the ruined earth and chose instead a single moment in the air." -Carolyn Parkhurst

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And, for physics geeks, how long would it take you to get there? Since the original question ignores air resistance (or you'd never make it all the way through to the other side) you may ignore air resistance in this part too.



42



:-)

seconds? leap years?
...

The only sure way to survive a canopy collision is not to have one.

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For the purposes of the problem, should we also assume that the Earth is a true sphere?

Then the volumetric radius is 6371 km.
thus the distance is 12742 km

What about gravity? g is 9.8 ish at the surface of the earth but as you move towards the centre, what happens?.. g = GM/(r^2) so as radius gets smaller g gets bigger so when r = 0 g is given by a divide by zero error!! bollox, my simple head hurts.



Newton's shell theorem takes care of that.
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The only sure way to survive a canopy collision is not to have one.

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So, For a solid sphere this means that for any particle, the only gravitational force it feels will be due to the matter closer to center of the sphere .....thus as r (the distance to go to the centre of the Earth) tends to 0 the mass below it will also tend to 0.




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The traveler accelerates toward the center of the Earth and is momentarily weightless when passing through the geometric center at about 7900 m/s or almost 17,700 miles/hr. The traveler would pop up on the opposite side of the Earth after a little more than 42 minutes. But unless he or she grabs something to hold on, they will fall back for a return journey and continue to oscillate with a round-trip time of 84.5 minutes.



(.)Y(.)
Chivalry is not dead; it only sleeps for want of work to do. - Jerome K Jerome

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So, For a solid sphere this means that for any particle, the only gravitational force it feels will be due to the matter closer to center of the sphere .....thus as r (the distance to go to the centre of the Earth) tends to 0 the mass below it will also tend to 0.




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The traveler accelerates toward the center of the Earth and is momentarily weightless when passing through the geometric center at about 7900 m/s or almost 17,700 miles/hr. The traveler would pop up on the opposite side of the Earth after a little more than 42 minutes. But unless he or she grabs something to hold on, they will fall back for a return journey and continue to oscillate with a round-trip time of 84.5 minutes.



The oscillation period is exactly the same as the orbital period of a satellite in a circular orbit at the same distance from the center (ignoring air resistance, of course). So if the satellite passes overhead as you jump down the hole, it will pass over as you emerge on the other side of the planet.
...

The only sure way to survive a canopy collision is not to have one.

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If i fell through I'd be about 50km off the East coast of Bermuda, hmmmmm wonder if that is inside the triangle
:)



Yep, me too. Hmmm...maybe all the people that disappear in the Bermuda Triangle end up in Perth?

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i would end up 886 miles North West of Ile Amsterdam part of the French Antarctic Lands.
I swear you must have footprints on the back of your helmet - chicagoskydiver
My God has a bigger dick than your god -George Carlin

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>The traveler would pop up on the opposite side of the Earth after a little
>more than 42 minutes.

That's true if the hole is drilled straight through the center of the earth. But what if it's drilled on a tangent, and you slide down the (frictionless) walls and slide up the other side? The suprising result is that it ALWAYS 42 minutes.

Which means that if you drill a tunnel from LA to NY, put a train in it with frictionless wheels, and pump all the air out, you could get from LA to NY in 42 minutes with zero energy expended. Actually any two places on the planet could be linked by such a tunnel - it would always take 42 minutes.

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>The traveler would pop up on the opposite side of the Earth after a little
>more than 42 minutes.

That's true if the hole is drilled straight through the center of the earth. But what if it's drilled on a tangent, and you slide down the (frictionless) walls and slide up the other side? The suprising result is that it ALWAYS 42 minutes.

Which means that if you drill a tunnel from LA to NY, put a train in it with frictionless wheels, and pump all the air out, you could get from LA to NY in 42 minutes with zero energy expended. Actually any two places on the planet could be linked by such a tunnel - it would always take 42 minutes.



Which, of course, is why my commute takes 42 minutes each way unless I have to stop for a Satanic traffic light.
...

The only sure way to survive a canopy collision is not to have one.

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