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How Much of the Earth Can You See at O… — Vsauce shadowing | TryShadowing
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Vsauce
How Much of the Earth Can You See at Once?
How Much of the Earth Can You See at Once?
Vsauce
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26:31 · Jul 17, 2017
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hey
vauce
Michael
here
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1
/590
0:11
hey vauce Michael here
0:13
and here I am the real Michael
0:16
this Michael was created by a brilliant young man named Mitchell who brought it
0:19
to me at a meet and greet after brain candy live it is
0:23
phenomenal and obviously the most handsome
0:26
Jack in the Box
0:27
ever Everest is a Mountain
0:30
that's 8.84 km tall
0:33
its size is impressive
0:36
or is it let's cut Earth
0:39
the entire planet right in half straight through Everest
0:43
and then start zooming out
0:45
as you can see
0:46
Everest's monumentality quickly disappears
0:50
against Earth's planetary ginor
0:53
mity compared to Earth's diameter
0:56
Everest in fact all of Earth's
0:58
ruggedness early registers now that can seem surprising
1:02
since we're often surrounded by diagrams
1:04
and maps and globes
1:06
that exaggerate Earth's topography
1:08
now there's a good reason to do that but it leads to a misconception
1:11
about just how smooth
1:13
Earth is here's a typical example
1:16
a cross-section of the United States that I found on Reddit
1:20
the vertical axis spans about 10,000
1:23
ft but the horizontal
1:25
axis represents nearly 14
1:27
million stretched to the same same scale
1:30
so as to mirror
1:31
reality the actual smoothness
1:34
of the earth becomes apparent
1:35
on this 1T diameter Globe
1:38
Everest is a bump
1:39
about 2 mm High
1:42
feels good but if the Earth was actually this small
1:45
Everest would be a bump
1:47
only a fifth of a millimeter
1:49
high it's 10 times taller
1:52
than it should be
1:54
only 24 people have seen
1:57
the Earth with their own eyes
1:59
as a Sur CLE
2:00
small enough to be looked right at
2:02
not as the whole world
2:04
but as a little thing
2:06
suspended alone in Space
2:08
the further away you are from a ball
2:11
the more of its surface you can see
2:13
now we don't always notice this because in our day-to-day lives most of the
2:17
balls we deal with are so small
2:19
they're almost always many of their own radi
2:22
away from us and the available
2:24
amount of their surface visible is near a maximum
2:27
or they're so big
2:29
like the Earth that we rarely get far enough away fast enough to notice
2:33
this property but the next time you're near a ball
2:37
get close to it
2:38
you'll see that as you get nearer
2:40
more of its surface
2:42
disappears behind the Horizon
2:44
but moving back up will make it available
2:47
again for most of us stuck our whole lives on Earth's surface
2:52
such an experience is
2:53
impossible with nothing around to block your view
2:57
5 km about 3 Mi
2:59
is about the furthest you can see
3:01
now Haze can limmit your view and Atmospheric
3:03
refraction can slightly extend it but for the most part everything you can see
3:07
happens within an area of just 80
3:09
Square km that's not bad
3:12
but it's tiny compared
3:13
with what there is to see
3:16
the higher up you go of course the further away you'll be able to
3:18
see that's why it's great to be a satellite
3:22
here's the International Space
3:23
Station yeah look at that nice big portion of the surface in view
3:28
unfortunately this isn't to scale
3:31
if the Earth were the size of an apple
3:34
how far away would the International
3:35
Space Station orbit like this far away
3:39
maybe this far away
3:40
maybe this far away
3:43
actually it orbits here
3:46
2.7 mm above the surface
3:49
that's how far the stem of this apple sticks up
3:53
that's not very far
3:55
oh here's another fun little two-scale
3:57
fact if the Earth were the size of an apple
4:00
your eyeball would be about the size of the
4:03
Moon we often imagine that from the International
4:06
Space Station astronauts see the Earth
4:09
like this but they're just not that far away
4:12
from where they actually orbit
4:14
International Space Station residents only see about 3%
4:18
of Earth's surface at any one time
4:21
and that 3% is too wide
4:23
to all fit within a window
4:25
when I was in Pittsburgh
4:26
their Science Museum had a mockup of part of the ISS
4:28
and as you can see see out of the window
4:31
Earth is still quite expansive
4:33
using special lenses images can be taken from the ISS
4:37
that look like circular
4:38
disc Earths But the lens is distorting
4:41
things here it's fitting much more into the picture in order to truly witness
4:44
Earth's entire shape with your own eyes
4:46
you would need to either
4:47
smash your face right up against a window or just be floating outside the
4:51
station and even then
4:52
you would have to move your head
4:54
to see from edge
4:56
to edge so how high up do you have to go to see the
5:01
edges of Earth all at once
5:04
and even if you did that
5:06
how much would you actually
5:08
see how much is there
5:11
to see earth is made
5:14
of stuff lots of stuff water and dirt and rocks and air all of
5:19
which are composed of atoms
5:21
tiny things so teeny
5:23
that a single drop of water
5:25
contains not a million
5:27
atoms not a billion at atoms
5:30
or a trillion or a quadrillion
5:32
or a quintilian but
5:35
five sextilion atoms earth
5:39
is made of even more stuff
5:40
not a septian atoms not an ocan
5:43
nonillion desan unilan dood deilan trillian
5:46
not even a quat turo deilan
5:49
but 100 Quin deilan
5:53
atoms but since we live
5:55
only on the surface
5:57
of our planet we unfortunately
5:59
can can't see most of those atoms
6:02
if the Earth was shaped
6:03
like a disc or an
6:05
icosahedron or say a
6:08
cube or a rectangular
6:11
prism or two stellated
6:15
rhombic do decahedrons we could see more of the earth than we normally
6:19
can but as things are we actually see
6:22
nearly the least of Earth's matter
6:25
possible because of all solids
6:28
a sphere which the Earth approximately
6:30
is has the smallest
6:32
surface area to volume ratio
6:34
the most stuff inside
6:36
and the least stuff
6:38
outside so how many of these 10 to the 50 atoms that make up
6:42
Earth are on the surface for us to see
6:45
that's not an easy question
6:47
for one thing technically
6:48
atoms on the surfaces of opaque things
6:51
like rocks and dirt
6:52
aren't the only Parts
6:54
involved in their appearances
6:56
subsurface scattering can and does
6:58
happen regardless attempting even a rough
7:02
approximation is Illuminating I asked Grant
7:06
from the YouTube channel three blue one brown
7:08
for some help and he pointed out
7:10
that if you calculate the number of circles
7:13
with atom-sized radi that could
7:15
packed optimally cover a sphere
7:18
with the surface area of Earth you get about 1.5
7:21
* 10 to 34
7:24
that's a lot of atoms
7:26
but then he pointed out that the Earth's
7:28
surface isn't smooth its roughness
7:31
provides extra surface area for atoms to occupy
7:34
without a complete description of the shape of Earth's surface
7:37
Every Mountain and Valley
7:39
every bump on every rock
7:41
this is just going to be hopeless
7:43
right well here's the thing
7:46
earth is made of little
7:48
rugged shapes that from far away
7:51
make big rugged shapes
7:53
in other words Earth's
7:55
surface can be described
7:57
as a fractal there's a regular
7:59
ity to its roughness
8:01
in fact mathematicians have even assigned a fractal
8:04
Dimension to Earth's 2.3
8:09
now to see what that means
8:10
I highly recommend Grant's video on fractal
8:13
Dimensions it's fascinating using
8:17
2.3 and assuming that it applies
8:19
from the scale of a human hair up to that of a mountain
8:22
Grant found that the number of atoms
8:24
on Earth's surface changes
8:26
significantly up from a power of 34
8:29
to a power of
8:31
37 that's a thousand
8:33
times more atoms so
8:36
maybe we shouldn't count Earth's roughness out just yet
8:39
it's smooth but not perfectly
8:42
to put that number in perspective
8:44
the human body contains
8:45
about 10 to the 27
8:47
atoms that's 10 power of 10
8:51
less than the surface of the Earth
8:54
10 power of 10 is 10 billion
8:57
there are about 7 and2 billion humans humans
9:00
so more or less
9:03
it can be said
9:04
that there are the same
9:05
number of atoms in every human body right now
9:10
as there are on the surface
9:12
of the Earth as I've shown before
9:15
all human bodies piled into one place
9:18
would barely even fill the Grand Canyon
9:21
but all human atoms
9:22
spread across the Earth
9:24
would almost perfectly cover it just one atom
9:28
deep fun fact fact the mass of the atmosphere
9:31
is about 2.5% less
9:34
than what you would get by multiplying
9:36
sea level pressure 14.7
9:39
lb per square inch
9:40
by the surface area of the Earth
9:42
because Earth's terrain displaces
9:44
about that much air
9:46
earth's surface is pretty cool
9:49
obviously I mean it's got lyen
9:51
and monster trucks and an island
9:54
in a lake on an island
9:57
in a lake on an island
9:59
but from down here on its surface
10:01
we just can't see that much of it your view of Earth is obstructed
10:05
by lots of opaque things
10:06
walls buildings trees rocks
10:09
terrain if Earth was flat
10:11
you could see further
10:13
but sorry it's a
10:15
rough world out there
10:19
or is it if you could hold the Earth in your hands
10:23
like this how bumpy
10:25
would it actually feel
10:27
we already saw that even our planet's biggest bumps barely register
10:31
relative to Earth's size
10:33
but let's go somewhere famously
10:34
flat where relative to our size
10:37
terrain rarely gets in the way of seeing lots of the planet
10:41
the US state of
10:44
Kansas I grew up here and took this footage while driving across the state
10:48
last year you can probably see why Kansas is often called
10:52
flatter than a pancake
10:54
however although it is famously
10:56
flat Kansas is not
10:58
the flattest US state
11:00
in a fantastic piece of research
11:02
Jerome Dobson and Joshua Campbell
11:04
defined looks flat like this
11:07
if from a given point
11:09
any part of the terrain
11:10
within the Horizon Rises more than
11:13
0.32 de up about the height of a 30 m Hill at the Horizon
11:19
a typical person would say
11:20
well hey that part's not flat
11:22
by cleverly applying this rule to topographical
11:25
data they were able to give every
11:27
state a FL flatness
11:30
score West Virginia was the least
11:34
flat Kansas was only the seventh
11:37
flattest Delaware Minnesota Louisiana
11:40
North Dakota and Illinois
11:41
are all by this method
11:43
flatter than Kansas as was the number one flattest
11:47
state Florida Adam Savage and I had the pleasure of visiting Florida with our
11:53
brain candy live show this year
11:55
and as this footage from a top the King Center in Melbourne Florida shows
11:59
it's pretty gosh dang
12:01
flat now even though Kansas
12:03
is not the flattest
12:05
it is the state most often ranked flattest when the general population is asked
12:10
it is truly scientifically
12:12
flatter than a pancake it's been demonstrated
12:14
but there's more to the story than that
12:17
in 2003 researchers took a 130
12:20
mm wide pancake procured from IHOP
12:23
and analyzed its local reliefs
12:25
they found the difference between high and low points was on the order of
12:28
about 2 mm if a typical pancake
12:31
like this was the size of Kansas
12:34
5 million times larger
12:36
2 mm High Peaks
12:38
would be 10 km
12:40
high mountains in comparison
12:42
Mount Everest is only about 8.8
12:45
km tall and Earth's
12:47
deepest Scar the marianus
12:49
trench is thought to be just under 11
12:52
km deep so not only
12:56
is Kansas about as smooth as a pan Pake
12:59
but so is every other state in the Union
13:02
and so is the entire
13:05
world if you were a giant
13:08
holding the planet in your hands like this
13:11
you and it would be torn apart by the immense tidal forces created by
13:14
your gravities if somehow you could avoid that though the planet would feel
13:19
not much rougher than running your hands
13:21
over a pancake but a soggy one right I mean
13:25
most of Earth's surface is covered
13:28
in water your hand would get
13:30
wet or would they
13:33
yes Earth is covered
13:35
in liquid but the depth
13:37
of that liquid like the mountains above just doesn't compare to the total
13:41
size of the planet
13:43
as it turns out
13:44
if the Earth was the size of a typical classroom
13:46
Globe like this one 1T
13:48
in diameter the volume of water
13:51
contained in above and on it
13:54
would only be about
13:56
14 ml that's this much water
14:02
it's kind of hard to believe because at this scale
14:04
spreading this much water across all of the ocean surfaces
14:07
would be pretty much impossible due to surface tension
14:10
but this is it
14:12
all of Earth's water
14:14
compared to all of Earth
14:17
90% of the space on our planet life can live in
14:21
is in here the other 10%
14:23
is dry land so no
14:25
you wouldn't get wrinkly fingers playing with an earth like this
14:29
you could sop it dry just with a paper
14:31
towel despite the incredible
14:33
area oceans cover on our planet
14:36
their depth is just nothing compared to the size
14:39
of our entire planet
14:42
now you may have heard it said that if the entire planet
14:44
were shrunk down to the size of a billiard ball
14:47
it would be smoother
14:49
than a billiard ball
14:51
after all we've seen so far that seems believable
14:53
but as it turns out
14:54
it's not true the misconception
14:57
stems from the interpretation
14:58
of the world pool Billiard
14:59
Association rules now according to them a ball must have a diameter
15:04
of 2.25 in plus or minus
15:07
5,000 of an inch
15:09
now some writers have taken this to mean
15:11
that pits and bumps
15:13
of 5,000 of an inch are allowed
15:15
proportionately on Earth that would mean a mountain that was 28
15:20
km high so since Earth has none of those
15:23
Earth must be smoother than a billiard ball
15:26
except if bumps that high were actually allowed on a pool ball
15:31
a ball covered with 120
15:33
grit sandpaper would be within regulation
15:36
clearly the 5000's rule is more about
15:39
roundness deviation from a sphere
15:42
and not texture in fact as microscopic
15:45
photography has shown imperfections
15:47
on regulation balls are only
15:49
one 100,000th of an inch or about half a micrometer
15:54
deep and high scaled down to the size of a billiard ball
15:58
Earth's Maring onest trench
16:00
would be 49 microm
16:02
deep so Earth is smoother
16:06
than a pancake but not
16:08
smoother than a billiard ball
16:10
nor as XKCD wonderfully showed
16:13
is Earth smoother than a bowling
16:15
ball but hold on
16:17
earlier we were using the word flat
16:19
now we're using the word
16:22
smooth that distinction is important
16:24
you see the Earth
16:25
isn't flat like a plane
16:29
instead it curves it's
16:32
a ball pieces of earth
16:35
like Kansas might be quite smooth
16:39
but they curve along with Earth
16:41
if you were to stand in the middle of Kansas
16:44
people on the Eastern or Western edges of the state would appear to be
16:48
not level with you
16:50
but about 8.1 km
16:52
below you that's nearly the height of Everest
16:56
and if they stood straight up
16:57
they'd be tilted nearly
16:59
2° relative to where you thought
17:01
up was now here's an interesting coincidence
17:04
generally speaking 1 mile from where you are
17:08
Earth curves down about 8
17:11
in 1 kilometer from where you stand
17:14
it curves down about 8
17:17
cm now the rate of drop due to curvature
17:20
isn't a linear one you can't just multiply
17:23
any Distance by eight to get the drop due to curvature
17:26
instead use an online calculator
17:28
like the one I've linked down in this video's description you can put in
17:31
any distance you want
17:33
anyway the visibility limit caused by Earth's curvature
17:36
is your horizon it encircles
17:39
you like a visual
17:40
cage but it's a cage
17:42
whose radius is determined
17:43
by how high up
17:45
your eyes are Conan O'Brien
17:47
at 6' 4 in tall
17:49
can see up to 5 km
17:52
in any direction but Snookie
17:54
at 48 can only see about 4.3
17:59
to find out how far away your horizon
18:01
is geometrically just use the online tools I've put down in the description
18:05
below Earth's texture can get in the way of your horizon
18:10
but can also cause things Beyond the Horizon to Peak into view
18:14
hey what's that.com factors all of this in
18:18
now if Earth was a smooth
18:20
sphere the view from a top Ben Nevis
18:22
the highest mountain in the British Isles
18:24
would end at the Horizon
18:26
131 km away about 80 mil
18:30
such an area would look like this
18:32
but factoring in Earth's ups and downs
18:35
here's a more precise boundary
18:37
of what you can see
18:39
lock TG Scottish gelic for Lake of death
18:43
is only about 10 miles from the peak
18:46
that's within an 80 M radius
18:48
but it can't be seen
18:49
because Terrain in the way
18:51
blocks it parts of the Atlantic
18:54
Ocean and the North Sea eight times further away can be seen
18:58
they lie at the limit of Earth's curvature
19:00
just before it bends the surface out of
19:02
sight these spikes extending
19:05
beyond the geometric Horizon are caused by things Beyond it that are tall enough
19:09
to Peak above Earth's curvature
19:11
in the case of Ben nevas
19:13
this includes high elevation parts of Northern
19:15
Ireland okay enough about the surface and what it's like close up let's go
19:20
further away and see more this will be fun
19:23
but there will be a trade-off
19:24
the further away you are from something
19:26
the smaller it will appear to be be
19:29
moving away from Earth will make more area available to see but that area
19:33
will take up less
19:34
of your field of view
19:36
it can be difficult to illustrate
19:38
this in a YouTube video because
19:40
your field of view the shape and size of what you can see with
19:44
your head still just by
19:46
moving your eyes around
19:47
is 120° up and down
19:51
and more than 180°
19:53
horizontal a screen is just a window
19:57
of that space nowhere close to filling it unless you get uncomfortably
20:02
close to help us visualize
20:04
large apparent sizes let's replace
20:06
the spherical Earth with a flat
20:08
disc that's always the same distance
20:11
from The Observer this disc can be given an apparent size equal to Earth's
20:15
from any altitude and the disc can contain
20:18
on it everything that would fit within your horizons
20:22
from any altitude okay so standing
20:25
on the surface looking straight down
20:27
Earth will take up nearly a full
20:30
180° of your field of view
20:33
with your arms extended
20:34
straight out parallel to Earth your fingers will point to the edges of the
20:38
planet Your Horizon from 400
20:42
km up about where the ISS orbits
20:45
3% of the earth's surface is within your horizon
20:48
but the Earth will only take up about
20:50
140° of your vision
20:52
your fingers would point to Earth's edges if you narrowed your arms angles
20:56
each by the width of two outstretched
20:58
fists one fist is about 10°
21:01
across at arms length
21:03
now you can move your eyes from edge to edge horizontally
21:06
here but you can't quite take in the full width
21:09
vertically but from more than twice this altitude
21:12
1,000 km away Earth is only
21:16
120° across that's one less fist width each
21:20
this is perfect that fits within our narrower
21:23
vertical field of view so
21:25
from 1,000 km up about 62
21:28
20 mes you can just start to see Earth
21:31
as a complete disc
21:33
right in front of you at once
21:34
however only 7% of Earth fits within the Horizon from up here
21:40
images of Earth taken by satellites
21:42
this far up like the suami
21:44
NPP look kind of weird
21:46
I mean North America doesn't actually take up this much
21:49
of the globe Earth's
21:51
120° width has been compressed
21:53
to fit in an image much
21:55
narrower compare Africa from its height to the famous Blue Marble picture taken from
22:00
45,000 km away the ladder
22:03
looks more realistic like looking at a globe
22:05
on your desk geosynchronous
22:08
satellites are about 35,000
22:10
km high from their altitude
22:14
43.4% nearly a whole half
22:16
of earth's surface is visible but the Earth only takes up a meager
22:21
17° you could completely
22:23
cover it with two outstretched
22:25
Palms that's incredible but what about from the Moon
22:29
well from that far away
22:30
Earth is only about
22:32
2° across you could block it out
22:35
with your out stretched
22:37
thumb however you can see
22:39
more of Earth you can see further around its curvature
22:41
from the Moon 49%
22:45
of earth's surface is
22:48
visible just 49 if you want to see
22:53
50 half of Earth's
22:55
surface at once you have to go even further
22:58
away in fact you have to go
23:01
infinitely far away which you can't
23:05
the most of a sphere you can see at once with your own eyes
23:08
is just half but in the real world
23:12
way before you were actually
23:14
infinitely far away the amount of light reaching you from Earth's surface would become
23:17
so small and infrequent
23:19
that you wouldn't be able to see anything at all
23:22
stars like our sun are
23:24
much brighter and bigger than the earth
23:26
but only a handful
23:27
have even with our best technology
23:29
been resolved as anything
23:31
larger than just a single
23:34
point from 1,000th of a lightyear away
23:37
our own Sun would look like every other star in the sky
23:41
a single point to the naked eye
23:44
only about as wide as our duratus
23:46
the widest star in our sky
23:49
from 91 light years away
23:52
the point of our sun
23:54
would dim to a level
23:55
undetectable by the naked eye
23:58
it would disappear most of the stars in the night sky you can see
24:03
with your naked eye are further away than that
24:05
we can see them though because they're brighter
24:08
and bigger than our own sun
24:10
which means if there's life out there
24:12
living in systems around the Stars we've marveled at
24:16
and written stories about since Humanity
24:19
began chances are we
24:22
are not part of their constellations
24:25
or folklore we're a dark patch in the sky
24:28
them an ignorable emptiness
24:31
framing other stars the ones they Marvel
24:34
at while not knowing
24:37
we're here or that there's anything
24:40
here and as always
24:43
thanks for watching if you don't follow me on Twitter or
25:01
Instagram you are missing out on a treasure
25:04
Trove of Premium content
25:08
so check that out
25:09
and know this I love you
25:13
oh and this Vsauce
25:15
shirt is only available
25:17
to curiosity box subscribers
25:19
this shirt comes in the latest
25:21
box if you sign up now
25:23
you will get this shirt
25:24
so long as you sign up before it sells out
25:26
the Curiosity box is good for all
25:29
brains it comes to your door four times a year
25:33
full of science gear and toys that I want you to have I want
25:36
you to hold and learn from
25:38
also a portion of the proceeds from every box goes to alzheimer's
25:42
research I'm incredibly proud of it but what's going on on this shirt
25:46
well it's modular multiplication
25:49
around a circle we have the numbers 1 to 40
25:52
around the outside of a circle connected to their product
25:55
with the number four
25:57
so one is connected
25:58
to four two is connected to 8 3 is connected to 12 and so
26:01
on even past 40
26:03
you can keep Imagining
26:04
the numbers continuing for instance 1 can become 41
26:07
two can become 42
26:09
and this emerges the Vsauce
26:12
V many other shapes can be made by using different multipliers
26:16
or different numbers around
26:17
the circle mathal logger has a fantastic
26:20
video on this topic which you should check out I've linked it down in
26:23
the description thank you
26:25
for being curious and as always thanks for watching
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