42 minutes
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Ronbo
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Interesting. 42 minutes to get juuuust a liiiitle short of the earth's surface on the other side. You have to allow for friction, even friction of the air inside the tunnel. Chances are, you stop just a little short of the surface, and then wave bye-bye to the people looking down at you, as you go right back the other way. You stop just a little shorter on the return trip, and continue to oscillate back and forth until you end up in the center of the earth as a cinder. 
Next guy to try it ends up crashing into the cinder that was you. Sounds like a perfect project for a government to undertake.
Next guy to try it ends up crashing into the cinder that was you. Sounds like a perfect project for a government to undertake.
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MTGuru
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Nah, you just have to slather yourself with Earth-Lube™ before you go. Easy!Ronbo wrote:Interesting. 42 minutes to get juuuust a liiiitle short of the earth's surface on the other side.
I saw an interview with this guy the other day:
http://www.abc.net.au/science/news/stories/s854796.htm
Funny, he didn't mention the dinosaurs ...
Vivat diabolus in musica! MTGuru's (old) GG Clips / Blackbird Clips
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Dr. Mierzwiak: Well, technically speaking, the procedure is brain damage.
Joel Barish: Is there any risk of brain damage?
Dr. Mierzwiak: Well, technically speaking, the procedure is brain damage.
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anniemcu
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Okay. Why?MTGuru wrote:... Nah, you just have to slather yourself with Earth-Lube™ before you go. Easy!...
anniemcu
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fyffer
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Anyone besides me want to actually see the actual proof for this? Seems like it's intuitively possible, but what about the degenerate case, say connecting two places that are relatively close to each other, say NYC and DC. The tunnel would indeed be a chord of the sphere, but the angle cut down through the earth's surface would be rather slight; only in a frictionless situation would this be possible.
Now I've done it. I'm gonna have to go figure this out.
I'll be back later.
Now I've done it. I'm gonna have to go figure this out.
I'll be back later.
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fyffer
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OK. I'm back.
I think they're wrong -- unless my math is bad, but that's not usually the case.
I came up with an answer of 120 minutes. If I can figure out a way to post all my calculations (short of scanning my chicken-scratch calculations in my notebook), I will, but I'm curious if there are any other math dorks out there willing to try their hand.
My formula ended up reducing to, simply:
2* sqrt( 2 * R / g )
R being the earth's radius (avg. radius = 62674425 m)
g being the acceleration of gravity ( 9.8 m/s^2 )
which is simply the Newtonian formula for calculating distance travelled under constant acceleration ( d = vt + (a * t^2) / 2 ), solving for t, with v (initial velocity) being zero, then doubling, since the distance is the Radius. This definitely makes sense for the case of going straight through the earth (along the diameter), but if you think about it, it also makes sense for the shorter chords; the acceration gets smaller and smaller as you shorten the chord, but it should get smaller in precise proportion to change in the angle (the degenerate case of the diameter, the angle is 180, or 0). The value of R (1/2 the distance travelled) gets smaller by a value of R*cos(angle), and so does the value of g (acceleration) by the same amount (** If there's any place I'm wrong, it's in this last point - someone please correct me if I need it)
Note that the distance between points on the surface of the sphere completely cancels out and is not a factor. Weird, but true.
So why do I get 120, and they get 42 (Besides the obvious answer)?
I think they're wrong -- unless my math is bad, but that's not usually the case.
I came up with an answer of 120 minutes. If I can figure out a way to post all my calculations (short of scanning my chicken-scratch calculations in my notebook), I will, but I'm curious if there are any other math dorks out there willing to try their hand.
My formula ended up reducing to, simply:
2* sqrt( 2 * R / g )
R being the earth's radius (avg. radius = 62674425 m)
g being the acceleration of gravity ( 9.8 m/s^2 )
which is simply the Newtonian formula for calculating distance travelled under constant acceleration ( d = vt + (a * t^2) / 2 ), solving for t, with v (initial velocity) being zero, then doubling, since the distance is the Radius. This definitely makes sense for the case of going straight through the earth (along the diameter), but if you think about it, it also makes sense for the shorter chords; the acceration gets smaller and smaller as you shorten the chord, but it should get smaller in precise proportion to change in the angle (the degenerate case of the diameter, the angle is 180, or 0). The value of R (1/2 the distance travelled) gets smaller by a value of R*cos(angle), and so does the value of g (acceleration) by the same amount (** If there's any place I'm wrong, it's in this last point - someone please correct me if I need it)
Note that the distance between points on the surface of the sphere completely cancels out and is not a factor. Weird, but true.
So why do I get 120, and they get 42 (Besides the obvious answer)?
___\|/______________________________
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I haven't had time to look them over yet, but there are several
equations (including oscillation) applied to the problem on this site:
http://hyperphysics.phy-astr.gsu.edu/Hb ... thole.html
EDIT: It looks like the acceleration due to gravity changes spherically
as you get closer to the center, so g in your equation is not constant, maybe?
equations (including oscillation) applied to the problem on this site:
http://hyperphysics.phy-astr.gsu.edu/Hb ... thole.html
EDIT: It looks like the acceleration due to gravity changes spherically
as you get closer to the center, so g in your equation is not constant, maybe?
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CHasR
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fyffer wrote:OK. I'm back.
I think they're wrong -- unless my math is bad, but that's not usually the case.
I came up with an answer of 120 minutes. If I can figure out a way to post all my calculations (short of scanning my chicken-scratch calculations in my notebook), I will, but I'm curious if there are any other math dorks out there willing to try their hand.
My formula ended up reducing to, simply:
2* sqrt( 2 * R / g )
R being the earth's radius (avg. radius = 62674425 m)
g being the acceleration of gravity ( 9.8 m/s^2 )
which is simply the Newtonian formula for calculating distance travelled under constant acceleration ( d = vt + (a * t^2) / 2 ), solving for t, with v (initial velocity) being zero, then doubling, since the distance is the Radius. This definitely makes sense for the case of going straight through the earth (along the diameter), but if you think about it, it also makes sense for the shorter chords; the acceration gets smaller and smaller as you shorten the chord, but it should get smaller in precise proportion to change in the angle (the degenerate case of the diameter, the angle is 180, or 0). The value of R (1/2 the distance travelled) gets smaller by a value of R*cos(angle), and so does the value of g (acceleration) by the same amount (** If there's any place I'm wrong, it's in this last point - someone please correct me if I need it)
Note that the distance between points on the surface of the sphere completely cancels out and is not a factor. Weird, but true.
So why do I get 120, and they get 42 (Besides the obvious answer)?
I flunked math.
BUT:
One can do a lot of slippin' in 42 minutes with a tube of KY.
.
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TonyHiggins
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Are these calculations inferring that the force of gravity is a point in the center of the earth? It's not. I'm thinking that gravity is pulling at you from the mass of the planet which is all around you so that at the center, you are in free-fall and not accelerating. So the pull is declining the closer you get to the center, your acceleration diminishes and vice versa as you leave the center for the other side. Maybe the math accounts for this. I don't know. Maybe that's the difference between 42 and 120 minutes. ???
I'll ask my son when he gets home from vacation. (brag, brag) He just graduated from UC Berkeley with a BS degree in physics and astrophysics.
Tony
I'll ask my son when he gets home from vacation. (brag, brag) He just graduated from UC Berkeley with a BS degree in physics and astrophysics.
Tony
http://tinwhistletunes.com/clipssnip/newspage.htm Officially, the government uses the term “flap,” describing it as “a condition, a situation or a state of being, of a group of persons, characterized by an advanced degree of confusion that has not quite reached panic proportions.”
