Earth is round?

[Ben Benoy]

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]

Ben shame on you !!!

I never took you for a flat Earther !

The world is not round, its SPHERICAL

Jeff [img]/phpBB/images/smiles/icon_smile.gif[/img]

[Espritch]

The world is not round, its SPHERICAL

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

[Spaceman Spiff]

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]

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. [img]/phpBB/images/smiles/icon_wink.gif[/img]

[MongotheGreat]

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]

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]

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. [img]/phpBB/images/smiles/icon_smile.gif[/img] 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]

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]

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( tan²(3t/2)*sin²(p) + sin²(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^-4 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. [img]/phpBB/images/smiles/icon_smile.gif[/img]

Ben Benoy

[Simon]

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]

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]

I believe you can delete the post yourself now using the edit function [img]/phpBB/images/smiles/icon_smile.gif[/img]

[Matthew Ota]

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]

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]

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]

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]

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]

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]

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]

I "sailed" across the Pacific on a US Navy helicopter carrier (the USS Belleau Wood), 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, 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" in the Ask 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]

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]

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]

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</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)

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]

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.]

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]

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]

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]

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.
[img]/phpBB/images/smiles/icon_biggrin.gif[/img] [img]/phpBB/images/smiles/icon_razz.gif[/img]

[David Simmons]

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.