i can understand how the force of gravity increases as you approach the center of a mass, but what's going on at that center point? an infinite force? nothing? does it all just cancel out?

a tard questions I know, but i'm curious and trying to kill off ignorance

5/22/2007 1:02:06 PM

Think of it like a swinging pendulum, but going back and forth in a sphere. When you hit the center, you'll fly by at whatever speed you're at and start heading back towards the surface (presuming this is a hollow earth we're talking about) and then you'll start being pulled back towards the surface... fly by again... etc until you eventually stop in the middle.


however this wouldn't happen since a hollow gravitational mass like this couldn't have an open center like you're talking about with the same sort of pull as a thick solid mass like the earth

[Edited on May 22, 2007 at 1:08 PM. Reason : ]

5/22/2007 1:07:11 PM

gravity only applies on macroscopic scales... at that level, the force is still very weak, and overpowered the electromagnetic forces

5/22/2007 1:07:49 PM

yeah aparently gravity is the weak sauce

5/22/2007 1:08:51 PM

Quote :

"1)Now i just want to know that if we consider the mass of earth above us do we have to consider the centre of gravity of that mass too. If so will there be two centre of gravity, one of the mass of earth above us and one of the mass of earth below us. 2)Do we have to consider the two earth peices as seperate bodies of differect masses? 3)Why does the gravity becomes zero at the centre of the earth? 4)I read somewhere that if a deep hole is dug from north pole of earth to south pole of earth and one slides down the hole from one end ,he would not come out from the other end instead he would keep oscillating between north pole and south pole inside the hole. Why is it so?"

Quote :

"1) Yes, you can view this as there being two centers of gravity. The effective force on you is the sum of the forces from those two centers of gravity. (There is no two forces "pulling you apart") 2) Yes, you consider it that way for the purpose of calculation. The whole "center of mass" trick is only an easier way to calculate the sum of all forces from all particles the Earth is composed of. 3) At the center of the Earth there is an equal mass on all sides of you (above your head and below your feet, left and right, in front and behind). The forces of gravity cancel out completely. 4) If you neglect friction then the following happens: You are accelerated by Earth's gravity (which gets weaker and weaker as you approach the center), building up more and more momentum until you reach the center. Your momentum carries you on, and when you have crossed the center, Earth's gravity will begin to increase again, but now in the other direction - you are decelerated. You gradually lose your momentum, until you just barely emerge from the hole's other end. Here your momentum is used up and you begin to fall again, repeating the whole process to the other direction, and so on, therby oscillating north and south for eternity. If you take friction (with the wall or the surrounding air) into account, then you are constantly decelerated by this friction and thus lose some of your energy to the wall or air. Your momentum will run out some time before you reach the other end and the amplitude of your oscillation will gradually decline, you will travel shorter and shorter distances from the center, until all your energy has been lost to friction and you rest at the center of the Earth."

[Edited on May 22, 2007 at 1:09 PM. Reason : ]

5/22/2007 1:09:05 PM

the gravity equation using center of mass equation is just an approximation. every particle of an object A is pulling every particle of object B towards it, and the objects are generally sufficiently far apart to just use the center of mass of each object as a good approximation.

as for when two particles become infinitesimally close to each other, i really have no idea, but I assume the 'strong' or 'weak' force or one of those other quantum forces dominates and repels the particles away.

5/22/2007 1:09:52 PM

^^Yeah the last paragraph there is basically what I wrote.

[Edited on May 22, 2007 at 1:10 PM. Reason : ]

5/22/2007 1:10:19 PM

5/22/2007 1:11:19 PM

Quote :

"Think of it like a swinging pendulum, but going back and forth in a sphere. When you hit the center, you'll fly by at whatever speed you're at and start heading back towards the surface (presuming this is a hollow earth we're talking about) and then you'll start being pulled back towards the surface... fly by again... etc until you eventually stop in the middle. however this wouldn't happen since a hollow gravitational mass like this couldn't have an open center like you're talking about with the same sort of pull as a thick solid mass like the earth"

Quote :

"4)I read somewhere that if a deep hole is dug from north pole of earth to south pole of earth and one slides down the hole from one end ,he would not come out from the other end instead he would keep oscillating between north pole and south pole inside the hole. Why is it so?""

See that's kinda what we were talking about. We were trying to imagine what the scenario would be in the evolution of travel, ie: how the time to get from Point A to Point B on the Earth has been sharply decreasing across the scope of history. Right now we can pretty much get to any point on Earth inside 24 hours. We were trying to think of what travel for people will be like when that time is reduced to an hour or two.

But then we realized there has to be a limit to the length of the trip because assuming consistent acceleration/deceleration, the human body can only endure so much force comfortably. So we set up the scenario where you'd travel to the farthest point from any position on the globe (the point opposite it on the surface) and just go straight through the globe. Assuming you're traveling in a vacuum, we figured if you fell through the earth you'd get to the other side in 38ish minutes.

But that's when we started arguing about what the force of gravity would do as you approached the center mass and we just kinda left things there.

I know, we're fucking dorks, but I love this shit

5/22/2007 1:29:06 PM

so, as you're bouncing up and down like a pendulum swings back and forth, and due to air friction, do you eventually stop in the middle of the earth and just float there?

5/22/2007 1:34:12 PM

In addition to what I wrote ^^

We picked 1 g because it was a comfortable acceleration on the human body (we're all pretty used to it), and something traveling to other side of the earth wouldn't need any external or internal assistance. You could let the force of gravity do all the work. With 3gs the time was like 20 minutes. The next step was to figure out what the time would be for going the length of half the circumference, but i wasn't sure how the rotational acceleration would factor into the equation, if at all.

5/22/2007 1:36:07 PM

you flyby and flyby thats why stuff orbits sutff. once u get close you just orbit

5/22/2007 1:36:46 PM

They should make you people take physics.

5/22/2007 1:43:52 PM

technically they did, but i wasn't very interested at the time and my professor was crappy

plus its been six years

5/22/2007 1:55:17 PM

gravitational force at the center of a perfect sphere is 0, for pretty much a point sized volume. so it would be much reduced but not entirely gone in every other instance....

5/22/2007 2:04:22 PM

I took AP Physics in HS and Physics in college.

I read all those physics books about quantum mechanics and time travel and string theory and such, so that's what I'm more versed in rather than kinematics.

5/22/2007 2:23:21 PM

at some level, gravity is not a well understood force

that is, the "why" is not very well understood

however, from a calculation stand point

the ability to get stuff done

gravity is very well known, and if you want to learn about it, you can study up on both classical mechanics and general relativity

[Edited on May 22, 2007 at 2:32 PM. Reason : .]

5/22/2007 2:25:38 PM

oh...

i read some of your other posts

if you could put a chamber in the center of the earth and sit in it you would feel 0 net force from gravity due to the fact that there is a spherically symmetric gravitation potential surrounding you

you would just float there
...

edit... actually, i'm not sure what you would do, because the earth is a rotating body moving through space

probably need read up and think about it

[Edited on May 22, 2007 at 2:32 PM. Reason : .]

5/22/2007 2:28:37 PM

mentok = mind-taker

nastoute = mind-blower

5/22/2007 2:30:38 PM

oooh yeah, that whole earth is rotating thing.. crap.. didn't think about the effects of that acceleration on the whole falling through the earth thing.

ugh this stuff is complicated

5/22/2007 2:34:24 PM

I say we get working on this giant hole from N to S and start making some profit off the ultimate ride. Its like jumping into a bottomless pit for real and shit

5/22/2007 2:47:43 PM

^ before we do that, we need to empty out all that lava in the middle of the earth and store it somewhere

5/22/2007 2:50:37 PM

Well you'd have to build a pretty strong tube and make it a vacuum because otherwise it'd be too slow.

Plus I'm pretty sure you can't dig a hole directly through the core of the earth. Not anytime soon anyway.

5/22/2007 2:50:40 PM

psh all just semantics, lets get some of you mechanical/structural engineers working on this, oh and as for the lava, i hear the middle east is a nice place this time of year to store lava.

5/22/2007 2:52:05 PM

couldn't you install some water-powered electric generators in a tunnel that runs through the center of the earth, and then pour water down to have an INFINITE SOURCE OF ENERGY?

5/22/2007 7:02:44 PM

...

5/22/2007 7:16:06 PM

If there were such a thing as a point mass then yes the force of gravity would get infinitely large as you approached the mass. Fortunately, mass is smeared out and things like the earth have the force of gravity decrease as you travel into the earth. If we assume that the earth has uniform density then the force of gravity decays linearly to zero as we travel to the center. All of these facts are easily derived as a consequence of Gaussian spheres applied to classical Newtonian gravity, a reasonable approximation for the moment. One will arrive at the same conclusions if you employ
Einstein's General Relativity. However, even General Relativity fails when it comes to point masses,
there would be a singularity in spacetime if there were such a thing as a point mass. The problem
is more likely with the concept of a point mass then General Relativity itself. That's what I think anyway.

It is worth noting that the infinity of the electric field due to a point charge is also problematic. For one thing the field has infinite energy. Mathematically point charges are fairly easily handled by the use of Dirac Delta "functions", I think this is not a necessary formalism to state classical E&M. I mean sure Griffiths is wall to wall Dirac Delta functions but this is more a notation convenience then a statement of fundamental physics. We use point charges because we either don't know or don't care what happens at a microscopic level. A classical apology for this is simply to posit that there really is no such thing as a point charge, rather all charge is smeared out in some tiny but unobservable sphere. It can be very very small and still the infinity is avoided. The other resolution to the problem involves quantum field theory.


Pragmatically speaking, if you could somehow drill a hole through the earth and create a vacuum so that you only experienced gravitational effects then nastoute pretty much explained it already. I'd add that we just need to think about the accelerated frame that the earth is, we're rotating about the axis and around the sun. The question is how big is the hole and can we be assured we will not slam into the side as the earth rotates into the freefalling daredevil. If we could drill along the axis of rotation then we could avoid that question so we'd only have to worry about the rotation around the sun. But that might be neglible, lets see assuming

A = -gr/R

which is correct(ignoring the rotation for a moment), it gives zero at the middle and A=g when r=R=radius of earth. Lets solve this, we can assume r=R at t=0 and V=0 at t=0 for the sake of discussion,

A = -(g/R)r = r''

This is the same math as a spring, the solution satisfying the initial conditions is,

r(t) = R*cos(sqrt[g/R]t)

We will reach r=0 after a quarter period, that happens when pi/2 = sqrt[g/R]t
the time to the middle would be,

t = (pi/2)*sqrt(R/g)

Lets see, R = 6,300,000 m and g=9.8 m/s^2 so t = 1259 s or t = 20.98. Wow, it'd take a whole day
to fall to the center of the earth in our model. (a more realistic model would have higher
density towards the core which would lead to a smaller time).

Now if the free faller was dropped from an apparatus attached to the earth then it would
naturally obtain the centripetal velocity of the earth, what we really need to worry about is
the straight line motion of the freefaller verses the (nearly) circular path of the earth. If you
think about it for a little the radial digression from the curved path would be

y = R( sec(theta) - 1 )

For a days worth of falling, theta = one degree , so

y = R(1/cos(1) - 1) = 960m

You'd need a big hole, never mind the lava and the cave people.

[Edited on May 22, 2007 at 10:56 PM. Reason : .]

5/22/2007 10:55:35 PM

mathman.. awesome explanation!

I have one question about this:

Quote :

"Lets see, R = 6,300,000 m and g=9.8 m/s^2 so t = 1259 s or t = 20.98. Wow, it'd take a whole day to fall to the center of the earth in our model. (a more realistic model would have higher density towards the core which would lead to a smaller time)."

I think you meant 20.98 minutes, not hours. I don't know how that'd effect what you did below that, but maybe that means we only have to worry about the cave men and lava.. not as much a big hole



[Edited on May 22, 2007 at 11:27 PM. Reason : bolding and such]

5/22/2007 11:27:13 PM

^thanks.

dang it, never fails. See why I stick to letters usually. 20 minutes would make a smaller hole work for sure, in fact if my calculations are correct this time the hole would only need to be a few meters in diameter.

( I thought it was strange I got almost a day... oh well )

[Edited on May 23, 2007 at 12:44 AM. Reason : .]

5/23/2007 12:42:58 AM

It's cool man

It's all irrelivent anyway. The technology to ever do this is soo far off that I'd be surprised if it ever happened.

5/23/2007 12:58:20 AM

so I woke up this morning and the first thought I had was I used the wrong radius in the last part. I should have used 93 million miles, but I used the radius of the earth instead. After correcting for this the hole needs to be about 30,000 meters, or about 19 miles wide, just to get to the center of the earth without hitting the sides.

5/23/2007 8:57:01 AM

yes, you would float in the middle of the earth.


i mean, if the pressure and heat didn't kill you first.

5/23/2007 9:08:15 AM

what if you took a whole bunch of different-weighing things/animals/people with you? would you all be floating in a line ordered from heaviest to lightest towards the sun (the next most massive object?) since the earth's net grav will then be zero? in effect, you will be wheeling around in the whole all in line

if the weak weak earth center gravity will allow the sun's gravity to affect you, i mean

5/23/2007 9:27:31 AM

it wouldn't affect you that much since if you got pulled off center, suddenly you wouldn't be in the middle any more, and the earth would recenter you.

5/23/2007 9:31:17 AM

seemed as if the simple explanation of "there's an equal amount of mass around you= equal gravitational forces= no net gravity" works better than going into subatomic physics and the fundamental forces

5/23/2007 11:20:29 AM

bunch of fat nerds might as well be yapping about gravy question

OHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

5/23/2007 11:21:15 AM

YES THE PLANE TAKES OFF IT'S THE FRICTION OF THE AIR OVER THE WINGS NOT THE SPEED AT THE WHEELS

5/23/2007 11:23:05 AM

Quote :

" hole needs to be about 30,000 meters, or about 19 miles wide, just to get to the center of the earth without hitting the sides"

If you drilled your hole right, it could be as small as you wanted it to be.

If you mean a hole that went straight through, so that if you looked through it, you'd see space, i don't think 19mi would be enough.

5/23/2007 12:36:24 PM

Quote :

"mathman: 93 million miles"

where does this come from? I'm confused..

5/23/2007 1:34:46 PM

legatic wins

5/23/2007 1:36:01 PM

did you know gravity was invented when Sir Issac Newton saw an apple fall? First recording in history of gravity. I guess things just floated on by before then.

5/23/2007 4:01:08 PM

^^^

93 million miles is the distance between the earth and the sun.

i am not sure why he used that. (or said that he should have)

5/23/2007 4:26:46 PM

Quote :

"moron If you drilled your hole right, it could be as small as you wanted it to be. If you mean a hole that went straight through, so that if you looked through it, you'd see space, i don't think 19mi would be enough."

I was talking about the diameter of the hole. The idea was to drill a hole along the axis of rotation for the earth then let the freefaller drop down that hole.

Quote :

"0EPII1 93 million miles is the distance between the earth and the sun. i am not sure why he used that. (or said that he should have)"

The reason I used that is that a freefaller in a vacuum sealed hole falling towards the center of the earth will hit the side of the hole if it moves too much. The reason is that the hole is moving in a circular arc. The radius of that arc is about 93 million miles. Once the freefaller let go to fall it will travel in a straight line with the direction of its initial velocity, however the earth will continue to follow its circular orbit, consequently the freefaller will hit the side of the hole.

Oops, this is wrong. The freefaller will also experience the same gravity due to the sun so it will not
travel in a straight line, but rather the same orbit as the earth, duh.

So yeah, the freefaller would just keep oscilating towards and away the center of the earth provided you could actually drill such a hypothetical hole.

[Edited on May 23, 2007 at 10:47 PM. Reason : .]

5/23/2007 10:46:30 PM

Quote :

"at some level, gravity is not a well understood force"

at very small levels actually.... quantum...


and what causes it (particle, wave etc) is even less known (besides mass and distance that is)

5/24/2007 8:43:19 AM

Quote :

"So yeah, the freefaller would just keep oscilating towards and away the center of the earth provided you could actually drill such a hypothetical hole."

Good stuff.. I'll get this guy started on it.

5/24/2007 10:04:58 AM

What about black holes? Does everything caught in one eventually make its way to a central mass? Does that central mass keep getting larger? etc.

5/24/2007 10:16:10 AM

^ I would recommend reading



http://www.amazon.com/Briefer-History-Time-Stephen-Hawking/dp/0553804367/ref=pd_bbs_sr_1/002-7633527-7882432?ie=UTF8&s=books&qid=1180024092&sr=8-1

and



http://www.amazon.com/Universe-Nutshell-Stephen-William-Hawking/dp/055380202X/ref=pd_bbs_sr_2/002-7633527-7882432?ie=UTF8&s=books&qid=1180024163&sr=8-2

for a good starter on blackholes, time/space, and other fun stuff.

5/24/2007 12:30:49 PM

isn't there also a shell therom for gravity?.... Like if you're inside a shell of mass you won't feel any gravity from that mass (assuming it's a homogenious, evenly distriputed sphere of mass)

5/24/2007 3:26:17 PM

^Gauss' Law applies to any inverse square force. There is no gradient in the potential (gravitational in this case) inside of a shell (of mass).

5/24/2007 4:16:57 PM

→→→→→→→→→→→→→→→→→→

5/24/2007 7:28:39 PM