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Allright...you Geology and Physics Guys

#24
AFAIK, if an object were dropped down a hypothetical hole through the earth, it would move back and forth from one side of earth to the other.

By Newton's First Law, an object in motion will remain in motion until an external force acts upon it. When the object is dropped, gravity will cause it to accelerate, but as the gravity tends to zero, when approaching the center, inertia will keep it moving until it passes through the center, where gravity will begin to act upon it again, in the opposite direction. When the force of gravity becomes strong enough to reverse the direction of movement, the process will repeat.
 
#25
bassybill said:
I was mistakenly thinking the force would increase as you go towards the centre of the Earth as it's inversely proportional to r squared. But your point about the mass is a valid one. The precise details of how this would work inside the mass of the Earth is trickier to calculate - details are here.

http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/earthole.html
Click to expand...

Oh right, the decreasing r would serve to increase g, not the other way around, but as r decreases so does m so the net effect is a decrease in g as r->0.
 
#28
bassybill said:
It sure does sound fun! If anyone wants to check the figures, I used six million meters as the radius of the spherical earth and a constant value of 9.81 N/kg for g. In practice this value would increase VERY significantly as you fell and this would increase the speed of the trip and shorten the time taken. It would also stretch and squeeze you into oblivion. ;)
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AFAIK g will decrease as you approach the center (should be by a factor proportional to r^3). And you need to consider this when calculating speed and travel time.
 
#30
NWB said:
Oh snot, I'm a geologist and I can't remember what the temperatures of the mantle, outer core, and inner core are.

There are hotter spots within the mantle that result in magma migrating to the surface in such places as Hawaii, Iceland, and Yellowstone. I find it interesting that these hot spots are stable over some fairly long periods of time as the crust slides around over them.
Click to expand...

Why would you admit you don't know, when it would be easy to google this information AND you get to say you do know the temperature of the Earth's core?:hiding:
 
#31
Say you dived into the hole from a position high above the surface of the Earth - like a satellite or something, a bit like Felix Baumgartner. Your weight (and acceleration) would increase as you approached the entrance to the hole, then start to decrease when you got inside until it was zero as you passed through the centre at very high speed. Interesting.

I might have a go at modelling this in Excel later. It could be a bit tricky with my level of mathematics. :eek:
 
#32
bassybill said:
Say you dived into the hole from a position high above the surface of the Earth - like a satellite or something, a bit like Felix Baumgartner. Your weight (and acceleration) would increase as you approached the entrance to the hole, then start to decrease when you got inside until it was zero as you passed through the centre at very high speed. Interesting.

I might have a go at modelling this in Excel later. It could be a bit tricky with my level of mathematics. :eek:
Click to expand...


see....now that's a bit too high....you're not seeing the commercial potential of this

dig the hole and come up with the suits.....that's the easy part...

then market it as ride of a lifetime....since you'd have, like, ports or windows or something...so the riders could see for themselves what the earth was made of....

then, you'd have dropped them from just high enough, that they would land softly as a feather on the mechanism you had set up on the other end....:D

davesignatureII-1.png
 
#33
bassybill said:
Say you dived into the hole from a position high above the surface of the Earth - like a satellite or something, a bit like Felix Baumgartner. Your weight (and acceleration) would increase as you approached the entrance to the hole, then start to decrease when you got inside until it was zero as you passed through the centre at very high speed. Interesting.

I might have a go at modelling this in Excel later. It could be a bit tricky with my level of mathematics. :eek:
Click to expand...


Suppose you dove from a position of 10 km (arbitrarily decided) above the surface of the Earth. You would plunge through the hole in the Earth and then rise above the hole on the other side of the planet only to come to a stop exactly 10km above the Earth on the other side (assuming the same scenario of no friction, etc.)


EDIT: I just remembered that general relativity has an effect on objects moving through a gravitaional field. I wonder how that affects the travel.

Have to get back to you all on that one. . . . .
 
#34
Lonesomedave said:
How hot is the Earth's core...and does the temperature increase in a linear fashion as you dig your (theoretical....:D) hole through the Earth?

I know, I could probably look this up on wiki etc, but I am in no hurray...and would like to hear the thoughts of anybody who cares to respond.

davesignatureII-1.png
Click to expand...

I made my living as a geologist (and engineer) for 35 years. I teach geology. I don't know - I'd have to Google it. (My guess is that it is not linear due to the changing composition of the various strata you would encounter.) Check it out.

601px-Temperature_schematic_of_inner_Earth.jpg
 
#35
hbarcat said:
Suppose you dove from a position of 10 km (arbitrarily decided) above the surface of the Earth. You would plunge through the hole in the Earth and then rise above the hole on the other side of the planet only to come to a stop exactly 10km above the Earth on the other side (assuming the same scenario of no friction, etc.)


EDIT: I just remembered that general relativity has an effect on objects moving through a gravitaional field. I wonder how that affects the travel.

Have to get back to you all on that one. . . . .
Click to expand...
General relativity is just another way of modelling the effects of gravity (in terms of spacetime curvature). It's applicable in a wider range of conditions than Newtonian mechanics, which becomes increasingly inaccurate when dealing with very, very high velocities (approaching that of light).

For the hole through the Earth scenario as described here, though, Newtonian mechanics would be more than accurate enough as you would be travelling at a tiny, tiny fraction of light speed.
 
#36
bassybill said:
General relativity is just another way of modelling the effects of gravity (in terms of spacetime curvature). It's applicable in a wider range of conditions than Newtonian mechanics, which becomes increasingly inaccurate when dealing with very, very high velocities (approaching that of light).

For the hole through the Earth scenario as described here, though, Newtonian mechanics would be more than accurate enough as you would be travelling at a tiny, tiny fraction of light speed.
Click to expand...

OK, Bill. So as you're falling toward the center of the earth, would you accelerate at a constant rate all the way to the center (32 ft/sec2​), or would your acceleration decrease as you got deeper, due to the gravity of the increasing mass above you? (9.8 m/sec2​ for all you metric types)
 
#37
Munjibunga said:
OK, Bill. So as you're falling toward the center of the earth, would you accelerate at a constant rate all the way to the center (32 ft/sec2​), or would your acceleration decrease as you got deeper, due to the gravity of the increasing mass above you? (9.8 m/sec2​ for all you metric types)
Click to expand...
See post 31. My initial approach to this was a gross oversimplification becuase I didn't think what would happen to your weight as you travelled.

Your weight (and therefore acceleration) is proportional to m1*m2/d squared (the m terms are the masses of you and Earth, and d is the distance between the centre of mass for each object). As you fell from high above the Earth towards the hole, the two (effective) masses would remain constant and therefore your weight would increase as you got closer and closer and d decreases. But as you enter the hole, the mass of the Earth affecting you starts to decrease as some of it is now above you rather than below you. This means your weight also decreases once you enter, according to the equations on the site Titus and I both linked to above. Your weight would actually decrease to zero at the instant you reach the centre - this seems intuitively correct to me now, as you'd have the mass distributed around you equally in all directions giving a resultant force of zero, i.e. weightlessness.
 
#39
bassybill said:
See post 31. My initial approach to this was a gross oversimplification becuase I didn't think what would happen to your weight as you travelled.

Your weight (and therefore acceleration) is proportional to m1*m2/d squared (the m terms are the masses of you and Earth, and d is the distance between the centre of mass for each object). As you fell from high above the Earth towards the hole, the two (effective) masses would remain constant and therefore your weight would increase as you got closer and closer and d decreases. But as you enter the hole, the mass of the Earth affecting you starts to decrease as some of it is now above you rather than below you. This means your weight also decreases once you enter, according to the equations on the site Titus and I both linked to above. Your weight would actually decrease to zero at the instant you reach the centre - this seems intuitively correct to me now, as you'd have the mass distributed around you equally in all directions giving a resultant force of zero, i.e. weightlessness.
Click to expand...

OK, so would you possess sufficient velocity (or momentum) at the center of the earth to continue through to the other side? (Assume no friction.) You would have no weight, but you'd still have mass so you could have momentum if you had velocity, since ρ=mv.
 
#40
Munjibunga said:
OK, so would you possess sufficient velocity (or momentum) at the center of the earth to continue through to the other side? (Assume no friction.) You would have no weight, but you'd still have mass so you could have momentum if you had velocity, since ρ=mv.
Click to expand...
You certainly would continue through, right until you reached a point the other side the same distance from the centre that you started from (assuming zero frictional losses). Then you'd repeat the journey backwards and so on, ad infinitum. The energy change is gravitational potential energy to kinetic energy and back again. It's actually simple harmonic motion, very similar to a pendulum. If you try to imagine a huge frictionless pendulum that could swing straight into the Earth and out of the other side, you'll get the idea.

I'm just finishing a model of this in Excel, will post it here with an accompanying explanation later today.
 

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