What if there was a pole, whose length was the circumference of the Earth?

1. Jun 7, 2009

Pshock92

Imagine a strange event:

Let's say that you had a pole, one that you were holding up vertically, that had the length of the circumference of the Earth (24,901.55 miles). Let's just pretend that, although the pole is extremely long, the pole does not wobble like long, skinny poles do. Let's also pretend that we have a stretch of land with no elevation changes and no oceans, sands, or anything. It's just a long grassland that goes all the way around.

Now, say we take our pole and we gently place it on the ground. What would happen?
I've narrowed it down to three possibilities:

1. The pole goes all the way around the Earth, and the two ends of the pole would meet - I've had a few people say this is what most likely will happen, and it's what I expected when I thought this up. I've also been told that it depends on the material of the pole.

2. Considering that the Earth is round, the straight pole would not go around the Earth, and would sort of just sit, jutting out into space - This is the common sense answer that people give me. I imagine this to be impossible: If the pole were to jutt out into space, then at one point that pole would have to get off the ground and elevate, for no particular reason. Would gravity allow that?

3. The pole would snap - This is what could happen if the pole was made of a material that would not allow it to go around the Earth. But, then again, it'd be strange to see the pole snap for no reason other than to be set on the ground.

My guess, as I've said before, is possibility one. Although the Earth is round, the landscape of it is flat (i.e. the ground we stand on is not round), so, the pole would have just flat land to rest on.

What do you think? I'd love new ideas to be brought foward!

2. Jun 7, 2009

SmashtheVan

My guess is that as the Earth spins it applies a torque at the base, and the bottom of the pole moves with the Earth. Since the center of mass would no longer be supported, it would fall towards the Earth. then two things can happen depending on the properties of the pole:

If the pole has a high resistance to bending, the pole will ultimately come to rest with the center of mass lying on the surface of the planet, with its sides sticking out straight across, out into space, with a slight bowing due to gravity(most affecting points of the pole closer to the CM)

If the pole has a very small resistance to bending, and no breakpoint, then i can imagine the wrapping around the Earth scenario

3. Jun 7, 2009

diazona

Well, the reason you're not getting a clear answer is probably that it's not a clear question. Do you mean to take into account the rotation of the Earth, or should this be an idealized non-rotating planet? In the latter case, what makes the pole move from its vertical position? And what do you mean by "the pole does not wobble" - is it rigid?

4. Jun 7, 2009

Mapes

If stood on its end, a pole this long made of any real material would http://en.wikipedia.org/wiki/Buckling#Self-buckling_of_columns" and fail. But if we imagine that this can't happen, then the pole is in only a metastable state when positioned on its end. If tipped off balance, it would wrap around the Earth, as this is the a lowest-energy configuration (the center of the pole's mass would be at the center of the Earth).

Last edited by a moderator: Apr 24, 2017
5. Jun 7, 2009

Mapes

No material is this rigid. Think about it. It would be like a bridge, ten thousand miles long, connected only at one end. A typical 1" diameter metal pole wouldn't even make it a few hundred feet without yielding.

6. Jun 7, 2009

SmashtheVan

if the pole is supposedly unbreakable, then who's to say its not incredibly inductile either?

7. Jun 7, 2009

Mapes

Well, presumably Pshock92 is asking about realistic material properties. A quick calculation suggests that a 1" diameter rod would have to have a stiffness of 1030 Pa to avoid wrapping around the Earth (calculated via the bending equation $\kappa = M/EI$, where $\kappa$, $M$, $E$, and $I$ are the curvature, bending moment, Young's modulus, and moment of inertia). This is about 1018 times stiffer than steel. Hardly "a very small resistance to bending."

8. Jun 7, 2009

Staff: Mentor

A solid, straight rod could be of almost any known material and wrap around the earth. It doesn't have to bend much for that.

9. Jun 7, 2009

DaveC426913

The rod would only have to deflect one degree over each 60 mile length. According to http://www.1728.com/circsect.htm" [Broken], that would mean, over 30 miles to each side, the rod would only have to deflect .297 miles or 1570 feet.

That is well within the ductility of any known material and surely not enough to break it. It is probably safe to say that even the theoretically most rigid material physically possible would bend without breaking.

Last edited by a moderator: May 4, 2017
10. Jun 7, 2009

Unit

my take on this is that because the curvature of the earth is so shallow in relation to the width of the pole, the pole would just warp around the entire earth, although it would look as if it was straight, just like the grassy field beneath your feet looks flat.

however, if the post was infinitely strong (haha), so that it wouldn't bend, wouldn't break, wouldn't yield under anything, it would be like balancing a thin straw on an orange.

also, inside my head i've always been imagining this pole as a hollow pole, what about all of you?

11. Jun 7, 2009

DaveC426913

It doesn't matter. The only thing that matters is the tensile strength of the material and whether it is a reall material or an ideal material.

12. Jun 8, 2009

qlc

first i looked at this:
24,901.55 miles (40,075.16 kilometers).

then i found out that:
Low Earth Orbit (LEO) - Geocentric orbits ranging in altitude from 160–2,000 km (100–1,240 miles); one revolution takes 90 minutes, the speed is 8 kilometers per second.
Medium Earth Orbit (MEO) - Geocentric orbits ranging in altitude from 2,000 km to just below geosynchronous orbit at 35,786 km (22,240 miles). Also known as an intermediate circular orbit.
Geosynchronous Orbit (GEO) - Geocentric orbit with an altitude of 35,786 km (22,236 statute miles) above mean sea level. The period of the orbit coincides with the rotation period of the earth: 24 hours; the speed is 3 km/s.
High Earth Orbit (HEO) - Geocentric orbit higher than 35,786 km (22,236 statute miles)

HEO is 35,786 km and the rods lenght is 40,075.16 kilometers
now i think that the rod whould fly off to space or start to orbit around earth rather than fall down on the earth trought the atmosphere.
the rod is simply too long, i mean wouldnt the earths centrifugal force be stronger at this point than the gravitational pull between the two objects.
what yall think ?

Last edited: Jun 8, 2009
13. Jun 8, 2009

Mapes

Hi qlc, welcome to PF. Calculate the height and speed of the pole's center of mass if the pole were standing on its end (and still intact). If the speed is too slow for its orbit, the center of mass will tend to move toward the Earth, not away from it.

14. Jun 8, 2009

Pshock92

Alot of people on her are siding with my theory, and are giving good evidence for it, which is good.
Is their any possibility that the pole would just jutt out into space? If, for some unknown reason, the pole would not wrap around the Earth, what would that look like? If you were to balance a thin straw on an orange, then the two ends of the straw would not be touching the orange. They'd just be jutting out into space.
Imagine this with the pole and the Earth. What would that look like from space? What would I see if I was on the Earth right at where the pole seizes to touch ground? Would I just see a pole slanting upward into the sky? Weird.

Again, I imagine this to be somewhat impossible. But, if under crazy cirumstances, it is possible, could someone explain it?

I thought of this whole thing when I was in 7th grade, and the next day tried to explain to some friends and an adult or two. They're first reaction was that the pole would jutt out into space. When I tried to explain why this was impossible, they all laughed at me. I suggested that the pole would wrap around, and they called me crazy.

It even led to one guy to look me in the face and say, "You're an idiot. You're going to be president of the United States one day, because you are such an idiot."
Fun little anecdote.

15. Jun 8, 2009

Pshock92

The exact, clear cut answer I wanted. Yay!

16. Jun 8, 2009

DaveC426913

If it were made of an imaginary material that had an unlimited stiffeness, yes.

Note that you could theoretically do this by making a truss (i.e. a bridge with one central pier and no endpoints). Huge increase in stiffness without the correspoinding increase in weight.

No. You would see a straight pole that disappeared into the misty horizon. It is the Earth that curves away from the pole, not the other way around. And from a six foot altitude, you cannot see the Earth curve away from you.

If you drove ten miles down the road and looked up, you'd see a line a few hundred feet in the air that ran horizontally from horizon to horizon. It would be virtually impossible to tell that one end was higher than the other.

It wouldn't be until you were in orbit that you would be able to see the curvature of the Earth, and thus how the Earth curves away from the pole.

Many, many people are intimidated by enquiring minds. Here, you have found a place where others are just like you who will appreciate and nourish an enquiring mind. We are glad to have you.

17. Jun 8, 2009

Klockan3

To me this means that the pole is infinitely stiff and therefore will balance off the earths surface.

18. Jun 8, 2009

Nick89

I can imagine how weird it will look to have an infinitely rigid pole laying on the surface of the earth. It would appear to just be a very large pole lying on the ground if you are near the 'contact point'. But if you move away from the contact point, it would appear to be floating in mid air!

Of course, even the slightest touch will make the pole tip over and find a new balance point (it may even 'roll' around the earth a few times hehe).

19. Jun 8, 2009

D H

Staff Emeritus
That's exactly how I looked at the problem. The OP essentially posited an unobtanium rod with infinite shear modulus and asked if it would bend. This is not an irresistible force / immovable object quandary. It is a resistible force versus an immovable object. The immovable object wins.

The answer would be a bit different had the OP posited the use of commercial-grade unobtanium, which has a very high, but not infinite shear modulus. Then the rod would partially wrap around the Earth. Some deformation would occur but the ends would stick out above the Earth. How much would occur bending would occur: You'll have to read the product spec.

20. Jun 8, 2009

diazona

Actually, I would think a slight touch would make the pole rock back and forth slightly. Or roll. It depends on which way the force was applied.