Prove the Earth is round

Yep, xouper, that's a 1959 Cessna 150, serial numer 17358. Looks like it's in North Carolina.

I still remember the one I flew in 1979 - N2592B.
 
To a seven-dimensional sentient being, the earth IS flat. At least, that's what that homeless guy told me.
 
Zep said:
Seriously, Xouper, you are making it a REASONABLE question and would be expecting a REASONABLE answer. And I'm sure we could calculate acceptable stuff by that or any of the other REASONABLE methods proposed above.
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Zep, I empathize with your sense of frustration but the constraints you invoke , -reasonable thought or processes-, are completely subjective ( contrasted by one's own views which appear to explainable and obvious ) and OUTSIDE the scope of formal scientific stricture. Reason is a human commodity and as such has some ( coff,coff ) wiggle room .The only way to contrast the subtlies of diverging opinion is to invoke the experts view or demonstrate factually the aspects or the views held of your opponents are fallacious.
 
Kumar said:
Terry,

Thanks for mentioning. But I could not follow this awnser. Now I ask in simple language. Just assume we are standing on ball like earth. If we travel one kilometer on it from one point to other point in straight line along with its curvature. How much we will be deep on 2nd point from the first point. Tell me in mm,cm,metre etc.
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I make it about 8cm. But note that if you go 2 km, it would be more than 16cm. That's what I meant about there not being a single number which is the slope of the earth.

--Terry.
 
Correct me if I am wrong, but if you are STANDING on a perfectly smooth sphere, wouldn't the slope be ZERO?

I mean, you are always the same level from the center.

Now the Earth has different slopes per kilometer because we have things like land masses, wind, gravitational forces, etc. The slope is different everywhere.
 
DangerousBeliefs said:
Correct me if I am wrong, but if you are STANDING on a perfectly smooth sphere, wouldn't the slope be ZERO?

I mean, you are always the same level from the center.
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The surface of a sphere in free space would be a graviational equipotential surface. But it wouldn't be flat, in the geometrical sense. Okay, you can't roll a ball down the slope, but that doesn't mean it isn't there. You can see it, as has been pointed out with the ship example.

--Terry.
 
CurtC: Yep, xouper, that's a 1959 Cessna 150, serial numer 17358. Looks like it's in North Carolina.
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Ain't the internet wunnerful? I didn't think to look it up.

North Carolina rings a bell, since that's Chuck Nelson's home state. When I flew 5858E, it was in Idaho and it was owned by Dan Gable. I met Dan and Chuck while we were all stationed at Mountain Home AFB in the early 1970s. At the time, Chuck owned a C-172, tailnumber 8222U. (Occasionally I would forget that U was uniform, and I'd call Boise tower from "8 triple 2 underwear" - they didn't always unkey their mic to hide their snickers.) When I made my first parachute jump in 1975, it was from 8222U with Chuck as the pilot. Later that same day, Chuck made his first parachute jump from 8222U with me as pilot. In both cases Dan was the jumpmaster. So now I wonder if Dan sold 5858E to Chuck. I guess I could go look it up. I haven't talked to either of those guys in years, kinda lost touch, I guess. If Chuck's not the current owner, then [voice=gildaradner] never mind [/voice]. :)
 
69dodge said:
How did you get 8 cm? I get about twice that.
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r<sup>2</sup> + 1000<sup>2</sup> = (r + h)<sup>2</sup>

where r = 6378100m

solve for h.

Actually, now I look at this, it's not exactly correct, since h is not normal to the tangent, as required by the problem. But that shouldn't make much difference given how small the angle is.

I dunno, maybe I just can't add up.

--Terry.
 
Please settle & make a common decision about the slope. Please give with the calculations.

Please also give justifications & proofs of being 'earth as round' understoodable to a common man.

Recently, I found a strange thing. A mountain some far but visible from my window, was seen on one day but not seen on other day then again seen on next day. Do the visibility of Ship can also behave in this manner. Just an halucination/illusion due to continious watching/expectation (as in desert) or due to atmospheric & pollutions obstacles or due to more humid atmosphere just above the sea level.
 
Kumar said:
Please settle & make a common decision about the slope. Please give with the calculations.

Please also give justifications & proofs of being 'earth as round' understoodable to a common man.

Recently, I found a strange thing. A mountain some far but visible from my window, was seen on one day but not seen on other day then again seen on next day. Do the visibility of Ship can also behave in this manner. Just an halucination/illusion due to continious watching/expectation (as in desert) or due to atmospheric & pollutions obstacles or due to more humid atmosphere just above the sea level.
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If a ship is beyond the horizon, then you wont see it regardless of how powerful your telescope is. The possibility of you seeing it is 0%.

When you have haze that limits your visibility, that possibility drops all the way down to 0%.
 
TillEulenspiegel said:

Zep, I empathize with your sense of frustration but the constraints you invoke , -reasonable thought or processes-, are completely subjective ( contrasted by one's own views which appear to explainable and obvious ) and OUTSIDE the scope of formal scientific stricture. Reason is a human commodity and as such has some ( coff,coff ) wiggle room .The only way to contrast the subtlies of diverging opinion is to invoke the experts view or demonstrate factually the aspects or the views held of your opponents are fallacious.
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Oh, I'm not having a problem with the difference of opinion at all. It's the attitude that is the problem.

I was happy to differ with Xouper in another thread in which we firmly held (hold?) differing views on a certain subject, but both of us were prepared to use reasoned argument to uphold our views, not just gainsaying each other and being deliberately obtuse (although I suspect Xouper might disagree on this too! :) ). The discussion was vigourous, but I was fully prepared to consider Xouper's arguments as they were both reasonable points and it was Xouper arguing FOR his own assertion. But this charade over here has been quite different so far.

Really, if this were a "proper" scientific forum, Kumar is the one making the assertion of a flat earth as an alternative to a round earth (which is not really a valid proposal to start with - there may be other alternatives besides those two), so he should really be defending his view, not calling on us to defend our own view. Which is why I called "troll" earlier.
 
Kumar said:
Please settle & make a common decision about the slope. Please give with the calculations.

Please also give justifications & proofs of being 'earth as round' understoodable to a common man.

Recently, I found a strange thing. A mountain some far but visible from my window, was seen on one day but not seen on other day then again seen on next day. Do the visibility of Ship can also behave in this manner. Just an halucination/illusion due to continious watching/expectation (as in desert) or due to atmospheric & pollutions obstacles or due to more humid atmosphere just above the sea level.
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For his next trick, he will prove sound travels faster than light because you can hear the train coming down the tunnel before you can see it.
 
Zep: I was happy to differ with Xouper

xouper: No you weren't.

Zep: in another thread

xouper: No, it was this thread.

Zep: in which we firmly held (hold?) differing views on a certain subject,

xouper: No, it wasn't.

Zep: but both of us were prepared to use reasoned argument to uphold our views,

xouper: I disagree.

Zep: not just gainsaying each other

xouper: Yes it was.

Zep: and being deliberately obtuse

xouper: Yes it was.

Zep: (although I suspect Xouper might disagree on this too! :) ).

xouper: Who, me?

Zep: The discussion was vigourous,

xouper: No it wasn't.

Zep: but I was fully prepared to consider Xouper's arguments

xouper: No you weren't.

Zep: as they were both reasonable points

xouper: Nope.

Zep: and it was Xouper arguing FOR his own assertion.

xouper: No I wasn't.



[/mode=montypython] :p
 
Originally posted by Terry
I dunno, maybe I just can't add up.
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No, you're right.

I figured out what my mistake was. I was calculating the angle between two points that are 1 km from each other. That angle corresponds to a slope of about 16 cm / km. In other words, if we consider the ground at one point to be horizontal, the ground at a point 1 km away has a slope of 16 cm / km. Now if you travel for 1 km along a slope of 16 cm / km, you'll end up 16 cm lower than you started. But the slope isn't 16 cm / km for the whole distance. It changes gradually from zero, near the first point, to 16 cm / km, near the second point. The average slope is therefore half the maximum, or 8 cm / km.

I think I will blame xouper for the confusion. :p He wrote:<blockquote>he is asking if you extend a line out over the ocean (tangent to where you are standing), how far above sea level will the end of a one kilometer line be?</blockquote>but in the same post, as if it were the same question, he also wrote:<blockquote>that is what I think Kumar had in mind - what is the instantaneous slope of a point on the ocean one kilometer away.</blockquote>
 
But the slope isn't 16 cm / km for the whole distance. It changes gradually from zero, near the first point, to 16 cm / km, near the second point. The average slope is therefore half the maximum, or 8 cm / km.
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69dodge,

Thanks & sorry to keep you tensed. Your above quote is not clear. Please make it bit clear. Please also give your calculations about the same i.e.based on measurements of arc and radius etc. of the earth.

All,

What is limit of the naked eyes of a common person to see the ship as sharply as at 15/20 yards? Pls consider normal vision & all other environmental factors/obstacles as mentioned by me. Pls don't consider telescope as I can only believe in naked eyes for solid/true proof.
 
69dodge: I think I will blame xouper for the confusion. :p He wrote:<blockquote>he is asking if you extend a line out over the ocean (tangent to where you are standing), how far above sea level will the end of a one kilometer line be?</blockquote>but in the same post, as if it were the same question, he also wrote:<blockquote>that is what I think Kumar had in mind - what is the instantaneous slope of a point on the ocean one kilometer away.</blockquote>
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AACCK, you're right, they aren't the same. It's not that I didn't know the difference, I just got sloppy in my writing. But it's an error, just the same, that would get marked wrong on an exam.

I got pretty much the same numbers, 8 and 16 cm, using the following method:

If we draw a circle centered at the origin with radius 6378.1 km (Earth's equitorial radius), and then we draw a horizontal line starting at the top of the circle <nobr>(0, 6378.1)</nobr> and going in the positive x direction for one km, we will be at the point P at <nobr>(1, 6378.1).</nobr>

If we draw a line L from point P to the origin, the slope of that line is obviously dy/dx = 6378.1.

Let S be the point where L intersects the circle. The instantaneous slope of the circle at S is perpendicular to L, obviously, and is thus -1/6378.1, or -.01568 (which is 15.68 cm for every km). We should be able to get the same answer using the first derivative, but why bother.

To get the distance between P and S, we need to find the coordinates of S, which we can do by solving the simultaneous equations for the circle and line L.

6378.1<sup>2</sup> = x<sup>2</sup> + y<sup>2</sup>
and
y = 6378.1 * x

We could then find the distance between P and S using the pythagorean theorem, but the angle is so small that for the purposes of this puzzle, we can consider the hypotenuse equal to the difference in the y-coordinates. I'm willing to bet the answer is the same for at least the first four significant digits. So we really only need to solve for the y-cooridnate of S, and we get

y = 6378.09992160674953642193261891392

Thus the distance from S to P is approximately 7.839 cm.
 
Here's a commonly used rule of thumb for estimating the distance it takes for a ship to disappear over the horizon. This distance is the sum of the ship's local horizon and the viewer's local horizon. To estimate the local horizon in miles, take the square root of the height above water in feet and multiply by 1.25.

For example, for eyeballs that are 6 feet above the water (~1.8 meters), the local horizon is about 3 miles (~5 km).

For a ship that's 65 feet tall (~20 meters) the local horizon is about 10 miles (~16 km).

Thus, if a ship sails north from Chicago in a straight line up the coast of Lake Michigan, staying within sight of land at all times, then to an observer standing on the beach at water level in Chicago, the ship will completely disappear over the horizon in about 13 miles (~ 21 km), which is well within the limit of the human eye, no telescope needed.

Because of this, I strongly suspect that most professional sailors, even those who never left the Mediterranean, have always known the Earth is round and not flat.

Using the above rule of thumb for a ship that is 7.8 cm tall, its local horizon is 1 km, which is consistent with previous results.
 
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