Saturday, September 15, 2012

Can the Great Wall of China seen from the Moon or from a Low Orbit Satellite

This article is dedicated to Captain  Lim Khoy Hing, a retired Senior Pilot with AirAsia Airbus A320 and AirAsia X A330/A340 who also used to fly the Boeing 777 with Malaysia Airlines in exchange for an answer he gave me when I asked him if in practice can an airport be seen from a height of 10,000 metres as an aircraft approaches it, and also on the rate of descend  

It was a follow-up on an earlier article where I wrote my own view on the visibility into the horizon from a height 
from a theoretical point-of-view. It is below:


The Dilemma of Visibility on the Great Wall of China from Space



lim ju boo


  
Summary:



The Great Wall of China cannot be seen neither from the Moon nor from a low earth orbit satellite as claimed by NASA astronauts.


The limiting visibility is the comparatively narrow width of the Great Wall which is only about 5 metres at least at Badaling just outside Beijing. At this width, the smallest angle at which a human eye can perceive an object, called the angular resolution, is only 0.07 of a degree or 4 arc minutes.



This is about 4.1 km away.  That’s the weakest link in that long chain of the Great Wall which extends a total length of between 8,851.8 and 21,196 km.



The Full Text:


The Great Wall of China was built during different historical periods, and in different sections.
On December 2008, a national survey team in China announced that the exact length of the Great Wall of China as was constructed during the Ming Dynasty (1368 AD - 1644 AD) was determined to be 8,851.8 km.


However, another archaeological survey found that the entire wall with all of its branches measure out to be 21,196 km (13,171 mi).[6]


Our Question:


Our question is not about ther age or length of the Great Wall of China. Our question is whether or not “it is the only man-made structure that can be seen from the Moon and from space” That’s what troubles many of us including astronauts from United States of America, and China as well.
There has been a lot of controversy whether or not the Great Wall of China could be seen from space or even from the Moon?    


Several United States astronauts have insisted that the Great Wall could be seen, whereas Chinese astronauts said that it could not be seen until they have to rewrite their own history books to refute the claims of the American astronauts. 


The author of this article has not gone into space to decide on this controversy, but he decided to use a combination of mathematics and his knowledge on the physiology of vision to theoretically decide on this issue.



But before that, here’s a report he read from Wikipedia at: 



http://en.wikipedia.org/wiki/Great_Wall_of_China


The last paragraph of the Wikipedia has this to say:


Visibility from low earth orbit


“A more controversial question is whether the Wall is visible from low earth orbit (an altitude of as little as 100 miles (160 km). NASA claims that it is barely visible, and only under nearly perfect conditions; it is no more conspicuous than many other man-made objects. Other authors have argued that due to limitations of the optics of the eye and the spacing of photoreceptors on the retina, it is impossible to see the wall with the naked eye, even from low orbit, and would require visual acuity of 20/3 (7.7 times better than normal).


Astronaut William Pogue thought he had seen it from Skylab but discovered he was actually looking at the Grand Canal of China near Beijing. He spotted the Great Wall with binoculars, but said that "it wasn't visible to the unaided eye." U.S. Senator Jake Garn claimed to be able to see the Great Wall with the naked eye from a space shuttle orbit in the early 1980s, but his claim has been disputed by several U.S. astronauts. Veteran U.S. astronaut Gene Cernan has stated: "At Earth orbit of 100 miles (160 km) to 200 miles (320 km) high, the Great Wall of China is, indeed, visible to the naked eye." Ed Lu, Expedition 7 Science Officer aboard the International Space Station, adds that, "it's less visible than a lot of other objects. And you have to know where to look."



In 2001, Neil Armstrong stated about the view from Apollo 11: "I do not believe that, at least with my eyes, there would be any man-made object that I could see. I have not yet found somebody who has told me they've seen the Wall of China from Earth orbit. ...I've asked various people, particularly Shuttle guys, that have been many orbits around China in the daytime, and the ones I've talked to didn't see it."


In October 2003, Chinese astronaut Yang Liwei stated that he had not been able to see the Great Wall of China. In response, the European Space Agency (ESA) issued a press release reporting that from an orbit between 160 and 320 km, the Great Wall is visible to the naked eye. In an attempt to further clarify things, the ESA published a picture of a part of the “Great Wall” photographed from Space. However, in a press release a week later (no longer available in the ESA’s website), they acknowledged that the "Great Wall" in the picture was actually a river.

Leroy Chiao, a Chinese-American astronaut, took a photograph from the International Space Station that shows the wall. It was so indistinct that the photographer was not certain he had actually captured it. Based on the photograph, the China Daily later reported that the Great Wall can be seen from space with the naked eye, under favorable viewing conditions, if one knows exactly where to look. However, the resolution of a camera can be much higher than the human visual system and the optics much better, rendering photographic evidence irrelevant to the issue of whether it is visible to the naked eye.


Limitation of vision:


The author knows from his knowledge in physiology and astronomy that our naked eye vision is limited to the size of an object at certain distances. 


This is known as the angular resolution.  This is the limit our best naked eye vision can see an object from a certain distance. This is about 4 arc minutes, or approximately 0.07°.  This corresponds to an object 1.2 m in size from a distance of 1 km (1000 metres).

 Anything smaller cannot be seen even with the best naked eye vision, unless magnified with the aid of a telescope or a pair of binoculars.


Now let’s work this out.  


The length of the Great Wall varies greatly at different sections.  Some gave the figure at 8,850 km (5,500 mi).[5] This is made up of 6,259 km (3,889 mi) sections of actual wall.  
Other estimates have put the Great Wall at 6,700 km. It all varies from how they measure it, and from which section to which section, or whether or not they integrate all the sections including the broken ones.  

 
Measurements taken at Badaling:


Even though the width and height vary a lot from section to section, the section I have been to was at Badaling. This is not far from the heart of Beijing. I also made a few measurements there using tapes and GPS instruments. The following was what I found.


This section is the highest section in the Jundu Mountain.  The measurements I made in this section measured 7.8 meters (25.6 ft) high, and it was about 5 meters (16.4 ft) wide.


However, the author cannot say the same for the entire length of the Great Wall. Several thousands of measurements need to be taken at random to come up with an un-bias statistical mean. Clearly this is not possible for the purpose of this article. So the author makes an un-intentional ‘bias’ assumption using the limited measurement he gathered at Badaling, and attempts to calculate out the argument. 


The Great Wall of China at 21,196 km, or even at 8,851.8 km is certainly horrendously long, and I in particular, like to salute the ancient Chinese for their stupendous engineering feat, for their toils and hardships involving hundreds of thousands of ancient Chinese who built this Great Wall across very rugged and very difficult mountain terrain using very primitive tools and limited building materials. 


Looking at that mammoth and unspeakable length of those structures we shall forever remember them for their labor, sufferings, their sacrifices, and their loss of lives. We greatly appreciate and honor them.



Visibility is as strong as its weakest link:



Our question as I believe, it is not the length of the Wall that makes it possible as the ‘only man-made object that can be seen from space or from the Moon’ as many in the past have claimed.

 
As I have already said, how small is small that limits our vision. And the smallest of this Great Wall is its breath (width) and never its enormous length.



Can we then see the narrow gauge of this Wall from a distance from space? This is similar to asking if it is possible to see a long strand of human hair lying on the ground  from a distance of just a few metres away?
                                                                                                                                                          

 We know that no matter how long a strand of hair be its visibility is limited by its width. This is the same as the saying   “a chain is only as strong as its weakest link”.


Visibility of a Human Hair:

 In short, are we able to see a long strand of a single human hair from say, 100 metres away? That is the question we need to answer. 



The diameter of human hair ranges from 17 to 181 µm (millionths of a meter) according to Brian Ley (1999).
Another estimate by Denny & Gayle Rossbach gave the figure as 25.4 µm or 2.54 x 10-5 of a metre.



A fair average diameter of a human hair I would say, is about 100 micrometre or 10 -4 metre
This means a strand of black human hair can only be clearly seen against a contrasting white background from a distance of about 0.082 metres or about 8 cm away.   


It can never be seen from 10 metres away no matter how long the hair. We shall come to this later.  Remember, the limiting factor is the very small width of the hair compared to its length.  
But the width of the Wall as I measured it at Badaling is just about 5.0 metres.



Visibility from the Moon:



It was also claimed that the Great Wall with a width of only 5 m across was even visible from the Moon?


The Earth-Moon distance varies over the course of the Moon’s elliptical path round the Earth.  This varies from 356,700 kilometres at perigee (nearest to Earth) to 406,300 kilometres at apogee (farthest away). Its average distance from Earth is 384,400 kilometers (384,400,000 metres).



At that distance, it is similar trying to look at a strand of hair 10 -4 metre across from a distance of 7488 metres or nearly 7.5 km away.  Is this possible?


Even if we try to look for a long strand of black hair lying on say, a perfect white, and perfectly flat marble floor from a distance of say 2 metres, this may still be possible with very good vision and plenty of light provided there is no obstruction between the eyes and the very bright white and flat floor. The black hair may still stand out against such white and bright background.



But imagine trying to look for the Great Wall from the Moon or even not far in space. One must remember the Great Wall is not like a strand of black hair on a perfectly white, flat, and unhidden bright floor. 


The Wall winds its way among torturous undulating mountain terrains which is almost the same colour as the mountains themselves, and continues to wind among millions of trees and other hidden backdrop among the undulating terrains seen at various angles. This is an added difficulty.


Reliefs and Shadows:

If one looks at the Moon with a pair of binoculars especially on one of its waning gibbous, waxing gibbous, waxing or gibbous crescent phases, or even during its quarter phases, when the Sun is at an angle on the lunar surface,   one can see a lot of mountains, elevations, valleys, craters, maria and oceanus, lacus, sinus paludes and many other features on it as the Sun cast long shadows on them, especially on the mountains over the valleys to accentuate their reliefs.

These features are hard to see if there are no shadows on them to ‘magnify’ their protrusions over the surface of the Moon during a full moon when sunlight is incidental, meaning sunlight shines directly at 90 degrees on the surface. They then cast no shadow.

Using this observation in lunar astronomy, one may argue the Great Wall can be seen towards the evening or in the early morning when the Sun cast a shadow of the Wall, length, breadth, height and all over it.

Unfortunately this is not true because the Wall blends with the rugged mountains, terrains, valleys, tress and all. It just gets camouflaged with the mountainous surroundings. If at all the Sun casts a shadow of the Wall to ‘enlarge’ it, remember the Sun will also cast the same shadows of the surrounding mountains, and blend them all into the surrounding areas.

 Furthermore, some sections of the Wall maybe in the valleys, and any shadow of a higher adjacent mountain may even put the Wall into darkness if sections of the Wall are in the valleys below.

It is not so easy to argue like that based on what we see on the Moon. On the Moon we cannot even see fine features on the mountains or valleys even with a telescope or with a good pair of binoculars.


Clouds too:


Not just that, clouds are perpetually all over the Earth’s atmosphere below to cover up everything that is below them unlike the Moon where there is no cloud.
Would any astronaut in his right sense of logic insist that he can see the Great Wall of China from such a distance in space with all the cloud veils and all the land camouflages hiding the Great Wall?     


Trigonometry:


We know in trigonometry that in a right angle triangle:
tan θ = opposite / adjacent…(1)


Since ‘opposite’ here means the width of the Wall. This is just 5 metres wide. We need to calculate out the ‘adjacent’ which is the distance of the Wall to an observer, and then calculate out the visual angular resolution until it is the smallest at a certain distance.



Below this, even the best of naked eyes vision can no longer see.  This is called the limiting angle of resolution, and it is just 0.07 of a degree or 4 arc minutes. 
That’s see how it works out.


Since tan θ = height or width (opposite) to the angle θ ÷ adjacent (distance of the object)
From (1), the adjacent = opposite ÷ tan θ

= 5 x 10 -3   km ÷ tan 0.07 = 4.1 km

(Where 5 metres = 5 x 10 -3   km = width of the Great Wall)



Thus we can conclude that the width of the Wall can no longer be visible at more than 4.1 km away.  That’s the weakest link in that long chain.


Perhaps with some luck we can just see a line without any detail if not hidden and not blended into the surrounded mountainous terrain, and if there is no cloud cover.  But I do not know as I am not an astronaut, and I have not even seen it from an aeroplane even 4 km above. That is the limit of our naked eye vision.



A Square Great Wall:


Let us now look at it in another way. Suppose we take the entire length of the Wall including all its branches at 21,196 km, and let us say we put all the bricks, stones, mud, etc together to form a square instead. How does that look?


Let us see how this works?


The surface area is length x breadth.

Hence average surface area of the Great Wall = (5 x 10-3) km wide x 21,196 km long = 106 sq km = 10.3 km on either side.

If that is the case, then 10.3 km / tan 0.07

=8, 430 km.


If, this is mathematical and physiological logic, the Great Wall can definitely be seen from outer space 8, 430 km from the surface of Earth. That for sure provided there is no cloud cover.


Volume of Great Wall:


But what happens if we were to take the entire Great Wall, its branches and length, height and width and crunch them all up together into an enormous ball of bricks and stones. What then would be the volume of this Sphere of Great Wall?


Its volume in its natural state, not as a sphere, would be:


21,198 km long x 5 x 10-3 km wide x 7.8 x 10-3 km high = 0.827 cubic km (827,000,000 cubic metres)


(1 cubic kilometer = 1 000 000 000 cubic meters)


Since the volume of a sphere is given as:
  

(4/3) π r 3 = 0.827 cubic km 0.826722

r3 = 0.827 / (4/3) π

Its radius (r) would be:

r = 3 √ [0.827 / (4/3) π]

= 3 √ (0.827 / 4.2) = 0.58 22242568 km in radius


Its diameter = 1.16 4448514 km in diameter


Such a ball of walls would just be visible at a distance of:


1.16 km / tan 0.07 = 950 km away


However, if the entire length of km were to be stretched out in a straight line, and if we assume we can also see the width of the Great Wall, then it would be visible from a distance of:


21,196 km / tan 0.07 = 17,349,153 km


But at last, this is still not possible, because:
·        
  • The Wall cannot be straightened out 
  • The width of the Wall at 5.0 metres cannot be visible at more than 4.1 km away.

     It would not be possible to see it even as a very fine line at either 950 km or worse still at 17,349,153 km even if stretched out.


That is the limiting angular resolution for visibility for the naked eyes.  This limit once again, is about 0.07 degree or about 4 arc minutes, or about 1.2 metres at 1000 metres.



Visibility of a Man:


A man with a height of 5 feet 6 inch (1.6764 metres = 1.6764 x 10 -3 km) can just be visible from a distance of:
1.6764 x 10 -3 / (tan 0.7) = 1.372 km (1,372 metres) away
He becomes invisible if he moves further away, unless we use a telescope or a pair of binoculars, and provided he is not hidden by obstacles along the line of sight.


Dimensions of building blocks:


I really do not know how many pieces of bricks and their total weight were used to construct the Great Wall. But from what I saw and examined at Badaling, the bricks, the steps, the walls and  block of  stones I saw were very solid, concrete and quite big. They must be very heavy and massive to have withstood the test of time for thousands of years.


The Wall was built since the 7th century BC. So the material used must have been very solid and very dense unlike our present bricks for modern houses. The section I saw at Badaling may have been rebuilt with big slaps of stones and huge bricks.

Even the ancient original sections must have been very heavy, non-erosive, and dense to withstand the test of time, else the entire Wall would have crumbled by now.

Some sections elsewhere were, and have been restored.  Previous sections may have been stones, boulders, fired mud with straws, and grains. We do not know for sure.


An estimate - Volume:

So it is difficult but not impossible to make an approximate mathematical construction on the density, amount, and mass of building material used.


Let us try.  Let us try using current building bricks we know better.


The density of bricks varies in their composition. Let us take 3 different types to compare.  The common red brick has a density of 1,922 kg / cubic metre, magnesia brick is 2,563 kg / cubic metre, whereas the fire clay brick is 2,403 kg / cubic metres.

Since we do not know the composition of the different bricks, stone, clay, maybe mud and straw as well to build the Great Wall, let us take the average of 3 samples of bricks from above. Their average density works out to be 2,296 kg per cubic metres.

This of course is far too small a sample number to be representative of the population of bricks. But this is the best data available for us for the purpose of this article. We can use them as test models.

But since the calculated volume of the entire Great Wall is estimated to be 827,000,000 cubic metres, the total weight would be:

 Density x volume = 2296 x 827,000,000 = 1.9 x 1012 kg or 1.9 x 109 metric tons or nearly 2,000 million metric tons.


The number of bricks:

Taking measurements of various bricks available, a single brick has a dimension of:

2 1/4" x 4" x 8" (0.05715 m x 0.1016 m x 0.2032 m) = 1.181 x 10-3 cubic metres per brick.
(1 inch = 0.0254 metre)


Since the volume of the entire Wall is about 827,000,000 cubic metres

It will require   827,000,000 / 1.181 x 10-3 = 7 x 10 11 standard size bricks to reconstruct the Wall using modern size bricks.  


That’s 700,000 million bricks all in by today’s standard.


Marvelous work of Engineering:


That was a horrendous weight of materials and also numbers used to construct the Great Wall of China. I just do not know how the ancient Chinese did that? 


This is completely awesome for anyone to think about even today! I completely salute to their toils, lives lost, and their great sufferings building that Wall winding all over the treacherous, inaccessible and high mountains over thousands of kilometers.
This Great Wall of China is truly one of the unexplained wonders of this world even by today’s technology.

An Analogy in Molecular Genetics:


I think the easiest way to explain or to understand whether or not the Great Wall of China as the only man-made structure that can be seen by the naked eyes from the Moon or from space as astronauts claimed, is not by using the combination of mathematics and the physiology of vision illustrated here, but to use molecular genetics as an analogy.

Let us visualize a single cell that represents this Earth that can just be seen by the naked eyes from space. Let the nucleus in the cell represent China, which is quite a large country on Earth. Obviously, we can only just see the cell (Earth), but not the nucleus (China) using the naked eyes.

But within the nucleus are long stretches of 23 pairs of chromosomes which represent the various sections of the Great Wall of China that can only be visible through a microscope.  That represents the visibility of the Great Wall through a telescope from the Moon.

However, within the Great Wall are the bricks, the stones and the mansions (watch towers) that make up the Great Wall. These are bases, the nucleotides and the genes (watch towers) along the sequence of DNA placed at intervals. These represent what we see along the length of the Wall at close-up.   

Obviously, we cannot see these proteins and the bases that make up the nucleotides of the DNA under microscope as much as we cannot see the individual bricks and building stones or the watch towels (genes) placed at intervals along the length of the Great Wall by using a telescope seen from the Moon.

In short, we can only see the length of the Great Wall, but not the individual stones and watch towers as much as we cannot expect to see the building blocks and genes of the chromosomes using a microscope.

 Conclusion:


The International Space Station is in a low Earth orbit (LEO) that varies from 320 km (199 mi) to 400 km (249 mi) above the Earth's surface. 


In which case, the mathematical calculations and the physiology of human vision tells me,  the Great Wall of China theoretically can never be seen even from an LEO satellite – not  even as an entire Wall.


The only exception is when the entire Great Wall of China were be made into a huge Square, or as a huge Ball of Wall. But that is not possible.
I am terribly surprised that NASA astronauts and Chinese astronauts both from two remaining superpowers, both with highly advanced Science and Technology need to argue about its visibility.

Maybe the American and Chinese astronauts were confused and were hallucinating in space under hypoxic environments? That, may be a possibility?


My simple conclusion is based on simple mathematics and physiology. Mathematics is logic to derive facts and figures, and facts and figure do not lie.


Mathematics is the Queen of Science, and Physiology is Queen of Medicine.


None of them lie.

3 comments:

Unknown said...

In first making your argument, you claim that American astronauts claim that The Great Wall can be seen from space, while also claiming that Chinese cosmonauts have correctly disputed this. However, deeper into the argument you make, you show that other American astronauts have disputed the claims of those who have claimed to see The Great Wall from space. From what I've read, most American astronauts have disputed the claims of being able to see The Great Wall from space, and many of those who claimed to see The Great Wall later recanted their claim after realizing they were mistaken. Making such enthnocentric, racist claims is silly and irrelevant to the topic.

Dr Bary T Birch said...

A highly analytical reductionist explanation just by using mathematics combined with the physiology of vision without even the need to be an astronaut on the moon. Very convincing with lots of scientific sense and logical, even to the extent of using molecular biology to illustrate. Fascinating!

Dr RT Cameron said...

Amazing explanation from a great scientific mind. Yes, I too agree we cannot see the Great Wall of China from the Moon based on your logical analysis

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