How Much of the Earth Can You See at Once?

hey vauce Michael here

and here I am the real Michael

this Michael was created by a brilliant young man named Mitchell who brought it

to me at a meet and greet after brain candy live it is

phenomenal and obviously the most handsome

Jack in the Box

ever Everest is a Mountain

that's 8.84 km tall

its size is impressive

or is it let's cut Earth

the entire planet right in half straight through Everest

and then start zooming out

as you can see

Everest's monumentality quickly disappears

against Earth's planetary ginor

mity compared to Earth's diameter

Everest in fact all of Earth's

ruggedness early registers now that can seem surprising

since we're often surrounded by diagrams

and maps and globes

that exaggerate Earth's topography

now there's a good reason to do that but it leads to a misconception

about just how smooth

Earth is here's a typical example

a cross-section of the United States that I found on Reddit

the vertical axis spans about 10,000

ft but the horizontal

axis represents nearly 14

million stretched to the same same scale

so as to mirror

reality the actual smoothness

of the earth becomes apparent

on this 1T diameter Globe

Everest is a bump

about 2 mm High

feels good but if the Earth was actually this small

Everest would be a bump

only a fifth of a millimeter

high it's 10 times taller

than it should be

only 24 people have seen

the Earth with their own eyes

as a Sur CLE

small enough to be looked right at

not as the whole world

but as a little thing

suspended alone in Space

the further away you are from a ball

the more of its surface you can see

now we don't always notice this because in our day-to-day lives most of the

balls we deal with are so small

they're almost always many of their own radi

away from us and the available

amount of their surface visible is near a maximum

or they're so big

like the Earth that we rarely get far enough away fast enough to notice

this property but the next time you're near a ball

get close to it

you'll see that as you get nearer

more of its surface

disappears behind the Horizon

but moving back up will make it available

again for most of us stuck our whole lives on Earth's surface

such an experience is

impossible with nothing around to block your view

5 km about 3 Mi

is about the furthest you can see

now Haze can limmit your view and Atmospheric

refraction can slightly extend it but for the most part everything you can see

happens within an area of just 80

Square km that's not bad

but it's tiny compared

with what there is to see

the higher up you go of course the further away you'll be able to

see that's why it's great to be a satellite

here's the International Space

Station yeah look at that nice big portion of the surface in view

unfortunately this isn't to scale

if the Earth were the size of an apple

how far away would the International

Space Station orbit like this far away

maybe this far away

maybe this far away

actually it orbits here

2.7 mm above the surface

that's how far the stem of this apple sticks up

that's not very far

oh here's another fun little two-scale

fact if the Earth were the size of an apple

your eyeball would be about the size of the

Moon we often imagine that from the International

Space Station astronauts see the Earth

like this but they're just not that far away

from where they actually orbit

International Space Station residents only see about 3%

of Earth's surface at any one time

and that 3% is too wide

to all fit within a window

when I was in Pittsburgh

their Science Museum had a mockup of part of the ISS

and as you can see see out of the window

Earth is still quite expansive

using special lenses images can be taken from the ISS

that look like circular

disc Earths But the lens is distorting

things here it's fitting much more into the picture in order to truly witness

Earth's entire shape with your own eyes

you would need to either

smash your face right up against a window or just be floating outside the

station and even then

you would have to move your head

to see from edge

to edge so how high up do you have to go to see the

edges of Earth all at once

and even if you did that

how much would you actually

see how much is there

to see earth is made

of stuff lots of stuff water and dirt and rocks and air all of

which are composed of atoms

tiny things so teeny

that a single drop of water

contains not a million

atoms not a billion at atoms

or a trillion or a quadrillion

or a quintilian but

five sextilion atoms earth

is made of even more stuff

not a septian atoms not an ocan

nonillion desan unilan dood deilan trillian

not even a quat turo deilan

but 100 Quin deilan

atoms but since we live

only on the surface

of our planet we unfortunately

can can't see most of those atoms

if the Earth was shaped

like a disc or an

icosahedron or say a

cube or a rectangular

prism or two stellated

rhombic do decahedrons we could see more of the earth than we normally

can but as things are we actually see

nearly the least of Earth's matter

possible because of all solids

a sphere which the Earth approximately

is has the smallest

surface area to volume ratio

the most stuff inside

and the least stuff

outside so how many of these 10 to the 50 atoms that make up

Earth are on the surface for us to see

that's not an easy question

for one thing technically

atoms on the surfaces of opaque things

like rocks and dirt

aren't the only Parts

involved in their appearances

subsurface scattering can and does

happen regardless attempting even a rough

approximation is Illuminating I asked Grant

from the YouTube channel three blue one brown

for some help and he pointed out

that if you calculate the number of circles

with atom-sized radi that could

packed optimally cover a sphere

with the surface area of Earth you get about 1.5

* 10 to 34

that's a lot of atoms

but then he pointed out that the Earth's

surface isn't smooth its roughness

provides extra surface area for atoms to occupy

without a complete description of the shape of Earth's surface

Every Mountain and Valley

every bump on every rock

this is just going to be hopeless

right well here's the thing

earth is made of little

rugged shapes that from far away

make big rugged shapes

in other words Earth's

surface can be described

as a fractal there's a regular

ity to its roughness

in fact mathematicians have even assigned a fractal

Dimension to Earth's 2.3

now to see what that means

I highly recommend Grant's video on fractal

Dimensions it's fascinating using

2.3 and assuming that it applies

from the scale of a human hair up to that of a mountain

Grant found that the number of atoms

on Earth's surface changes

significantly up from a power of 34

to a power of

37 that's a thousand

times more atoms so

maybe we shouldn't count Earth's roughness out just yet

it's smooth but not perfectly

to put that number in perspective

the human body contains

about 10 to the 27

atoms that's 10 power of 10

less than the surface of the Earth

10 power of 10 is 10 billion

there are about 7 and2 billion humans humans

so more or less

it can be said

that there are the same

number of atoms in every human body right now

as there are on the surface

of the Earth as I've shown before

all human bodies piled into one place

would barely even fill the Grand Canyon

but all human atoms

spread across the Earth

would almost perfectly cover it just one atom

deep fun fact fact the mass of the atmosphere

is about 2.5% less

than what you would get by multiplying

sea level pressure 14.7

lb per square inch

by the surface area of the Earth

because Earth's terrain displaces

about that much air

earth's surface is pretty cool

obviously I mean it's got lyen

and monster trucks and an island

in a lake on an island

in a lake on an island

but from down here on its surface

we just can't see that much of it your view of Earth is obstructed

by lots of opaque things

walls buildings trees rocks

terrain if Earth was flat

you could see further

but sorry it's a

rough world out there

or is it if you could hold the Earth in your hands

like this how bumpy

would it actually feel

we already saw that even our planet's biggest bumps barely register

relative to Earth's size

but let's go somewhere famously

flat where relative to our size

terrain rarely gets in the way of seeing lots of the planet

the US state of

Kansas I grew up here and took this footage while driving across the state

last year you can probably see why Kansas is often called

flatter than a pancake

however although it is famously

flat Kansas is not

the flattest US state

in a fantastic piece of research

Jerome Dobson and Joshua Campbell

defined looks flat like this

if from a given point

any part of the terrain

within the Horizon Rises more than

0.32 de up about the height of a 30 m Hill at the Horizon

a typical person would say

well hey that part's not flat

by cleverly applying this rule to topographical

data they were able to give every

state a FL flatness

score West Virginia was the least

flat Kansas was only the seventh

flattest Delaware Minnesota Louisiana

North Dakota and Illinois

are all by this method

flatter than Kansas as was the number one flattest

state Florida Adam Savage and I had the pleasure of visiting Florida with our

brain candy live show this year

and as this footage from a top the King Center in Melbourne Florida shows

it's pretty gosh dang

flat now even though Kansas

is not the flattest

it is the state most often ranked flattest when the general population is asked

it is truly scientifically

flatter than a pancake it's been demonstrated

but there's more to the story than that

in 2003 researchers took a 130

mm wide pancake procured from IHOP

and analyzed its local reliefs

they found the difference between high and low points was on the order of

about 2 mm if a typical pancake

like this was the size of Kansas

5 million times larger

2 mm High Peaks

would be 10 km

high mountains in comparison

Mount Everest is only about 8.8

km tall and Earth's

deepest Scar the marianus

trench is thought to be just under 11

km deep so not only

is Kansas about as smooth as a pan Pake

but so is every other state in the Union

and so is the entire

world if you were a giant

holding the planet in your hands like this

you and it would be torn apart by the immense tidal forces created by

your gravities if somehow you could avoid that though the planet would feel

not much rougher than running your hands

over a pancake but a soggy one right I mean

most of Earth's surface is covered

in water your hand would get

wet or would they

yes Earth is covered

in liquid but the depth

of that liquid like the mountains above just doesn't compare to the total

size of the planet

as it turns out

if the Earth was the size of a typical classroom

Globe like this one 1T

in diameter the volume of water

contained in above and on it

would only be about

14 ml that's this much water

it's kind of hard to believe because at this scale

spreading this much water across all of the ocean surfaces

would be pretty much impossible due to surface tension

but this is it

all of Earth's water

compared to all of Earth

90% of the space on our planet life can live in

is in here the other 10%

is dry land so no

you wouldn't get wrinkly fingers playing with an earth like this

you could sop it dry just with a paper

towel despite the incredible

area oceans cover on our planet

their depth is just nothing compared to the size

of our entire planet

now you may have heard it said that if the entire planet

were shrunk down to the size of a billiard ball

it would be smoother

than a billiard ball

after all we've seen so far that seems believable

but as it turns out

it's not true the misconception

stems from the interpretation

of the world pool Billiard

Association rules now according to them a ball must have a diameter

of 2.25 in plus or minus

5,000 of an inch

now some writers have taken this to mean

that pits and bumps

of 5,000 of an inch are allowed

proportionately on Earth that would mean a mountain that was 28

km high so since Earth has none of those

Earth must be smoother than a billiard ball

except if bumps that high were actually allowed on a pool ball

a ball covered with 120

grit sandpaper would be within regulation

clearly the 5000's rule is more about

roundness deviation from a sphere

and not texture in fact as microscopic

photography has shown imperfections

on regulation balls are only

one 100,000th of an inch or about half a micrometer

deep and high scaled down to the size of a billiard ball

Earth's Maring onest trench

would be 49 microm

deep so Earth is smoother

than a pancake but not

smoother than a billiard ball

nor as XKCD wonderfully showed

is Earth smoother than a bowling

ball but hold on

earlier we were using the word flat

now we're using the word

smooth that distinction is important

you see the Earth

isn't flat like a plane

instead it curves it's

a ball pieces of earth

like Kansas might be quite smooth

but they curve along with Earth

if you were to stand in the middle of Kansas

people on the Eastern or Western edges of the state would appear to be

not level with you

but about 8.1 km

below you that's nearly the height of Everest

and if they stood straight up

they'd be tilted nearly

2° relative to where you thought

up was now here's an interesting coincidence

generally speaking 1 mile from where you are

Earth curves down about 8

in 1 kilometer from where you stand

it curves down about 8

cm now the rate of drop due to curvature

isn't a linear one you can't just multiply

any Distance by eight to get the drop due to curvature

instead use an online calculator

like the one I've linked down in this video's description you can put in

any distance you want

anyway the visibility limit caused by Earth's curvature

is your horizon it encircles

you like a visual

cage but it's a cage

whose radius is determined

by how high up

your eyes are Conan O'Brien

at 6' 4 in tall

can see up to 5 km

in any direction but Snookie

at 48 can only see about 4.3

to find out how far away your horizon

is geometrically just use the online tools I've put down in the description

below Earth's texture can get in the way of your horizon

but can also cause things Beyond the Horizon to Peak into view

hey what's that.com factors all of this in

now if Earth was a smooth

sphere the view from a top Ben Nevis

the highest mountain in the British Isles

would end at the Horizon

131 km away about 80 mil

such an area would look like this

but factoring in Earth's ups and downs

here's a more precise boundary

of what you can see

lock TG Scottish gelic for Lake of death

is only about 10 miles from the peak

that's within an 80 M radius

but it can't be seen

because Terrain in the way

blocks it parts of the Atlantic

Ocean and the North Sea eight times further away can be seen

they lie at the limit of Earth's curvature

just before it bends the surface out of

sight these spikes extending

beyond the geometric Horizon are caused by things Beyond it that are tall enough

to Peak above Earth's curvature

in the case of Ben nevas

this includes high elevation parts of Northern

Ireland okay enough about the surface and what it's like close up let's go

further away and see more this will be fun

but there will be a trade-off

the further away you are from something

the smaller it will appear to be be

moving away from Earth will make more area available to see but that area

will take up less

of your field of view

it can be difficult to illustrate

this in a YouTube video because

your field of view the shape and size of what you can see with

your head still just by

moving your eyes around

is 120° up and down

and more than 180°

horizontal a screen is just a window

of that space nowhere close to filling it unless you get uncomfortably

close to help us visualize

large apparent sizes let's replace

the spherical Earth with a flat

disc that's always the same distance

from The Observer this disc can be given an apparent size equal to Earth's

from any altitude and the disc can contain

on it everything that would fit within your horizons

from any altitude okay so standing

on the surface looking straight down

Earth will take up nearly a full

180° of your field of view

with your arms extended

straight out parallel to Earth your fingers will point to the edges of the

planet Your Horizon from 400

km up about where the ISS orbits

3% of the earth's surface is within your horizon

but the Earth will only take up about

140° of your vision

your fingers would point to Earth's edges if you narrowed your arms angles

each by the width of two outstretched

fists one fist is about 10°

across at arms length

now you can move your eyes from edge to edge horizontally

here but you can't quite take in the full width

vertically but from more than twice this altitude

1,000 km away Earth is only

120° across that's one less fist width each

this is perfect that fits within our narrower

vertical field of view so

from 1,000 km up about 62

20 mes you can just start to see Earth

as a complete disc

right in front of you at once

however only 7% of Earth fits within the Horizon from up here

images of Earth taken by satellites

this far up like the suami

NPP look kind of weird

I mean North America doesn't actually take up this much

of the globe Earth's

120° width has been compressed

to fit in an image much

narrower compare Africa from its height to the famous Blue Marble picture taken from

45,000 km away the ladder

looks more realistic like looking at a globe

on your desk geosynchronous

satellites are about 35,000

km high from their altitude

43.4% nearly a whole half

of earth's surface is visible but the Earth only takes up a meager

17° you could completely

cover it with two outstretched

Palms that's incredible but what about from the Moon

well from that far away

Earth is only about

2° across you could block it out

with your out stretched

thumb however you can see

more of Earth you can see further around its curvature

from the Moon 49%

of earth's surface is

visible just 49 if you want to see

50 half of Earth's

surface at once you have to go even further

away in fact you have to go

infinitely far away which you can't

the most of a sphere you can see at once with your own eyes

is just half but in the real world

way before you were actually

infinitely far away the amount of light reaching you from Earth's surface would become

so small and infrequent

that you wouldn't be able to see anything at all

stars like our sun are

much brighter and bigger than the earth

but only a handful

have even with our best technology

been resolved as anything

larger than just a single

point from 1,000th of a lightyear away

our own Sun would look like every other star in the sky

a single point to the naked eye

only about as wide as our duratus

the widest star in our sky

from 91 light years away

the point of our sun

would dim to a level

undetectable by the naked eye

it would disappear most of the stars in the night sky you can see

with your naked eye are further away than that

we can see them though because they're brighter

and bigger than our own sun

which means if there's life out there

living in systems around the Stars we've marveled at

and written stories about since Humanity

began chances are we

are not part of their constellations

or folklore we're a dark patch in the sky

them an ignorable emptiness

framing other stars the ones they Marvel

at while not knowing

we're here or that there's anything

here and as always

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oh and this Vsauce

shirt is only available

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the Curiosity box is good for all

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research I'm incredibly proud of it but what's going on on this shirt

well it's modular multiplication

around a circle we have the numbers 1 to 40

around the outside of a circle connected to their product

with the number four

so one is connected

to four two is connected to 8 3 is connected to 12 and so

on even past 40

you can keep Imagining

the numbers continuing for instance 1 can become 41

two can become 42

and this emerges the Vsauce

V many other shapes can be made by using different multipliers

or different numbers around

the circle mathal logger has a fantastic

video on this topic which you should check out I've linked it down in

the description thank you

for being curious and as always thanks for watching