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.
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:
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.
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!
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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