# Thread: Earth is round?

1. Established Member
Join Date
Oct 2001
Posts
165
On 2001-10-23 20:19, David Simmons wrote:

No, It's not a myth. I've heard this one too about the Akashi Bridge near Kobe, the world's longest suspension bridge. It's about 2km between the towers, and the tops of the towers are about a meter farther apart than at the base.

Akashi Kaikyo Bridge (see Q.3)

It's quite an engineering feat, this one. It's an especially beautiful sight at night when it's lit up. It's also really cool when seen from the window of a jet just after taking off from Osaka airport at sunset. In addition, I once had the privledge of sailing under it on a ferry just before it's completion. Magnificent.

_________________
David Hall
I have no doubt that the bridge is an engineering feat. But for the tops of two perpendicular (pointing toward the center of the earth) towers separated by 2 km to be 1 meter further apart than the bottoms, they would have to be over 3 km tall. At least according to my computation.
I think you'd better run your numbers again, David. The Japanese company who designed this bridge tested it for earthquakes and typhoons. It's first test was the Kobe quake of, I think, '95. It's still standing.

2. Member
Join Date
Oct 2001
Posts
79
Wow, I'm glad that people are thinking. For the record, I am not actually a flat Earther. Think I mentioned this, but just thought I'd make it clear. Also, Spiff (Spaceman? Ah... Harry Nilssen), I'm sorry you think that I'm moving the goalposts on you, that wasn't my intention. I originally intended the explanations to be on a low level, and not require super precision instruments or serious globetrotting, hence the reference to 7 league boots. [img]/phpBB/images/smiles/icon_smile.gif[/img] I don't necessarily know that it's impossible to determine the flatness of the Earth using only local measurements.

Ok, what else, sorry if my "weaseling" seems like weaseling, I thought that I'd try to give other people a chance to point out how the explanations didn't really work on the local level...

With that in mind:

• I think that flying around the world counts as boots. But that's just me...
• Concerning the radio waves which don't go to China unless you bounce them off the ionosphere, is it possible to tell the difference between a signal sent directly and one bounced in such a manner? If not, then you have demonstrated that signals can't be sent arbitrarily far without appropriate atmospheric conditions, which is compatible with the Disc model of the universe<sup>TM</sup>
• In re the class project (with plumb bobs), the difference between the angle between the plumb bob and a ray of the sun of one class and the angle of the class to the North can be worked out to be, in radians, the North-South distance between the two classes divided by the radius of the Earth. So if one class is 300 miles to the North, the difference in the angles is 500/6350 radians, or about 4.5 degrees. Now my question is, couldn't this be due to the rays of the sun not coming down to the Earth in a parallel fashion, for instance if the sun is close to the Earth?
• Bridges: is the skewedness of the bridge towers enough to actually see? I mean, 1 meter difference between top and bottom seems like a lot, but in the picture you can't tell.

Ok, I think that's it for now.. I'm glad to see that people are getting into the spirit of this.

Ben Benoy

3. Established Member
Join Date
Oct 2001
Posts
143
On 2001-10-23 20:45, James wrote:

I think you'd better run your numbers again, David. The Japanese company who designed this bridge tested it for earthquakes and typhoons. It's first test was the Kobe quake of, I think, '95. It's still standing.
I'm having trouble tying the statement that the bridge was tested for earthquakes and typhoons with how much further apart the tops of the towers are than the bottoms.

Let's get numerical. Assume the towers are 200 meters tall. 100 meters above the ground and 100 meters below the ground for anchoring. At ground level they are 2 km apart.

The angle subtended from the center of the earth is:

angle = 2 km/radius of the earth. This works out to 3.14*10^-4 radians. <font color="blue">(edited to get the right number)</font>

The bottoms of the towers are apart by a distance of:

bottom distance = angle*(radius of the earth - 100 meters)

The tops are apart by a distance of:

top distance = angle*(radius of the earth + 100 meters)

The top distance - bottom distance = 6.4 cm.<font color="blue">(also edited)</font>

In a 2 km span that is 32 parts/million which is getting down the order of the accuracy for ball bearing manufacture.

<font size=-1>[ This Message was edited by: David Simmons on 2001-10-23 21:40 ]</font>

<font size=-1>[ This Message was edited by: David Simmons on 2001-10-24 06:45 ]</font>

4. Member
Join Date
Oct 2001
Posts
68
[quote]
[*] Concerning the radio waves which don't go to China unless you bounce them off the ionosphere, is it possible to tell the difference between a signal sent directly and one bounced in such a manner? If not, then you have demonstrated that signals can't be sent arbitrarily far without appropriate atmospheric conditions, which is compatible with the Disc model of the universe<sup>TM</sup>

Okay, instead ofrandomly distributed radio waves, take a highly coherent and powerful laser beam, take it to California, set it up pointing exactly parallel to the ground. Then, take a boat(sufficiently large as to diminish wave action) and set up a detector large enough to cancel out the wave action.
Then, start moving exactly away from the beam, keeping it in your detector and measure its vertical position as you move away. Eventually the laser will move off of the detector and will actually be above it.
This negates your flat-earthers debate of the ship dissappearing from the bottom up. This also demonstrates that light moves tangent to the spherical surface of Earth and not parallel to its surface.

_________________
Mongo like candy!

<font size=-1>[ This Message was edited by: MongotheGreat on 2001-10-23 23:47 ]</font>

5. Established Member
Join Date
Oct 2001
Posts
2,683
I think you'd better run your numbers again, David. The Japanese company who designed this bridge tested it for earthquakes and typhoons. It's first test was the Kobe quake of, I think, '95. It's still standing.
I'm having trouble tying the statement that the bridge was tested for earthquakes and typhoons with how much further apart the tops of the towers are than the bottoms.
Well, I am just going by the info given in the link. Here's the exact quote:

<pre>
Q3 ?F Does the curvature of the earth affect the bridge structure ?

A3 : In the Akashi Kaikyo Bridge, the
distance between the two main towers (base)
is 1,991m, while the distance between tops
of the towers (297m above the base) is
1991.93m. That difference is responsible for
the curvature of the earth.

</pre>

(I didn't know that this was responsible for the earth's roundness, but that's broken English for you.[img]/phpBB/images/smiles/icon_biggrin.gif[/img])

The link also goes on to say that the bridge rode out the 7.2 magnitude Kobe earthquake just fine, but the distance between the spans increased by 1 meter. This happened after the towers were completed and they were busy stringing the cables.

<hr>

David Hall
"Dave... my mind is going... I can feel it... I can feel it."

<font size=-1>[ This Message was edited by: David Hall on 2001-10-23 22:58 ]</font>

<font size=-1>[ This Message was edited by: David Hall on 2001-10-23 23:00 ]</font>

6. Established Member
Join Date
Oct 2001
Posts
143
David Hall wrote:

Well, I am just going by the info given in the link. Here's the exact quote:

In the Akashi Kaikyo Bridge, the
distance between the two main towers (base)
is 1,991m, while the distance between tops
of the towers (297m above the base) is
1991.93m. That difference is responsible for
the curvature of the earth.

(I didn't know that this was responsible for the earth's roundness, but that's broken English for you.[img]/phpBB/images/smiles/icon_biggrin.gif[/img])

The link also goes on to say that the bridge rode out the 7.2 magnitude Kobe earthquake just fine, but the distance between the spans increased by 1 meter. This happened after the towers were completed and they were busy stringing the cables.

David Hall
Redoing my numbers using the correct height of the towers of 297 meters and a span of 1991 meters at the surface I get the tops are 9.3 cm. wider than the bottoms, not 93 cm.

Now the tops might be 1 meter wider for structural reasons. Maybe they leaned them away and the weight of the bridge brings them back. I don't know. But the increase because of the curvature of the earth would be 9.3 cm.

7. I trust your numbers. Some time in the murky past, the trivia magnet buried deep in my mind latched onto a statement that (due to the curvature of the Earth) the towers of the Golden Gate Bridge are 5/8 inch (1.6 cm) out of parallel.

_________________
"Sin lies only in hurting other people unnecessarily. All other sins are invented nonsense. (Hurting yourself is not sinful--just stupid.)" [Robert A. Heinlein]

<font size=-1>[ This Message was edited by: Kaptain K on 2001-10-24 05:20 ]</font>

8. Established Member
Join Date
Oct 2001
Posts
2,683
Redoing my numbers using the correct height of the towers of 297 meters and a span of 1991 meters at the surface I get the tops are 9.3 cm. wider than the bottoms, not 93 cm.

Now the tops might be 1 meter wider for structural reasons. Maybe they leaned them away and the weight of the bridge brings them back. I don't know. But the increase because of the curvature of the earth would be 9.3 cm.
Ok, I'll buy that, too. Looks like someone got the wrong decimal place there. I wouldn't even have a chance at actually calculating it myself mathematically, so I'll trust you.

Still, there is a measurable difference, albeit small. I didn't realize it was THAT small though. Thanks for catching the error.

9. Member
Join Date
Oct 2001
Posts
14
On 2001-10-23 20:48, Ben Benoy wrote:
[*] Concerning the radio waves which don't go to China unless you bounce them off the ionosphere, is it possible to tell the difference between a signal sent directly and one bounced in such a manner? If not, then you have demonstrated that signals can't be sent arbitrarily far without appropriate atmospheric conditions, which is compatible with the Disc model of the universe<sup>TM</sup>
[/list]

Ok, I think that's it for now.. I'm glad to see that people are getting into the spirit of this.

Ben Benoy
Ben,
About the radio waves, talk to your nearest Ham radio operator. He/she should be able to set up a class demonstration for long distance communication. There is a distinct difference between radio waves that bounce off the Ionosphere and line-of-sight. IIRC, there is a frequency shift and power loss when radio waves are bounced off the Ionosphere. Also, certain frequencies and layers of the Ionosphere are better than others for bouncing. Some Hams even bounce signals off the Moon. Another thing, some Hams have satellite tracking equipment for communicating on Hamsats and with the ISS. Here's a question for your class: How can a satellite orbit a "flat earth"?
Good luck!

Kevin Hovis
KC0JYW - another one of my interests!

<font size=-1>[ This Message was edited by: K. Hovis on 2001-10-24 09:46 ]</font>

10. Member
Join Date
Oct 2001
Posts
61
Re: Class Project
If the Earth were flat, then no matter how far away the sun was, there would never be an Arctic Circle. Draw a horizontal line on a paper. Now mark a point above that line to represent the god Mercury in his chariot crossing the sky at noon. All points along that line would have a direct line of sight to the sun god. Not only that, but from two different points, you would be able to determine how far up Mercury's chariot was.

Start with point A and point B at a distance d to the north. A makes an angle theta with the sun, and B makes an angle phi. The angle between the hypotenuse of A and the hypotenuse of B is phi - theta. By trigonometric Law of Sines, you should be able to compute the hypotenuses (hypoteni?) of both A and B. And from there, by basic trig, you can compute how high up Mercury's chariot is. If the assumption that the Earth is flat is correct, then you should be able to take another point C still further north of B and run the numbers and come up with the same distance. If the numbers don't add up, then the hypothesis is flawed.

11. On 2001-10-23 23:44, David Simmons wrote:
Redoing my numbers using the correct height of the towers of 297 meters and a span of 1991 meters at the surface I get the tops are 9.3 cm. wider than the bottoms, not 93 cm.
As a point of interest, this is just slightly smaller than the diameter of a regulation softball.

Now, as far as seeing the curvature of the earth without having to travel, I vote for the eclipse method... get in your Eclipse, and drive real fast all the way around... no, wait... I meant the edge of the earth's shadow on the moon during a lunar eclipse. Once, it could be a coincidence. Twice, well, maybe. But every time? That's proof positive that the earth is a sphere.

12. Member
Join Date
Oct 2001
Posts
79
To repeat, not a flat Earther, and not actually trying to demonstrate that the Earth is round/flat to anybody. The original post says that a method is sought to demonstrate the curvature to a young person, using local effects. That is, no traveling great distances, not using satellites, etc. It is entirely possible that this is not something which can be done. Perhaps I should have left this as a coffee table discussion, given the responses I seem to have generated, but that's a question for a different day. On the plus side, we seem to have uncovered a bit of Bad Astronomy (or Geography...) from Japan, so that's cool.

Ok, let's return to the issue at hand. Thank you for letting me know about the frequency shift due to reflecting off the ionosphere. I don't know enough about HAM radioing to say whether this is conclusive or not. The point here is that just because you can send signals very far away by pointing up, does not in itself imply that the Earth is round. The same mechanism would also apply to a flat Earth. Mountains after all get in the way of radio signals to far off places. Heck, walls can interfere with signals, or the weather. The experiment with sending out a ship looks basically identical to sending a boat across Lake Tahoe, which would be far and away less expensive.

Also, as has been pointed out, the geometry of the Earth on the local level is essentially Euclidean, but long distance surveying makes use of the fact that the Earth is round. However, long distance surveying also has to take into account atmospheric refraction, etc. Even with the best sextant in the world, your sight on a far off mountain peak can be thrown way off by atmospheric effects.

Ok, that's all.

Ben Benoy

I feel like I've been branded a flat Earther or something. Probably because I'm left handed. That's the hand to use, well nevermind.

13. Established Member
Join Date
Oct 2001
Posts
143
On 2001-10-24 14:09, Ben Benoy wrote:

Also, as has been pointed out, the geometry of the Earth on the local level is essentially Euclidean, but long distance surveying makes use of the fact that the Earth is round. However, long distance surveying also has to take into account atmospheric refraction, etc

Ben Benoy
Actually, you can survey long distances without worrying about atmospheric refraction. The method is called "triangulation" which is not the same thing as the means of determining distances to astronomical objects.

What is done for long distance surveying is to lay out a proposed line that is to be surveyed. Then the line is broken into short segments so that refraction and, yes, the curvature of the earth can be ignored. Each short segment is one leg of a triangle that closes back to its individual starting point. This allows each individual survey line segment to be closed back on itself so the errors do not accumulate. Futhermore, the surveyor knows at all times what the error of closure is and if it is greater than the survey specification allows, the segment can be resurveyed to get back within specs.

There are interesting tricks to all trades.

14. Established Member
Join Date
Oct 2001
Posts
321
Yes it was. And I believe the certain day was the equanox.

He would have nailed the size of the earth, except he couldn't accurately measure the distance between the two towns he used. So he hired a person to pace it off, and he got an answer that was pretty darned good, considering.

On 2001-10-23 07:44, SeanF wrote:
Wasn't it Eratosthenes who approximated the circumference of the Earth with pretty good accuracy way back in like 200 BC?

As I recall, there was a well in Egypt (or somewhere) that, at noon on a certain day, the sun shone directly down the well. By going some known distance away and measuring an object's shadow at the same time, he was able to calculate the angle between those two positions and hence the Earth's circumference . . . also thereby demonstrating that the Earth is round.

15. Member
Join Date
Oct 2001
Posts
79
On 2001-10-24 14:30, David Simmons wrote:
On 2001-10-24 14:09, Ben Benoy wrote:
<snip>
However, long distance surveying also has to take into account atmospheric refraction, etc

Ben Benoy
Actually, you can survey long distances without worrying about atmospheric refraction. The method is called "triangulation" which is not the same thing as the means of determining distances to astronomical objects.

What is done for long distance surveying is to lay out a proposed line that is to be surveyed. Then the line is broken into short segments so that refraction and, yes, the curvature of the earth can be ignored. Each short segment is one leg of a triangle that closes back to its individual starting point. This allows each individual survey line segment to be closed back on itself so the errors do not accumulate. Futhermore, the surveyor knows at all times what the error of closure is and if it is greater than the survey specification allows, the segment can be resurveyed to get back within specs.

There are interesting tricks to all trades.
Actually, you still have to be aware that refraction is taking place. In Jon Krakauer talks about this in Eiger Dreams with regard to the height of Everest. Basically, air has a coefficient of refraction which is dependent on temperature, pressure and water content. And these are never actually constant. This site offers an explanation of how this works. Notice that there are tricky assumptions which must be made.

Anyway, that's all she wrote.

Ben Benoy

16. Established Member
Join Date
Oct 2001
Posts
1,080
Hey Ben. What about my idea of plotting the given flight paths of airlines on a globe, say between New York and Hong Kong, then showing that this is in fact the shortest distance between the 2 points (ok... you can use string rather than cutting the globe in half if you want), even though it goes up over the Arctic. Cheap, fuctional, and can be done from your living room.

17. Established Member
Join Date
Oct 2001
Posts
100
Well, my usual favourites are

1. Time zones. You try getting time zones on a flat Earth. It just cannot be done.

2. Gravity. Having a flat Earth would bring about the reasonable assumption that the Earth is stationary. This would place the Sun in an orbit at 30,000km high (geo) for it to orbit the assumed unchanged mass of the Earth in 24 hours. This has the nice side-effect of making geo satellites impossible as well as unnecessary.

3. Large suspension bridges. The Humber Bridge's towers are four inches further apart at the top than they are at the bottom, to account for the curvature of the Earth. Total span is about 1.5km.

4. The moon's orbit and phases. Should the sun orbit the Earth every 24 hours, which would be a necessity for a flat earth, then lunar phases would not exist in their present form. Also, since the moon would be ten times further away than the sun, then the moon would...umm..it just wouldn't work as we see it. I can't think of any way of preserving phases, having the moon ten times further away than the sun, keeping gravity constant and agreeing with data known since ancient times.

5. Lunar eclipse shadows could be used, but these only infer a round earth, and cannot differentiate between a disc and a sphere. The Greeks and Romans believed the Earth was a disc.

H@

18. Established Member
Join Date
Oct 2001
Posts
845
Can I be of help with that bridge? I think that if anyone can find me exact statistics for the bridge, bordering on plans, I could do all this.

But I would really need exact measurements of everything, and preferably in simple english because english is not my language. I mean I can talk but I can't make any real points because nobody understands what I'll say. The other way around is the same thing, I am not so solid.

Well, say it if you need it.

Well, I guess Ben could certainly do it. I see only one way to settle this: Ben and me, in the ring, for a match of Greco-Roman wrestling. [img]/phpBB/images/smiles/icon_biggrin.gif[/img]

<font size=-1>[ This Message was edited by: Mr. X on 2001-10-25 13:39 ]</font>

19. On 2001-10-24 14:09, Ben Benoy wrote:

I feel like I've been branded a flat Earther or something. Probably because I'm left handed. That's the hand to use, well nevermind.
A simple astronomical philippic? [img]/phpBB/images/smiles/icon_lol.gif[/img]

20. Or how I was Phil Plaited into submision [img]/phpBB/images/smiles/icon_lol.gif[/img] [img]/phpBB/images/smiles/icon_lol.gif[/img]

21. Established Member
Join Date
Oct 2001
Posts
197
On 2001-10-24 14:09, Ben Benoy wrote:
To repeat, not a flat Earther, and not actually trying to demonstrate that the Earth is round/flat to anybody. The original post says that a method is sought to demonstrate the curvature to a young person, using local effects. That is, no traveling great distances, not using satellites, etc.
Actually the standing on a tall mountain and looking out over the horizon is something that can be done locally if you live on/near such mountains. The high school that I went to was on a mountain that was ~1.5km above sea level with a 180 degree view of the horizon. When I was younger, we went to a field trip to that high school so that we could look out at the horizon and see the curvature of the Earth. It was enough to convice me. [img]/phpBB/images/smiles/icon_razz.gif[/img]

22. Member
Join Date
Oct 2001
Posts
79
Ok, since some things seem to be repeated, let us recap:

If you live in a mountain region, it is indeed possible to see the Earth curve away. I've done it myself.

If you live near a large body of water with good weather, you can see ships/boats/buildings from the middle up, but never the bottom.

I do not think that the arguments about asking pilots how they get to various places counts, although it is certainly valid, because it does not confine to the original intent of the question.

Likewise for timezones, if you don't have some form of very rapid communication or transportation, timezones don't matter because you don't know they're there.

Radio waves are basically out for the same reason as timezones, because if you have radio waves you don't have to bother bouncing them off of anything, you just ask your best friend in London what time it is.

Concerning eclipses, the arclength of the shadow of the Earth which covers the moon is very small, look at the pictures here and tell me that this is definately a section of a circle. Lunar eclipse pictures Also, you would need to see several to be sure that you weren't seeing an ellipse projected onto a sphere. How often do eclipses occur at your house? [img]/phpBB/images/smiles/icon_smile.gif[/img]

Have to go to class. Sigh.

Ok, that's all.

Ben

23. Established Member
Join Date
Oct 2001
Posts
898
Alan Lightman (you know, the physics prof. at MIT that wrote Einstein's Dreams) wrote an article on how we know the Earth is round. The original article appeared in Science 82, vol 3., no. 2. however a copy of the article can be found online here.

It appears we have to give Ari credit for proving the Earth is round and Eratosthenes for accurately measuring the Earth's size.

24. Established Member
Join Date
Oct 2001
Posts
100
Don't be so hasty to throw timezones out. You may not have a telephone, but many others do and will readily confirm that calling somebody in a distant timezone will often lead to a lot of swearing when you wake them at their 3am.

H@

25. I can confirm that people calling me from California at 9 pm their time do not get a warm reception from me.

26. Established Member
Join Date
Oct 2001
Posts
845
On 2001-10-26 08:01, ToSeek wrote:
I can confirm that people calling me from California at 9 pm their time do not get a warm reception from me.
Don't forget it's a collect call too! [img]/phpBB/images/smiles/icon_lol.gif[/img]

27. On 2001-10-26 08:36, Mr. X wrote:
On 2001-10-26 08:01, ToSeek wrote:
I can confirm that people calling me from California at 9 pm their time do not get a warm reception from me.
Don't forget it's a collect call too! [img]/phpBB/images/smiles/icon_lol.gif[/img]
If it's a collect call at that hour, they're out of luck. [img]/phpBB/images/smiles/icon_evil.gif[/img] [img]/phpBB/images/smiles/icon_wink.gif[/img]

28. Actually, I recall being up in a plane once and not only noticing the earth's curvature but also getting an almost visceral realization of just how enormous this planet is. It was almost like a religious experience.

29. Established Member
Join Date
Oct 2001
Posts
2,683
On 2001-10-26 08:53, ToSeek wrote:
Actually, I recall being up in a plane once and not only noticing the earth's curvature but also getting an almost visceral realization of just how enormous this planet is. It was almost like a religious experience.
I had a similar experience about 2 years ago. Flying from Japan to the U.S. we fly north almost to the Arctic circle. Looking north out of my window in the middle of the night at 30,000 feet I could see the sky glow on the horizon. It took me a minute to realize it was neither the glow of sunrise or sunset, and a thrill ran through my body as I realized it was actually the glow of the noonday sun on the other side of the world!

It was at that moment that the true sphericity of the world hit home with me. I'll never forget it.

30. Member
Join Date
Oct 2001
Posts
61
The gist of most replies seems to be: no, you cannot just stand in your backyard and point to the sky or sun or clouds and say "See, there's proof the Earth is round." All suggestions for determining proof seem to involve either travel or some contact with people far away.

People of ancient times believed the Earth was flat because locally it looks flat, and most people never traveled far from whatever valley or plain or town in whiched they lived. And for those that did travel, transportation was so slow, one would never really experience any form of jet lag. Understanding the spherical nature of the Earth had to wait for the invention of accurate timepieces and an age of enlightenment when people would wonder about such things as shadow length (and be able to travel far to make such measurements and compare).

For a child, if you want to show that the Earth is a sphere without an extended road trip, show him a globe. You can find one at Discovery Store.

<center>
<img scr="http://shopping.discovery.com/DiscoveryStore/images/products/large/759415_lg.jpg">
</center>

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•