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Ben Benoy
2001-Oct-22, 11:58 PM
Ok, this is something I've been meaning to post for a few weeks, but figured I'd wait until the new board came up, so we could start with some good astronomy type questions. So here goes:

How can you tell that the Earth is round?

Yeah yeah, you go up into a spaceship and look down. Fabulous. Assuming you can't actually take a peek yourself, how do you convince somebody that the Earth is round. Explanations would ideally be easy enough to explain to a young person (aka child), and not require said child to have 7 league boots. But that's the ideal.

What else? Oh yes, both answers and rebuttles are asked for and welcomed.

For example, if Joe Schmo says "Well, when ships sail away, you see the bottoms disappear first, so obviously they are going down around the curve of the Earth," then it is acceptable and even preferred that somebody say:

"Oh really? Well the ocean is a pretty wavy place, so maybe it's just that we see waves in between, or that fog/mist/other particulates scatter the light before I see it. No demonstration."

Everybody cool on the rules of the contest? I already have rebuttles for the more common ones, but everybody feel free to enter the fray.

Ok, have fun everybody!

Ben Benoy

Phobos
2001-Oct-23, 12:37 AM
Ben shame on you !!!

I never took you for a flat Earther !

The world is not round, its SPHERICAL

Jeff /phpBB/images/smiles/icon_smile.gif

Espritch
2001-Oct-23, 01:20 AM
The world is not round, its SPHERICAL

Well, you have him there. But now you have to prove it.

Spaceman Spiff
2001-Oct-23, 01:21 AM
Ask an airline pilot how he flies the shortest route from Chicago to Beijing,
China (very nearly the same latitude). In euclidian space that's obvious, but we live on a spherical planet and the pilot must use spherical geometry, rather than euclid's.

And those were rather flimsy excuses explaining away the disappearing ship.
I am sure experiments could be designed to refute each of your excuses.

Is this general astronomy? or does this really belong on another BadAstro board?

Torsten
2001-Oct-23, 02:38 AM
OK, what about Aristotle's (?) explanation. Watch enough lunar eclipses and you'll notice the shadow of the Earth crossing the Moon is always round. Only a spherical object could cast a shadow like that.

And guess what! You'll be happy to learn that this is the explanation that Gerardus Bouw, our favourite geocentrist, uses to explain that the Earth is not flat. So it must be right. /phpBB/images/smiles/icon_wink.gif

MongotheGreat
2001-Oct-23, 03:12 AM
I must bring forth the fact that radio waves can't be sent from USA to China directly, without bouncing them off satellites or the ionosphere. This is due to the fact that the radio waves go off on a tangent line to the surface and out into space and do not circle the Earth. This wouldn't be so on a flat Earth. On a flat Earth, you could send a signal straight to China (assuming you had sufficient ground clearence).

By the way, I believe this thread is just meant to bring out the various proofs that the Earth is round, just to better our understanding of them.

David Simmons
2001-Oct-23, 03:57 AM
Changes in Polaris' angle above the horizon with distance traveled north or south only make sense if the path is an arc of a circle, or very nearly so.

Land surveyers use plane geometry which doesn't work over large distances. The methods of spherical geometry, however, do fit the surface of the earth very closely. For example, if you survey a large triangle, the sum of the interior angles is greater than 180 deg.

<font size=-1>[ This Message was edited by: David Simmons on 2001-10-22 23:57 ]</font>

Ben Benoy
2001-Oct-23, 05:34 AM
Ack! I put "explain to a child" when I meant "demonstrate to". Darn it all to heck! <font size=-2>Dig that not swearing!</font>

Anyhow, it seems like people are getting into the spirit of things and thinking about this. I submit some problems with the above demonstrations, as follows:


Ships and the sea: I don't think that my explanations for how ships bottoms disappear first are flimsy. From the balcony of the building I'm in right now, you can see one of the channel islands. The top of it anyway. The bottom is almost always obscured by haze.

Concerning airline pilots, the arc of their flight is only curved if you draw it on the wrong kind of map. On an appropriate projection, the path of the airplane is a straight line, as we would like. May be your continents don't look quite the way you want, but continents weren't designed for your approval. So there. /phpBB/images/smiles/icon_smile.gif Also, this requires quite a bit of "take my word for it." How do I know that pilots aren't just joshing with me?

Lunar eclipses happen pretty infrequently. Also, you need to see them from different locations and with the moon in different parts of the sky for the demonstration to work. Furthermore, if the Earth were a disk, its shadow on the moon would be a section of an ellipse, which looks basically like a circle for small arclength.


Ok, that's enough for now. Other people, feel free to pop in and try to refute the arguments. Basically we're looking for something that doesn't require that you go off globetrotting, or need anything really fancy.

As a disclaimer, I am not a flat Earther. I just thought it would be an interesting excercise, as Mongo suggested.

Ok, happy browsing. Dig the new board, go BA.

Ben Benoy

Peter B
2001-Oct-23, 05:56 AM
Why not use the method I think Alfred Wallace (the other evolution guy) suggested.

Take a long, straight, smooth body of water (like a canal). At intervals of, say, a kilometre, place posts in the water. Each post has a hole the same distance above the water.

If the Earth is flat, you'll be able to see through all three holes. However if the Earth is curved (at least in that direction), you won't.

I'm sure people will be able to work out refinements of the method which would, in theory, allow you to even calculate the circumference of the Earth, if it was spherical.

Ben Benoy
2001-Oct-23, 06:43 AM
On 2001-10-23 01:56, Peter B wrote:
Why not use the method I think Alfred Wallace (the other evolution guy) suggested.

Take a long, straight, smooth body of water (like a canal). At intervals of, say, a kilometre, place posts in the water. Each post has a hole the same distance above the water.


It's actually a good idea. Just as a rough calculation: on the surface of the Earth, 1km is 1/6350 radians. (Taking the diameter of the Earth to be ~12700 km, which is close enough for government work)

If we work out the geometry, we see that the difference between the point that we sight through the first two holes and the hole we drilled is:

R * ( sqrt( tan<sup>2</sup>(3t/2)*sin<sup>2</sup>(p) + sin<sup>2</sup>(p) ) - 1 )

where R is the radius of the Earth, t is the angle on the surface of the Earth, or 1/6350 radians, and p is (pi - t)/2, the angle between the line that we sight and the post we sight it through.

Running the numbers gives you something like a difference of 1.57 * 10<sup>-4</sup> meters, or about 15 centimeters. Now the question is, is this good enough to convince? It's pretty good, and you only need a 2 km stretch. What does every body else think?

here I've switched from being the devil's advocate to Peter B's. Hrm... Anyhow, let's just hope I can do geometry in the wee hours, or I've just messed everybody up. /phpBB/images/smiles/icon_smile.gif

Ben Benoy

Simon
2001-Oct-23, 08:24 AM
I'm surprised nobody's suggested this yet, 'cause it's a pretty simple one: Focault's Pendulum (sp?). Anyway, the idea is thus: You take about 30 meters of rope, hang it from something sufficiently high (ideally indoors), tie a big weight to the end, and give it a swing. Every five or ten minutes you mark the path it swings along. And after a while you see that the path slowly rotates. The pendulum isn't rotating though, it's the floor -the earth- rotating below it. Simple.

Yeah, the roof it's attached to rotates also, but most of the ones I've seen have a swivel that lets it move freely.

Actually, would this work at or near the equator? I really don't think so; it would work best at high latitudes.

...Arg! *headslap* Dude, that doesn't tell you it's round, only that it's rotating. Sorry, ignore my half-baked rambles. But it IS a good way to show someone that it rotates.

<font size=-1>[ This Message was edited by: Simon on 2001-10-23 04:26 ]</font>

Mr. X
2001-Oct-23, 09:32 AM
Yargh! Doesn't delete!
<font size=-1>[ This Message was edited by: Mr. X on 2001-10-23 13:34 ]</font>

<font size=-1>[ This Message was edited by: Mr. X on 2001-10-23 13:34 ]</font>

Roy Batty
2001-Oct-23, 09:35 AM
I believe you can delete the post yourself now using the edit function /phpBB/images/smiles/icon_smile.gif

Matthew Ota
2001-Oct-23, 11:32 AM
I would use the lunar eclipse method. It is easy to demonstrate using a bright point light source, and a couple of balls. Slowly pass the farther ball behind the middle ball, observing from behind the light source. You will then see a curved shadow transit over the farther ball.

Matthew Ota
Orange County Astronomers
http://www.ocastronomers.org/
Telescopes In Education
http://www.tie.jpl.nasa.gov


<font size=-1>[ This Message was edited by: Matthew Ota on 2001-10-23 07:34 ]</font>

SeanF
2001-Oct-23, 11:44 AM
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.

Matherly
2001-Oct-23, 11:51 AM
I thought the BA worked this out somewhere on the main board.

To paraphrase him. First observe the changes in the time zones (say by being in New York and calling someone in L.A.0 This establishes a curve of the Earth in a E-W direction. However, as the BA pointed out, the Earth still could be a cylander. So next, you establish the view of the night sky from a given point. Then you start going South (or North, doesn't matter). As you go, the view of they sky changes as stars set behind you and new ones rise in front of you. Eventually, you will go all the way around and the view will be the same. That would establish a N-S curve which when added to the E-W curve would suggest a sphereical planet.

Additionally, you could use the Egyptians' test. If I'm not mistaken, they used an experiemnt like this:

Plant a stake in the ground. Then plant a stake far to the North of the first one. Measure the length of the shadows at local noon (the same for both stakes singe they ate on the same longitude). The Northern-most stake should have a longer shadow because the N-S curve of the Earth puts it at a greater angle to the sun. (at least I think thats how it works).

Spaceman Spiff
2001-Oct-23, 12:37 PM
Look Ben,

If you keep moving the goal posts and flippantly cast off good explanations (without suggesting improvements), then
you won't find one. THE POINT IS YOU (OR SOME
SURROGATE) DO HAVE TO DO SOME TRAVELING TO DETERMINE THE SPHERICITY OF THE EARTH. Locally on a surface of a large sphere, the geometry is very nearly euclidian (except very locally with the local topography dominating).

and here's back at you:

You don't have to take an airline pilot's say
so. His/her jet can be tracked on radar. Surveyors/navigators/mappers knew of the positions and sizes of continents long before we had satellites with gps. If Beijing is (roughly) due east of Chicago, how is it that one must fly towards Alaska to land in Beijing along the shortest route? Ditto for ship travel across oceans. Here is one for you: let's say you are a manager of an express mail company that assumes the earth's geometry is euclidean - how long will it take before late arrivals and fuel costs force you into bankruptcy?

Regardless as to what optical effects you
have looking out YOUR window (aerosol scattering, various refractions due to air inversions and the like), there'll be somebody else who has a clear view to all ships coming over their horizon. And I can send messages via laser beam as long as the ship remains above the horizon. And I am sure there are many more such demonstrations. I'll bet sailors of long ago knew more about this from personal experience than we've posted here.

Where do jets and satellites come from and go to? (ideally, you are on a ship in the middle of the ocean where you have a clear view of your horizon in all directions - but that's not required). If they fire a laser beam into the sky to produce a "fake star" (as is done for adaptive optics on telescopes), why does it's altitude change?

Erostasthenes (or his footman) had to travel
the length of Egypt to determine the size of the sphere we live on to understand how the Sun could be directly overhead in Aswan but not so in Alexandria. This is similar to the changing altitude of Polaris - and for that matter why is it again that Chileans can observe stars never visible here (and vice-versa)?

And careful observations of lunar eclipses do demonstrate Earth's general shape (and SO WHAT that they don't occur very often - the ancient greeks simply observed, used geometry and inferred the Earth's shape and a heck of a lot more).

Take three widely separated surveyors and have them carefully map out the properties of a triangle. This CAN be done, but of course it requires information over a distance not
insigificant to the Earth's curvature.

We can bounce laser beams off the surface of
the Moon. One observer does this when the Moon is high overhead, the other at the same moment but located some miles due west where the Moon is just rising. They'll determine different distances corresponding to the
radius of a nearly spherical Earth (depending upon the circumstances, such as their latitude).

If there are so-called "holes" in these experiments, why don't you try to figure out what should be done to fill them in? Obviously, nobody here has the time to design a detailed experiment - but we've certainly given you experiments that can be done to demonstrate Earth's geometry.

Spaceman Spiff
2001-Oct-23, 12:44 PM
On 2001-10-23 04:24, Simon wrote:
I'm surprised nobody's suggested this yet, 'cause it's a pretty simple one: Focault's Pendulum (sp?). Anyway, the idea is thus: You take about 30 meters of rope, hang it from something sufficiently high (ideally indoors), tie a big weight to the end, and give it a swing. Every five or ten minutes you mark the path it swings along. And after a while you see that the path slowly rotates. The pendulum isn't rotating though, it's the floor -the earth- rotating below it. Simple.

Yeah, the roof it's attached to rotates also, but most of the ones I've seen have a swivel that lets it move freely.

Actually, would this work at or near the equator? I really don't think so; it would work best at high latitudes.

...Arg! *headslap* Dude, that doesn't tell you it's round, only that it's rotating. Sorry, ignore my half-baked rambles. But it IS a good way to show someone that it rotates.

<font size=-1>[ This Message was edited by: Simon on 2001-10-23 04:26 ]</font>


Actually, it does demonstrate something about the shape of what's spinning. The pendulum goes around in 24 hours at the poles, but never moves along the equator.

Timm
2001-Oct-23, 12:46 PM
You could calculate from how far huge mountains like the Himalayas(sp?) should be visible on a flat and on a spherical earth. On a flat earth you should be able to see them from nearly anywhere - assuming a free line of sight and a cloud-free sky - but as the earth is round you can't.
I think the horizon would look diferent on a flat earth, but I have no Idea how...

K. Hovis
2001-Oct-23, 01:03 PM
Ben, I'm a private pilot. You can clearly see
the curvature of the Earth at lower altitudes
that what airliners fly at. I like to get above the haze layer and see how the haze curves out as far as you can see. Around here , you ususally need to get to 6,000 - 8,000 ft to clear the haze. Go to your local general aviation field and see if you can charter a light plane. The cost shouldn't be too awfully high and the view from the front right seat is well worth it and better than from an airline seat, unless you're an airline pilot...

Tim Thompson
2001-Oct-23, 02:16 PM
I "sailed" across the Pacific on a US Navy helicopter carrier (the USS Belleau Wood (http://www.lha3.navy.mil/)), from Hawaii to San Diego, in the summer of 1987. The convoy destroyer escorts were about 100 miles ahead of us, but visible in the distance from the Belleau Wood. I observed both destroyers from the flag bridge in high power binoculars, in clear weather over the open ocean. Haze & other obscurities were not an issue. I could see small structures including the struts and small microwave dishes on the masts of the destroyers, yet the much larger ship hulls were invisible behind the curvature of the Earth. I watched them for quite a while, specifically so that I could observe the waves and know that they were not obscuring the ship (I knew the distance from radar and the wave height). I consider it a pretty clear demonstration of the "ship behind the curve of the Earth effect". I could, quite literally, see the small, thin communications mast, sticking right out of the clean surface line of the ocean.

But a more practical application is to look across the surface of a large lake (like Lake Tahoe (http://www.keeptahoeblue.com/), where I often work). Over the course of 10 miles, a circle with the radius of the Earth will drop away from a straight line, by about 16 feet, creating a visible effect. Small structures are always hidden by the curvature of the Earth, across large open bodies of water. This effect was described in a letter in the American Journal of Physics, but it was many years ago and I can't find the original any more. However, it is described, under the title "Earth's Curvature (http://mathforum.org/dr.math/problems/choksi1.27.97.html)" in the Ask Dr. Math (http://mathforum.org/dr.math/) forum. You should be able to both "explain" and "demonstrate" this effect, to your favorite child, provided you can travel to a handy lake that is large enough (an adventure to which most children do not usually object).

Iain Lambert
2001-Oct-23, 02:23 PM
It may be an urban myth, but I remember being told how one demonstration of the curvature was that its necessary to take into account how much further apart the tops of large bridges are than the bottom of them, if you don't want them to fail to join up correctly when you build them! Presumably the distance on a pretty big bridge is going to be well outside the tolerance for the distance, so this makes sense.

Wally
2001-Oct-23, 02:33 PM
To further what Spaceman Spiff suggests with airline flight paths. You can get known flight paths from several locals on the internet (I would imagine). Then, go buy yourself a globe (or several), and show how each flight path is actually the "great circle" (e.g. the path that cuts the earth into 2 equal halves, thus making it the shortest route possible between 2 points on a sphere). I say get several globes so that you can actually cut 'em in half along the flight paths and show you end up with 2 equal halves of earth. May get expensive, but what the heck. . .

David Hall
2001-Oct-23, 03:08 PM
On 2001-10-23 10:23, Iain Lambert wrote:
It may be an urban myth, but I remember being told how one demonstration of the curvature was that its necessary to take into account how much further apart the tops of large bridges are than the bottom of them, if you don't want them to fail to join up correctly when you build them! Presumably the distance on a pretty big bridge is going to be well outside the tolerance for the distance, so this makes sense.



<center>http://www.occn.zaq.ne.jp/cuaea503/akashi_bridge.jpg
http://www.occn.zaq.ne.jp/cuaea503/akashi_bridge.jpg</center>


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) (http://www.hsba.go.jp/hasi-inf/e-qa.htm)

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
Dave? What are you doing, Dave?

<font size=-1>[ This Message was edited by: David Hall on 2001-10-23 11:15 ]</font>

Irishman
2001-Oct-23, 04:01 PM
Another neat effect of a curved Earth - the moon. To prove longitude, just compare the times for dawn and dusk at different locations around the globe. Look at when the moon rises over the horizon in New York vs. Los Angeles, for instance. Bingo, curved from East to West.

For North South, use the moon at approximately 1/4 - a little crescent or gibbous works fine, but gets harder to see. Look at the terminator line on the surface. Look at the angle the terminator line makes with the horizon. Now compare with the angle at a different latitude - say New York vs Miami. Then compare at the equator, and then go to Argentina or Australia and check that angle. You will notice the angle leans the other direction. This is directly due to the fact that your observational horizon is the tangent of the curved Earth at your latitude.

I think there will be a slight variation in angle at any given latitude due to the orbit of the moon not being coplanar with the equator, but it wouldn't be as dramatic as the shift from the north to south hemisphere.

Bob S.
2001-Oct-23, 04:09 PM
Class project:
(must be coordinated with another class in same time zone, preferably directly north or south and some distance away [as in hundreds of miles])

Student must find a perfectly level ground, or lacking that, construct such a platform. Also will need a rod 1 meter in length. At noon precisely, using a plum bob to stand the rod straight up, measure the length of shadow.

At the exact same time, another student from another class living directly north or south and some distance away does the exact same thing.

Having two sides of a right triangle, they should be able to determine the angle of the hypotenuse to the horizontal leg.

They should then exchange data.

Having two different angles will show that the Earth is spherical. Knowing the distance between the two schools will also enable them to measure just how big the Earth is since that distance will correspond to an arclength of the Earth's circumference.

Azpod
2001-Oct-23, 06:11 PM
Actually you don't need to go into space to see that the Earth is round. If you can get to a cliff or a mountaintop of a height of over 2km with a clear view of the horizon, you can see that the horizon is curved! The higher you get, the more noticable that curvature is. From a height of ~4km (the highest mountain that I have been on), it's impossible not to blantantly see the curvature of the Earth.

However, this doesn't work well in planes, because you can't see a great deal of the horizon, so the curving looks like an effect of the plane's window-- even though it isn't.

As I grew up in the mountains, I noticed the curving horizon effect many times, and I was always impressed by it.

Chip
2001-Oct-23, 06:55 PM
At Wendover Utah, near the Lake Bonneville Salt Flats, it is possible to see the curvature of the Earth at the horizon. (At least according to the Utah tourist bureau.) The ground is flat to the horizon for over a hundred miles from that viewpoint. So you could send the inquisitive child to Utah.
(-;

Mr. X
2001-Oct-23, 08:45 PM
Judging by the people on it, I'd say the Earth is SQUARE. Totally, 90 degree angles 4 times with four sides RIGOROUSLY the same length, SQUARE. And boy, do I mean SQUARE. Maybe even CUBIC. God, this planet is SQUARE.
/phpBB/images/smiles/icon_biggrin.gif /phpBB/images/smiles/icon_razz.gif

David Simmons
2001-Oct-24, 12:19 AM
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) (http://www.hsba.go.jp/hasi-inf/e-qa.htm)

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.

James
2001-Oct-24, 12:45 AM
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) (http://www.hsba.go.jp/hasi-inf/e-qa.htm)

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.

Ben Benoy
2001-Oct-24, 12:48 AM
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. /phpBB/images/smiles/icon_smile.gif 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

David Simmons
2001-Oct-24, 01:36 AM
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>

MongotheGreat
2001-Oct-24, 02:25 AM
[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>

David Hall
2001-Oct-24, 02:53 AM
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./phpBB/images/smiles/icon_biggrin.gif)

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." (http://www.occn.zaq.ne.jp/cuaea503/whatnots/2001_feel_it.wav)

<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>

David Simmons
2001-Oct-24, 03:44 AM
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./phpBB/images/smiles/icon_biggrin.gif)

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.

Kaptain K
2001-Oct-24, 09:18 AM
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>

David Hall
2001-Oct-24, 12:14 PM
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.

K. Hovis
2001-Oct-24, 01:45 PM
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>

Bob S.
2001-Oct-24, 02:16 PM
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.

Donnie B.
2001-Oct-24, 05:41 PM
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.

Ben Benoy
2001-Oct-24, 06:09 PM
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.

David Simmons
2001-Oct-24, 06:30 PM
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.

aurorae
2001-Oct-24, 08:48 PM
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.

Ben Benoy
2001-Oct-25, 01:57 AM
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 (http://tchester.org/sgm/analysis/peaks/refraction.html) 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

Wally
2001-Oct-25, 01:06 PM
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.

Hat Monster
2001-Oct-25, 04:01 PM
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@

Mr. X
2001-Oct-25, 04:25 PM
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. /phpBB/images/smiles/icon_biggrin.gif

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

Donnie B.
2001-Oct-25, 05:58 PM
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? /phpBB/images/smiles/icon_lol.gif

Kaptain K
2001-Oct-25, 06:38 PM
Or how I was Phil Plaited into submision /phpBB/images/smiles/icon_lol.gif /phpBB/images/smiles/icon_lol.gif

Azpod
2001-Oct-25, 06:41 PM
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. /phpBB/images/smiles/icon_razz.gif

Ben Benoy
2001-Oct-25, 07:07 PM
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 (http://eclipse-chasers.com/gallery.htm) 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? /phpBB/images/smiles/icon_smile.gif

Have to go to class. Sigh.

Ok, that's all.

Ben

Wiley
2001-Oct-25, 07:23 PM
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 (http://www.cnde.iastate.edu/staff/swormley/mcc/HOMEWORK/homework.01.09.24.pdf).

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

Hat Monster
2001-Oct-26, 03:35 AM
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@

ToSeek
2001-Oct-26, 12:01 PM
I can confirm that people calling me from California at 9 pm their time do not get a warm reception from me.

Mr. X
2001-Oct-26, 12:36 PM
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! /phpBB/images/smiles/icon_lol.gif

ToSeek
2001-Oct-26, 12:52 PM
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! /phpBB/images/smiles/icon_lol.gif


If it's a collect call at that hour, they're out of luck. /phpBB/images/smiles/icon_evil.gif /phpBB/images/smiles/icon_wink.gif

ToSeek
2001-Oct-26, 12:53 PM
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.

David Hall
2001-Oct-26, 01:10 PM
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.

Bob S.
2001-Oct-26, 03:28 PM
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 (http://shopping.discovery.com/).

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

The Bad Astronomer
2001-Oct-26, 05:32 PM
I think you meant this:

http://shopping.discovery.com/DiscoveryStore/images/products/large/759415_lg.jpg

Wiley
2001-Oct-26, 06:09 PM
On 2001-10-26 11:28, Bob S. wrote:
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).



What's your definition of ancient people? Educated people since the third century B.C. have known the Earth is round. Aristotle had these reasons to believe the Earth is round:

1.) Lunar eclipses.
2.) A ship's mast disappears last.
3.) The sun rises and sets at different times as you move east-west.
4.) Different stars as you move north-south.

Granted reasons three and four require travel or foreign contact, but reasons one and two Ari could do himself. About one hundred years after, in the second century B.C., Eratosthenes calculated the size of the Earth within about 16% error.

We did not have to wait for "accurate timepieces". (For accurate calculation of longitude, we did.) And we definitely did not have to wait for the age of enlightment.

You seem to making a mistake I've seen many other people make - my apologies if I'm infering something that's not there. Just because a culture is less technologically sophisticated does not make them stupid. These cultures are just smart and curious as we are and have a sophisticated and intimate knowledge of the world in which they live.

Ben Benoy
2001-Oct-26, 09:53 PM
I have been told in this thread a couple of times that you can't just point up into the sky and say "Look! The Earth is round." However, several people have pointed out that if you have a clear day and live in a fortunate location, you can just look out your window. So it is possible. And it is possible without precise measurements or fancy equipment. Apparently nobody can think of any other ways to demonstrate this.

Ben

Before everybody jumps all over me again, I will clarify: no one can come up with anything else which is does not require fancy equipment, precise measurements, travel (in person or by telephone), or several years of waiting for lunar eclipses.

Wiley
2001-Oct-26, 10:12 PM
On 2001-10-26 17:53, Ben Benoy wrote:
I have been told in this thread a couple of times that you can't just point up into the sky and say "Look! The Earth is round." However, several people have pointed out that if you have a clear day and live in a fortunate location, you can just look out your window. So it is possible. And it is possible without precise measurements or fancy equipment. Apparently nobody can think of any other ways to demonstrate this.

Ben

Before everybody jumps all over me again, I will clarify: no one can come up with anything else which is does not require fancy equipment, precise measurements, travel (in person or by telephone), or several years of waiting for lunar eclipses.




Perhaps a better way is to try to prove the Earth is round by contradiction. What would be a required property for a flat Earth? And can this be "easily" disproved?

For instance for a flat Earth the sun must rise at the same time everywhere. However this can't be disproved without a telephone or travel.

<font size=-1>[ This Message was edited by: Wiley on 2001-10-26 18:14 ]</font>

David Simmons
2001-Oct-27, 12:35 AM
On 2001-10-26 14:09, Wiley wrote:

Aristotle had these reasons to believe the Earth is round:

3.) The sun rises and sets at different times as you move east-west.



I'm puzzled as to how Aristotle could know that the sun sets at different times as you move east and west.

Local noon was just the time the sun was in the south, and it still is. If it weren't for rapid communication, travel and world-wide business interests, who in Athens would care what time it is in Rome?

nathan_russ
2001-Oct-27, 06:32 AM
I know this doesn't exactly prove that the Earth is spherical but what about the stars?
I have never seen Polaris by looking into the sky, because I live in Australia. So how do I know that it exists? Of course I believe it does exist, so where is it? Obviously it must be on the other side of the planet, so at the very least the planet has two sides, (although technically a sphere only has one side) and without actually bothering to do any calculations or anything, I'm sure that at different latitudes different stars can be seen, so at least this infers the Earth has opposing sides (without being technical), and is curved from South to North, and I'm sure observing celestial motion will help to prove the spherical nature of the earth.

Wally
2001-Oct-29, 12:34 PM
Before everybody jumps all over me again, I will clarify: no one can come up with anything else which is does not require fancy equipment, precise measurements, travel (in person or by telephone), or several years of waiting for lunar eclipses.




I don't agree Ben. You earlier state that my suggestion of taking the documented flight path(s) of trans-Pacific or Atlantic flights and drawing them on a globe and showing they are indeed on the "great circle" between the origin and destination as not conforming to your original question, but I see nothing in your first post that would disqualify this method. Methinks you're unwilling to accept anyone's answer at this point! /phpBB/images/smiles/icon_wink.gif

David Hall
2001-Oct-29, 12:53 PM
Well, as far as I can see it, there is no way to directly prove the earth is round just from standing in one place.

Determining roundness requires measuring angles; from the relative positions of heavenly bodies to different points on the ground, or from one point on the surface to others. Both of these conditions require either travel or time to calculate. There just isn't any other way to get these measurements.

The only way mentioned that doesn't require direct measurement of angles is from observing lunar eclipses, and that still requires multiple observations over time and/or from different locations.

So there are many ways to prove sphericity, but they do require some effort. You can't just walk out of your house and point to it.

Kevin J. Ashley
2001-Oct-31, 10:06 PM
I think Wiley was on the right track. To explain this to a child start from what they are willing to accept and use it as evidence that a flat Earth does not fit with that.

Here is my approach. First find out whether the child believes that Australia (or some place on the other side of the world) exists. Then find out if the child agrees that TV can show something happening now at a place far away. Now show the child a live TV broadcast from the remote location where it is daytime while it is night in the child's location. In order for this to happen, the sun must be on the other side of an Earth of some shape other than flat.

This is the time zone demonstration except that the child is viewing the difference in time directly through the TV camera. Although this might not be completely conclusive to the child, it should get them thinking.

It just occurred to me that letting a child monitor a webcam showing something like the Eiffel Tower would let them have this experience as well.

<font size=-1>[ This Message was edited by: Kevin J. Ashley on 2001-11-02 17:28 ]</font>

ljbrs
2001-Nov-25, 07:40 PM
Earth is an oblate spheroid.

ljbrs /phpBB/images/smiles/icon_wink.gif /phpBB/images/smiles/icon_wink.gif /phpBB/images/smiles/icon_wink.gif

GrapesOfWrath
2001-Nov-26, 02:14 PM
On 2001-11-25 14:40, ljbrs wrote:
Earth is an oblate spheroid.

ljbrs :wink: :wink: :wink:


Earth is approximately an oblate spheroid.

I'll see your three winks, and raise you one (http://mentock.home.mindspring.com/agu1992.htm).

ljbrs
2001-Nov-27, 01:00 AM
On 2001-11-26 09:14, GrapesOfWrath wrote:


On 2001-11-25 14:40, ljbrs wrote:
Earth is an oblate spheroid.

ljbrs /phpBB/images/smiles/icon_wink.gif /phpBB/images/smiles/icon_wink.gif /phpBB/images/smiles/icon_wink.gif


Earth is approximately an oblate spheroid.

I'll see your three winks, and raise you one (http://mentock.home.mindspring.com/agu1992.htm).



Touché!!! You win hands down!

However, on second thought, that was a *.com* site, and I always prefer the *scientific* kind from websites graced with *.edu* or *.gov*, with the exception of *Bad Astronomy* (because it has a bona fide astronomer at the helm).

Now, seriously, where did I put my horoscope?

ljbrs /phpBB/images/smiles/icon_smile.gif /phpBB/images/smiles/icon_wink.gif

Irishman
2001-Nov-29, 02:43 PM
I still think there is a way to do it by observing the phases of the moon. I'm not sure my previous post on this topic was entirely correct, but I'd be curious for the BA's take on how phases of the moon appear.

Here is my thinking from some limited and non-scientific observations. If you watch the phases of the moon, you note how it goes from a tiny crescent to a "half moon", all the way to full. Watch from wherever you are and note that the line between the points of the crescent or the tops of the gibbous part do not run perfectly vertical. It is fairly easy to conclude that the moon is spherical just from that, and it is also pretty evident that the phase of the moon depends upon the moon to sun geometry. However, I think it can be shown that the appearance of the phases also depends upon the relationship of both the moon and sun to the Earth.

That is a direction perhaps someone might want to pursue. I would, but I'm not meticulous enough to mess with it right now.

Phil S
2001-Nov-29, 03:55 PM
I used to work at a 12-story building in Mountain View CA, from which I could see San Francisco about 30 mi away, with water in between. This guy in an adjacent cubicle had a telescope for examining the view more closely.

The bottom few floors of the Transamerica building appeared to be missing, although we never counted the number of floors to see how many were below the horizon.

The Richmond bridge, about 50 miles away was completely invisible, although its towers were probably some 400 feet above the water.

The earth was definitely round.

Phil S
2001-Nov-29, 04:00 PM
Sorry if this thought has been posted before:

Couldn't Eritosthenes's results also be explained in terms of a flat earth and a sun that was much closer?

I don't mean to suggest that this is true, but couldn't it have been an alternate explanation with the facts available to the ancient greeks?

Or, if an eclipse had already convinced them that the earth was round, why not a much larger round earth and a much closer sun?

Like this:
<pre><code>
O sun
|
|
|
|
|
|
|
|
|
|_________
no yes
shadow shadow
</code></pre>



<font size=-1>[ This Message was edited by: Phil S on 2001-11-29 11:01 ]</font>

Bob S.
2001-Nov-30, 03:25 PM
Couldn't Eritosthenes's results also be explained in terms of a flat earth and a sun that was much closer?
I don't mean to suggest that this is true, but couldn't it have been an alternate explanation with the facts available to the ancient greeks?
Or, if an eclipse had already convinced them that the earth was round, why not a much larger round earth and a much closer sun?


See my second "class project" posted on Oct. 23, page two of this discussion. I mention the math and geometry for such a proof.

Manchurian Taikonaut
2004-Mar-08, 09:24 AM
The Globe

What did the ancients know?


Akkadians an old race of Mesopotamia knew lots of stuff, people of the Indus valley, the famous Greek Aristarchus and Aristotle, the Chinese astronomers in history, the Celts and builder of Stonehenge 2 700 BC ? , the Babylonians and the Romans, Ionians and Inca.

They used many models and measurements to predict that the Earth was a sphere, geometry, observation, math, eclipse, trigonometry....
Galileo agreed with the Copernicus ideas that Earth is not the center of the planetary system. The Galileo discovery that Venus has phases just like Earth's Moon confirmed that venus orbits the Sun and supported the heliocentric mode
The giant Library in Alexandria was one of the most famous centers of learning in the ancient worlds. The Museum was a center for scientific, geographical and mathematical research. One of its geographers, Eratosthenes knowing that the Earth was a sphere, said that the Sun was at least 20 times farther away than the Moon ( wrong answer but good work!! )
Chinese astronomers record a solar eclipse 2136 BC, Huainanzi relates a legend in which the sage of the king Yu race determined the size of the earth by ordering officials to walk to the ends of the earth, east-west and north-south, and gives both distances as 233,500 li and 75 steps ( a "Li" is an old measuremnet equals about half of a kilometre or one third of a mile ) it is a set of measurements that could, in principle, have been made by people on foot.
Other mathematical works use gnomon shadow measurements and the properties of right triangles to calculate this information. They assumed that the heavens were a round hemisphere (or canopy) over an earth that was both square and flat. Then other values could be taken. They also used gnomon shadow measurements to measure the “height of heaven,” the distance of the apex or the hemisphere from the earth’s surface. Measurements were taken at noon from a series of gnomons 1000 li apart due north-south.
An 8-foot gnomon cast a shadow of 1 foot 6 inches the shadow decreased an inch for each thousand li due south, and increased an inch for each thousand li north. Thus each thousand li of terrestrial distance corresponded to an inch of shadow length. The passage concludes that the distance from the northernmost gnomon to the subsolar point where the gnomon has no shadow was 60,000 li. It appears to use the properties of similar triangles to calculate the vertical distance from that point to the sun as 80,000 li. The similar triangles are ABC (whose height is the gnomon BC) and ADE, where DE is the height of the sun. The same techniques are used to calculate both terrestrial and celestial distances where no alternative direct measurement is available, or as one text puts it: “Heaven cannot be climbed like a staircase” .
The Greeks knew lots of stuff. Their knowledge that the Earth and Moon are spherical was widespread in the Greek world by the fifth century B.C. Aristotle argued that the circular shadow projected by the Earth when it eclipsed the Moon was clear evidence of the Earth's spherical nature. This argument had been known for a long time. Hipparchus was one of the greatest men of time. He lived around 120 BC. He developed the first star catalog, listing some 850 stars, and he calculated the lenght of a year within 6 minutes. He knew of the concept of the the circular motions. He also calculated precession, or wobble, of the Earth's axis by comparing his own observations with those made in Alexandria 150 years earlier and in ancient Babylonia.
Early celtic peoples and tribes in parts of England, France, Scotlands were also skilled astronomers created calendars from changes they saw in the Moon. Some ancient people around 5,000 years ago set up large stones to mark the movement of the Sun and other stars such as Stone henge. These people alos understood the earth was a sphere? One possibility is that the shadow of the earth cast on the Moon during an eclipse is always round. However, the idea that we are seeing the Earth's shadow cast on the Moon is, if you think about it, a very bold one
Back to another great man was from the Mediterranean world,his name Eratosthenes , he had the idea that the world was a sphere, and from the earlier maths of Aristarchus that the Sun was at least 20 times farther away than the Moon (the correct value is nearer 400), reasoned that rays of sunlight ought to be almost parallel when they reach the Earth, enabling him to measure the Earth's circumference. Eratosthenes chose observing stations at Alexandria ( famous library of the wonders of the world ) and Syene to the south, on the Nile River. For the time of the experiment he chose local noon on the day of the summer solstice, which comes at the same moment at both sites because they are very nearly on the same meridian of longitude. He probably selected that day, since the Sun was as far north as it would be during the year, meaning that it would pass very near the zenith at local noon at Syene.
At noon he had an observer in Syene observed that the Sun was directly overhead, while another observer in Alexandria found the Sun to be 7o south of the zenith. Measurers had paced off the distance between the two cities as about 4900 stadia (1 stadium is an old measurement and = 0.16 kilometer). Because a straight line cuts two parallel lines at equal angles, the angle at the center of the Earth is equal to the zenith angle, 7o. Working a simple proportion, Eratosthenes found that the Earth's circumference was as follows: C/4900 stadia = 360o /7o, or C = 252,000 stadia, or about 40,320 kilometers (km). In principle, Eratosthenes' experiment was correct. Although his measuring technique was very inaccurate by modern standards, his results were surprisingly close to today's true mean value of 40,030 km.
Zhang Sui from the Chinese Tang era (700 ) also understood that the earth was a globe and was the first man to describe proper stellar motion, or the apparent motion of stars across the plane of the sky relative to more distant stars, but Edmond Halley is credited with this discovery in 1718. What happen the west, did you peoples forget about Ancient romes and old Chinese charts?
The Polish astromoner Nicolaus Copernicus also knew the earth was round and used mathematical proofs to revive the earth centred heliocentric models of the Greeks and other people.without the aid of a telescope, concluded from his observations that it made more sense to have the sun as the centre of the solar system. He kept his ideas of a heliocentric solar system secrets to himself until he published them at the age of seventy in "De Revolutionibus Orbium Coelestium"
Another inventor from China, Zhang Heng thought Pi was the squares roots of 10 = 3.16 he was a Chinese astronomer and mathematician. He constructed a celestial globeknowing that the world was round, "The sky is like a hen's egg, and is as round as a crossbow pellet; the Earth is like the yolk of the egg, lying alone at the centre. The sky is large and the Earth small."
Galileo came from Italy, he done lots of research into physics. He studied at pisa. Galileo Galilei built his first telescope without ever having seen one assembled. This telescope had two lenses and magnified objects to three times their size. Galileo Galilei soon after in 1610 finds Callisto, Europa, Ganymede, and Io. The West was kind of in a dark ages witch hunt. His books were banned, he was forbidden to teach the Copernican view, and he was confined to his house until death.

George
2004-Mar-08, 03:49 PM
Before everybody jumps all over me again, I will clarify: no one can come up with anything else which is does not require fancy equipment, precise measurements, travel (in person or by telephone), or several years of waiting for lunar eclipses.

How about some garden hose for non-fancy equipment?

Stretch out a several hundred feet of garden hose and make it level by either line of sight or tight stringline. Put a "T" in the middle then turn each end up to the same height as the top of the "T". Cap the "T". Fill the hose with water, remove cap and watch the water come out. You will see the water level drop on the ends about an 1/8" or so depending on length.

When sewer lasers were first introduced to utility contractors they learned, the hard way, that the curvature of the earth could not be ignored.

[They later learned that the glue used for the pvc pipe also had to be taken into consideration due to refraction. Blowers were used to solve this problem.]

milli360
2004-Mar-08, 05:55 PM
Stretch out a several hundred feet of garden hose and make it level by either line of sight or tight stringline. Put a "T" in the middle then turn each end up to the same height as the top of the "T". Cap the "T". Fill the hose with water, remove cap and watch the water come out. You will see the water level drop on the ends about an 1/8" or so depending on length.
I was a little dubious, so I checked this out. Using 600 (several hundred) feet of hose with the outlet in the middle, and using a value for the Earth's radius of 3959 miles, the difference between the sphere and a straight line of sight would be sqrt( (3959*5250)^2+300^2)-3959*5280. That's only a fortieth of an inch--which could be offset by local density anomalies.

George
2004-Mar-08, 08:52 PM
Stretch out a several hundred feet of garden hose and make it level by either line of sight or tight stringline. Put a "T" in the middle then turn each end up to the same height as the top of the "T". Cap the "T". Fill the hose with water, remove cap and watch the water come out. You will see the water level drop on the ends about an 1/8" or so depending on length.
I was a little dubious, so I checked this out. Using 600 (several hundred) feet of hose with the outlet in the middle, and using a value for the Earth's radius of 3959 miles, the difference between the sphere and a straight line of sight would be sqrt( (3959*5250)^2+300^2)-3959*5280. That's only a fortieth of an inch--which could be offset by local density anomalies.

Your math looks, essentially, fine to me. But, you have to remember, a Texas backyard is a tad bigger. A good hose will run about 1,300 feet. :lol:

:oops: Seriously, the laser mfg. required us to get the contractors to check grade after 2 or 3 hundred feet "due to the curvature of the earth". :roll: ....and to think I never checked it out ... :-?

The Watcher
2004-Mar-09, 12:49 AM
I know it's been suggested already but.....
Next time you're in Cape Town South Africa, take a trip to the top of table mouintain and wait for sunset. Look out over the ocean and scan left to right, you will see the curve of the earth. Breathtaking, Especially when I wasn't expecting it! At first I didn't believe it and looked for some other explaination, but the curve of the earth was the only answer.
The glow of the milky-way is amazing from there as well.

One thought occurs which hasn't been mentioned yet, (and it's a local effect) is by taking a local Ordnance Survey map (Thats the UK name) and by using the scale, very carefully measure the distance between two points that are a reasonable distance apart and, driveable to.
Then, actually go and drive between the points, measure it for real and see what the difference in distance is. Granted you may need a pretty accurate measure on both accounts but, in essence the map should show a slightly longer distance because it dipicts a 3D world on a 2D surface.

To explain: If you take a 3D object say the intact peel of half of an orange and flatten it...well... it doesn't make a nice 'square' flat surface. To make it 'complete' with no holes (ie a 3" square of peel) you would need to stretch the peel in a few directions therefore distorting the surface area. This is similar to all maps. They show a 'stretched' surface which isn't absolutley accurate to the real world.

After a few short road trips discovering that all map measurments are slightly longer than the 'actual' measurements, should bring you to the conclusion that either the map makers measuring equipment is rubbish, your measuring equipment is rubbish or that the surface you are driving on is spherical! (As if you are driving on top of a very large sphere.) Obviously you could argue that it's the natural lay of the land on a flat earth but, you would discover the same effect anywhere in the world.

(The smaller the scale of the map the more inacurate -scale wise- it is. I think!)

I'm not an expert on maps so maybe someone else can confirm or deny this idea.
The Watcher

George
2004-Mar-09, 01:24 AM
I would think you would need to do this on the salt flats where ground variations do not become the predominant factor.

The distance would need to be significant. I get a little more than 6 feet extra distance due to curvature in a 10 mile line-of-sight stretch of perfect grade road (1 meter in about 30 km).

If you decide to do this, roll out a hose while you go and fill it with water, and.... :wink: (You should get a water column in the middle about 1.5 meters high in a 30 km hose).

[edit: hope I'm right this time, Milli360] :)

harlequin
2004-Mar-09, 02:14 AM
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. [snip]


You might call it cheating, but TV/telephone is a simple way to do it in your living room. Watching or talking to someone live on the opposite side world sort of makes it obvious.

What is traveling great distances? When I visit my brother three states to the West I can easily notice the change in when the Sun comes up.

I might also bring up the Foucault Pendulum which shows that the Earth is rotating.

russ_watters
2004-Mar-09, 04:18 AM
[edit: holy dead thread, Batman!]

milli360
2004-Mar-09, 05:23 AM
After a few short road trips discovering that all map measurments are slightly longer than the 'actual' measurements, should bring you to the conclusion that either the map makers measuring equipment is rubbish, your measuring equipment is rubbish or that the surface you are driving on is spherical! (As if you are driving on top of a very large sphere.)
If your method of measurement is driving, I'm gonna go with option B. :)