Random Thought Thread

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Do pilots ever see the curvature of the earth from high altitudes? If so, how do they react?
Absolutely, we do. On a routine basis in fact. And contrary to the uninformed and utterly ignorant conjecture of those in the science-denial & flat earth communities, this aligns perfectly with the expectations according to the known dimensions of our planet.
When most folks think of curvature, they’re usually only thinking about transverse curvature. Or sometimes described as “left to right” - this is purely two-dimensional.
Transverse curvature viewed from just 20,000ft. The sharp contrast of a dry atmosphere and setting sun over continental Australia helps to discern the very subtle arc (photo by me):
main-qimg-9af4384b3afbc423acd14a0912833693-lq

But, because the Earth is a sphere, the surface actually curves in three dimensions. This longitudinal curvature is what many might describe as “horizon dip” or declination. Although it might be an after thought to some, it is actually more readily observable than the classic “left to right” curvature, at least, at typical aeronautical altitudes. That is because, small angles appear exaggerated when viewed longitudinally. If you have an billiard ball cue with a slight bend, it may be impossible to perceive it without setting a ruler against it. But, look down the length of the cue, and you’ll very likely see the bend. Transverse & longitudinal curvature can be described as curvature in the x- & y-axis’, respectively.
Both transverse and longitudinal curvature evident here at 41,000ft, looking at the terrestrial horizon formed by the Pacific Ocean (curved water, indeed!) far off to the southwest of Chile in South America. The declination of the terrestrial horizon is about 3.8° below true level. The clarity of these results are indisputable
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We’ve all seen this photograph or one like it and were told that it proves that the Earth is flat. When I went to high school, geometry was an elective that I took, but many did not, so I understand that many seeing this photo do not know geometry. This geometry was first organized by Euclid over 2000 years ago. It is still taught because it hasn’t changed and is known to be correct.

Let’s put an observer on the surface of a sphere. The sphere is very large relative to the observer. We’ve all seen this illustration of how a sight line works on a curve.

main-qimg-f73d88c07eb69fe149901e22be9c9bdf

Take this illustration and rotate it around the axis passing vertically through the observer. The circle becomes a sphere and you can see that the distance from the observer to the horizon is the same in all directions. A line that encloses a space and is equidistant at all times from a central point is the definition of a circle. So if you are directly above the observer and could see a line that marks his horizon, you would see a circle with the observer at the center. This is basic geometry, so we should all agree this is true. Euclid knew it over 2000 years ago.
Now come down until you are at the same level as the observer. You now see the same circle of horizon. You and the observer are now seeing the same angle to the horizon line no matter what direction you look. You see a straight, level line. This is still basic geometry.
So it should be obvious to anyone that the straight, level horizon does not prove a flat Earth. It, however, does not disprove it, but the photo does. Look at the horizon. It is a sharp, well defined line. On a flat Earth, there would be no horizon. No matter what direction you were looking, there would be something visible above the water, either land, or that ice wall flat Earthers claim exists. If the atmosphere was completely clear, you would see something above the water in the distance. It might take a telescope, but it would be there. Of course, the atmosphere is not completely transparent, so you can’t see that far.

main-qimg-de1bae5e6be3cf88724b32a364c51253

On a flat Earth, the water would gradually fade into atmospheric haze. The horizon would be an indistinct haze band between sea and sky. There would be no line. Therefore, the photograph presented to prove that the Earth must be flat actually proves the opposite. Only a hazy band would be visible on a flat Earth, a sharp horizon line can only exist on a spherical Earth. The above photo was altered in Photoshop to illustrate how the flat Earth view might appear.
And for those that take issue with calling this proof because proof only exists in booze, printing, and mathematics, I used geometry here, and that is math.

Some additional notes. The radius of the Earth is: 6378km, 3963mi equatorial, 6357km, 3950mi polar and 6371km, 3958mi average. For an adult male of average height, standing at the water’s edge, the horizon is approximately 2.8 miles away. Referring to the diagram above, the distance to the horizon, d = √(2rh + h^2).
Someone will eventually notice that the sight line to the horizon is below horizontal and will say that on a sphere, you need to be looking down at the horizon. This is absolutely correct. The angle in degrees = 90-arccos(d/r+h). I calculated it for that average observer and it comes out to 0.04°. Let me put that in perspective. I have a 4 foot spirit level. If I level it perfectly, to aim it down 0.04°, I need to drop one side approximately 1/32 inch. If you look really carefully, you might be able to see that the bubble is slightly off to one side out of level. Standing on the shore looking out, I can guarantee you that you can’t see the difference between perfectly level and 0.04° below level.
I should not have to say that the illustration is not to scale. If it was, the stick figure on the Earth would have to be about 1500 miles tall, or the Earth would have to be only about 32 feet in diameter
 
We’ve all seen this photograph or one like it and were told that it proves that the Earth is flat. When I went to high school, geometry was an elective that I took, but many did not, so I understand that many seeing this photo do not know geometry. This geometry was first organized by Euclid over 2000 years ago. It is still taught because it hasn’t changed and is known to be correct.

Let’s put an observer on the surface of a sphere. The sphere is very large relative to the observer. We’ve all seen this illustration of how a sight line works on a curve.

main-qimg-f73d88c07eb69fe149901e22be9c9bdf

Take this illustration and rotate it around the axis passing vertically through the observer. The circle becomes a sphere and you can see that the distance from the observer to the horizon is the same in all directions. A line that encloses a space and is equidistant at all times from a central point is the definition of a circle. So if you are directly above the observer and could see a line that marks his horizon, you would see a circle with the observer at the center. This is basic geometry, so we should all agree this is true. Euclid knew it over 2000 years ago.
Now come down until you are at the same level as the observer. You now see the same circle of horizon. You and the observer are now seeing the same angle to the horizon line no matter what direction you look. You see a straight, level line. This is still basic geometry.
So it should be obvious to anyone that the straight, level horizon does not prove a flat Earth. It, however, does not disprove it, but the photo does. Look at the horizon. It is a sharp, well defined line. On a flat Earth, there would be no horizon. No matter what direction you were looking, there would be something visible above the water, either land, or that ice wall flat Earthers claim exists. If the atmosphere was completely clear, you would see something above the water in the distance. It might take a telescope, but it would be there. Of course, the atmosphere is not completely transparent, so you can’t see that far.

main-qimg-de1bae5e6be3cf88724b32a364c51253

On a flat Earth, the water would gradually fade into atmospheric haze. The horizon would be an indistinct haze band between sea and sky. There would be no line. Therefore, the photograph presented to prove that the Earth must be flat actually proves the opposite. Only a hazy band would be visible on a flat Earth, a sharp horizon line can only exist on a spherical Earth. The above photo was altered in Photoshop to illustrate how the flat Earth view might appear.
And for those that take issue with calling this proof because proof only exists in booze, printing, and mathematics, I used geometry here, and that is math.

Some additional notes. The radius of the Earth is: 6378km, 3963mi equatorial, 6357km, 3950mi polar and 6371km, 3958mi average. For an adult male of average height, standing at the water’s edge, the horizon is approximately 2.8 miles away. Referring to the diagram above, the distance to the horizon, d = √(2rh + h^2).
Someone will eventually notice that the sight line to the horizon is below horizontal and will say that on a sphere, you need to be looking down at the horizon. This is absolutely correct. The angle in degrees = 90-arccos(d/r+h). I calculated it for that average observer and it comes out to 0.04°. Let me put that in perspective. I have a 4 foot spirit level. If I level it perfectly, to aim it down 0.04°, I need to drop one side approximately 1/32 inch. If you look really carefully, you might be able to see that the bubble is slightly off to one side out of level. Standing on the shore looking out, I can guarantee you that you can’t see the difference between perfectly level and 0.04° below level.
I should not have to say that the illustration is not to scale. If it was, the stick figure on the Earth would have to be about 1500 miles tall, or the Earth would have to be only about 32 feet in diameter
Good morning hopper. You’re killing my buzz…🥹
 
I think it was called a match box......back in the day ....
You're older than me. A nickel bag was a quarter ounce in my era.
1977... remember when an oz was called a LID
A lid was 3/4 ounce in my day. Nickel bag, dime bag, lid (which was the most popular in my day for some weird reason*) and an ounce, $20.

*I think a lid was popular because it left you enough out of a twenty to buy munchies and drinks.
 
Weed when I started buying was 35.00 an oz for years thru my 20s. I had heard of a nickel bag and a dime bag but only from mostly the lower areas of the city where they must have not smoked like me although I remember buying a 1/4 oz when weed was less available. Fortunately, there have been only a few dry spells for me but I learned by the second dry spell to stock up and stay ahead.
 
Just proving a point. I could take my Wife and Big up in a rocket ship into space and show them that the earth was round and when we landed they would just say the windows they looked out was a TV screen the government put in place to lie to them about Flat earth.😁
The government is so smart they built a dome around Flat earth to keep us in and won't let us close to the edge to see what's there.😁
When everything is a conspiracy it's hard to convince them of reality. But I'm use to it.
Nothing new to me. Living with my Wife is like living with Big except she is a lot prettier thank fking God.😁
 
you could not take us into outer space , rockets and satellites can only make it into low earth orbit , the Van Allen belts would cook us alive

watch what happens when a rocket goes straight up instead of at an angle….the rocket will hit the dome that covers earth…the firmament above , like the Bible says

please tell Mrs Hopper to keep her chin up , the Truth will be revealed soon!




 
you could not take us into outer space , rockets and satellites can only make it into low earth orbit , the Van Allen belts would cook us alive

watch what happens when a rocket goes straight up instead of at an angle….the rocket will hit the dome that covers earth…the firmament above , like the Bible says

please tell Mrs Hopper to keep her chin up , the Truth will be revealed soon!





Told ya. Now all our rockets are bouncing off a dome.😂😂😂
Big we have plenty pictures of earth from space. I know,I know,,,,the government is lying to us and all those pilots are part of a Round earth conspiracy.😴
 
Your so funny bro. You know thousands of ppl have watched NASA and other private companies launch rockets that went into space,,right. We have a Space Station we can see round earth from.Oh wait,,it's not in space it's under our Dome Right? And the pictures sent back to earth or just drawings on a window the government wants us to see to cover up that the earth is flat.😁
Can you please tell me the upside to this conspiracy about the government lying about earth being round. What would be the point?
So the Sun is Flat too?😱
 
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