How Much of the Earth Can You See at Once?

published on July 12, 2020

Hey, Vsauce, Michael hereAnd here, I am the real MichaelThis Michael was created by a brilliant young man named Mitchell,who brought it to me at a meet-and-greet after Brain Candy LiveIt is phenomenal and obviously the most handsome jack-in-the-box everEver-est is a mountain that's 8848 km tallIts size is impressive

Or is it?(Characteristic music of Vsauce, get prepared to be mind = blown)Let's cut Earth, the entire planet, right in half,straight through Everest, and then start zooming outAs you can see, Everest's monumentality quickly disappears against Earth's planetary ginormosityCompared to Earth's diameter

Everest—in fact, all of Earth's ruggedness—barely registersThat can seem surprising, since we are often surrounded by diagrams and maps and globesthat exaggerate Earth's topographyThere is a good reason to do that,but it leads to a misconception about just how smooth Earth isHere's a typical example:

A cross section of the United States that I found on redditThe vertical axis spans about 10,000 ft,but the horizontal axis represents nearly 14 million ftStretched to the same scale so as to mirror reality,the actual smoothness of the Earth becomes apparentOn this 1 ft diameter globe,

Everest is a bump about 2 mm highFeels good!But if the Earth was actually this small,Everest would be a bump only 02 mm highIt's 10 times taller than it should beOnly 24 people have seen the Earth, with their own eyes, as a circle small enough to be looked right at;

Not as the whole world, but as a little thing suspended alone in spaceThe further away you are from a ball, the more of its surface you can seeWe don't always notice this,because in our day-to-day lives,most of the balls we deal with are so smallthey're almost always many of their own radii away from us,

And the available amount of their surface visible is near a maximumOr, they're so big, like the Earth, that we rarely get far enough away fast enough to notice this propertyBut the next time you are near a ball, get close to itYou'll see that as you get nearer, more of its surface disappears behind the horizon,but moving back up will make it available againFor most of us, stuck our whole lives on Earth's surface,

Such an experience is impossibleWIth nothing around to block your view,5 km (about 3 mi) is about the furthest you can seeHaze can limit 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 km^2That'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 will be able to seeThat's why it's great to be a satelliteHere's the International Space StationYeah, look at that nice bit portion of the surface in viewUnfortunately, this isn't to scaleIf the Earth were the size of an apple,

How far away would the International Space Station orbit?Like this far away?Maybe this far awayMaybe this far awayActually, it orbits… here,27 mm above the surface

That's how far the stem of this apple sticks upIt's not very farOh, here's another fun little to scale fact:if the Earth were the size of an apple, your eyeball would be about the size of the moonWe 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 timeAnd that 3% is too wide to all fit within a windowWhen I was in Pittsburgh, their science museum had a mock-up of part of the ISSAnd as you can see, out of the window, Earth is still quite expansiveUsing special lenses, images can be taken from the ISS that look like circular disk Earths,

But the lens is distorting things hereIt's fitting much more into the pictureIn order to truly witness Earth's entire shape with your own eyes,you would need to either smash your face right up against the windowor just be floating outside the stationAnd 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 atomstiny things so teeny that a single drop of water contains not a million atoms,

Not a billion atoms, or a trillion, or a quadrillion, or a quintillion but 5 sextillion atomsEarth is made of even more stuff:not a septillion atoms, not an octillion, nonillion,decillion, undecillion, duodecillion, tredecillion,not even a quattuordecillion but 100 quindecillion atomsBut since we live only on the surface of our planet, we unfortunately can't see most of those atoms

If the Earth was shaped like a disk or an icosahedron,or, say, a cube, or a rectangular prism, or two stellated rhombic dodecahedrons,we could see more of the Earth than we normally canBut as things are, we actually see nearly the least of Earth's matter possiblebecause 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 10^50 atoms that make up Earth are on the surface for us to see?That's not an easy questionFor one thing, technically, atoms on the surfaces of opaque things like rocks and dirtaren't the only parts involved in their appearancesSub-surface scattering can and does happenRegardless, attempting even a rough approximation is illuminating

I asked Grant from the YouTube channel 3Blue1Brown for some helpAnd he pointed out that if you calculate the number of circles with atom-sized radiithat could, packed optimally, cover a sphere with the surface area of Earth, you'll get about 15×10^34That's a lot of atomsBut then he pointed out that the Earth's surface isn't smoothIts 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 gonna be hopeless, right?Well, here's the thing, Earth is made of little rugged shapes that from far away make big rugged shapesIn other words, Earth's surface can be described as a fractalThere is a regularity to its roughnessIn fact, mathematicians have even assigned a fractal dimension to Earth's surface: 23

To see what that means, I highly recommend Grant's video on fractal dimensionsIt's fascinatingUsing 23 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 37That's 1000 times more atoms

So, maybe we shouldn't count Earth's roughness out just yetIt's smooth, but not perfectlyTo put that number in perspective, the human body contains about 10^27 atomsThat's 10 powers of 10 less than the surface of the Earth10 powers of 10 is 10 billionThere are about 75 billion humans

So, more or less, it can be said that there are the same number of atoms in every human body right nowas there are on the surface of the EarthAs 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 deepFun fact: the mass of the atmosphere is about 25% lessthan what you would get by multiplying sea level pressure (147 psi) by the surface area of the Earth

Because Earth's terrain displaces about that much airHuh, Earth's surface is pretty coolObviously, I mean it got lichen and monster trucksand an island in a lake on an island in a lake on an islandBut from down here, on its surface, we just can't see that much of itYour 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 thereOr 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 sizeBut 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 KansasI grew up here and took this footage while driving across the state last yearYou can probably see why Kansas is often called "flatter than a pancake"However, although it is famously flat, Kansas is not the flattest US stateIn 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 032° up

(about the height of a 30 m hill at the horizon),a typical person would say, "Hey! That part's not flat!"By cleverly applying this rule to topographical data, they were able to give every state a flatness scoreWest Virginia was the least flatKansas was only the seventh flattestDelaware, Minnesota, Louisiana, North Dakota and Illinois are all, by this method, flatter than Kansas

As was the number 1 flattest state: FloridaAdam Savage and I had the pleasure of visiting Florida with our Brain Candy Live show this year,and as this footage from atop the King Center in Melbourne, Florida shows, it's pretty gosh dang flatEven though Kansas is not the flattest,it is the state most often ranked flattest when the general population is askedIt is truly, scientifically flatter than a pancake—it's been demonstrated

But there's more to the story than thatIn 2003, researchers took a 130 mm wide pancake procured from IHOP and analysed its local reliefsThey found the difference between high and low points was on the order of about 2 mmIf a typical pancake like this was the size of Kansas, 5 million times larger,2 mm high peaks would be 10 km high mountainsIn comparison, Mount Everest is only about 88 km tall

And Earth's deepest scar, the Marianas Trench, is thought to be just under 11 km deepSo, not only is Kansas about as smooth as a pancake, but so is every other state in the unionand so is the entire worldIf 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 gravitiesIf somehow you could avoid that though,

The planet would feel not much rougher than running your hands over a pancakeBut a soggy one, right?I mean, most of Earth's surface is covered in water—your hands would get wetOr 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, 1 ft in diameter,the volume of water contained in, above and on it would only be about 14 mLThat's this much waterIt's kinda hard to believe because at this scale, spreading this much water across all of the ocean surfaceswould be pretty much impossible due to surface tensionBut, this is it:

All of Earth's water compared to all of Earth90% of the space on our planet life can live in is in hereThe other 10% is dry landSo, no, you wouldn't get wrinkly fingers playing with an Earth like thisYou could sop it dry just with a paper towelDespite the incredible area oceans cover on our planet,

Their depth is just nothing compared to the size of our entire planetYou 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 ballAfter all we've seen so far, that seems believable, but as it turns out, it's not trueThe misconception stems from the interpretation of the World Pool-Billiard Association's rulesAccording to them, a ball must have a diameter of 225 in ± 0005 in

Some writers have taken this to mean that pits and bumps of 0005 in are allowedProportionately, on Earth, that would mean a mountain that was 28 km highSo, since Earth has none of those, Earth must be smoother than a billiard ballExcept if bumps that high were actually allowed on a pool ball,a ball covered with 120 grit sandpaper would be within regulationClearly, the 0005 in 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 1/100,000 in,or about 05 μm deep and highScaled to the size of a billiard ball, Earth's Marianas Trench would be 49 μm deepSo, Earth is smoother than a pancake but not smoother than a billiard ballNor, as xkcd wonderfully showed, is Earth smoother than a bowling ballBut hold on, earlier we were using the word "flat", now we were using the word "smooth"

That distinction is importantYou see, the Earth isn't flat like a plane (or is it?)Instead, it curvesIt's a ballPieces of Earth, like Kansas, might be quite smooth, but they curve along with EarthIf 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 81 km below youThat's nearly the height of EverestAnd if they stood straight up, they'd be tilted nearly 2° relative to where you thought up wasHere is an interesting coincidence:generally speaking, 1 mi from where you are, Earth curves down about 8 in;

1 km from where you stand, it curves down about 8 cmThe rate of drop due to curvature isn't a linear oneYou can't just multiply any distance by 8 to get the drop due to curvatureInstead, use an online calculator like the one I have linked down in this video's descriptionYou can put in any distance you wantAnyway, 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 areConan O'Brien, at 6 ft 4 in tall, can see up to 5 km in any direction,but Snooki, at 4 ft 8 in, can only see about 43 kmTo 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 peek into viewHeyWhatsThatcom factors all of this inIf Earth was a smooth sphere, the view from atop Ben Nevis, the highest mountain in the British Isles,would end at the horizon 131 km away (about 80 mi)Such an area would look like thisBut factoring in Earth's ups and downs, here's a more precise boundary of what you can see

Loch Treig, Scottish Gaelic for "lake of death", is only about 10 mi from the peakThat's within an 80 mi radius, but it can't be seen because terrain in the way blocks itParts of the Atlantic Ocean and the North Sea 8 times further away can be seenThey lie at the limit of the Earth's curvature, just before it bends the surface out of sightThese spikes extending beyond the geometric horizonare caused by things beyond it that are tall enough to peek above Earth's curvature

In the case of Ben Nevis, this includes high elevation parts of Northern IrelandOK, enough about the surface and what it's like close up, let's go further away and see moreThis'll be fun, but there'll be a trade-offThe further away you are from something, the smaller it will appear to beMoving away from Earth will make more area available to see, but that area will take up less of your field of viewIt 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 you head still,just by moving your eyes around, is about 120° up and down and more than 180° horizontalA screen is just a window of that space—nowhere close to filling it, unless you get uncomfortably closeTo help us visualize large apparent sizes, let's replace the spherical Earth with a flat diskthat's always the same distance from the observerThis disk can be given an apparent size equal to Earth's from any altitude,

And the disk can contain on it everything that would fit within your horizons from any altitudeOK, so, standing on the surface looking straight down, Earth will take up nearly a full 180° of your field of viewWith your arms extended straight out, parallel to Earth,your fingers will point to the edges of the planet: your horizonFrom 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 fistsOne fist is about 10° across at arm's lengthYou can move your eyes from edge to edge horizontally here, but you can't quite take in the full width verticallyBut from more than twice this altitude, 1000 km away, Earth is only 120° acrossThat's one less fist width each

This is perfectThat fits within our narrower vertical field of viewSo, from 1000 km up (about 620 mi),you can just start to see Earth as a complete disk right in front of you at onceHowever, only 7% of Earth fits within the horizon form up hereImages of Earth taken by satellites this far up, like the Suomi NPP, look kinda weird

I mean, North America doesn't actually take up this much of the globeEarth's 120° width has been compressed to fit in an image much narrowerCompare Africa from its height to the famous blue marble picture taken from 45,000 km awayThe latter looks more realistic, like looking at a globe on your deskGeosynchronous satellites are about 35,000 km highFrom their altitude, 434%—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 palmsThat's incredibleBut what about from the Moon?Well, from that far away, Earth is only about 2° acrossYou could block it out with your outstretched thumb

However, you can see more of Earth—you can see further around its curvatureFrom the Moon, 49% of Earth's surface is visibleJust 49If you want to see 50, half of Earth's surface at once, you have to go even further awayIn fact, you have to go infinitely far away, which you can'tThe 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 surfacewould become so small and infrequent that you wouldn't be able to see anything at allStars, 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 pointFrom 1/1000 of a light-year 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 R Doradus, the widest star in our skyFrom 91 light-years away, the point of our Sun would dim to a level undetectable by the naked eyeIt would disappearMost 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 marvelled at

And written stories about since humanity began,chances are, we are not part of their constellations or folkloreWe're a dark patch in the sky to them,an ignorable emptiness framing other stars, the ones they marvel atwhile not knowing we're here, or that there is anything hereAnd as always, thanks for watching!

(Music reinforcing existential crisis)If you don't follow me on Twitter or Instagram, pffft, you are missing out on a treasure trove of premium content,so check that outAnd, know this, I love youOh, and this Vsauce shirt is only available to Curiosity Box subscribersThis shirt comes in the latest box

If you sign up now, you will get this shirt, so long as you sign up before it sells outThe Curiosity Box is good for all brainsIt comes to your door, 4 times a year, full of science gear and toys that I want you to have,I want you to hold and learn fromAlso, a portion of the proceeds from every box goes to Alzheimer's researchI'm incredibly proud of it

But what's going on on this shirt?Well, it's modular multiplication around a circleWe have the numbers 1 to 40, around the outside of a circle, connected to their product with the number 4So, 1 is connected to 4, 2 is connected to 8, 3 is connected to 12 and so on, even past 40You could keep imagining the numbers continuingFor instance, 1 can become 41, 2 can become 42

And this emerges—the Vsauce VMany other shapes can be made by using different multipliers or different numbers around the circleMathologer has a fantastic video on this topic, which you should check outI have linked it down in the descriptionThank you for being curious and as always, thanks for watching!

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