How Much of the Earth Can You See at Once?

hey Vsauce 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 eight point eight four eight kilometers tall its size is impressive or is it let's cut earth the entire planet write an app straight through Everest and then start zooming out as you can see Everest SMAW new mentality quickly disappears against Earth's planetary ginormous 'ti compared to Earth's diameter Everest in fact all of Earth's ruggedness barely 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 feet but the horizontal axis represents nearly 14 million stretched to the same scale so as to mirror reality the actual smoothness of the earth becomes apparent on this one foot diameter globe Everest is a bump about two millimeters high feels good but if the earth was actually this small Everest would be a bump only 1/5 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 circle 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 radii away from us and the available amount of their surface visible as 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 are 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 review 5 kilometers about 3 miles is about the furthest you can see now haze can limit your view an atmospheric refraction can slightly extend it but for the most part everything you can see happens within an area of just 80 square kilometers 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 with the International Space Station orbit like this far away maybe this far away maybe this far away actually it orbits here 2.7 millimeters above the service that's how far the stem of this Apple sticks up that's not very far oh 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 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 three percent of Earth's surface at any one time and that three percent is too wide to all fit within a window when I was in Pittsburgh their science museum had a mock-up of part of the ISS and as you can see out of the window earth is still quite expansive using special lenses images can be taken from the ISS that look like circular discs Earth's but the lenses 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 atoms or a trillion or a quadrillion or a quintillion but five sextillion atoms earth is made of even more stuff not a septal Ian Adams not an octal Ian non-alien Dessel Ian undecillion duo de silient Redis iliyan not even a Quattro de Cillian but 100 Quin de Cillian atoms but 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 who stellated rhombic dodecahedron 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 ten to the fifty 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 radii that could packed optimally cover a sphere with the surface area of Earth you get about 1.5 times ten to the 34th 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 gonna 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 regularity to its roughness in fact mathematicians have even assigned a fractal dimension to Earth's surface 2.3 now to see what that means I highly recommend grants video on fractal dimensions it's fascinating using two point three 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 powers of 10 less than the surface of the earth 10 powers of 10 is 10 billion there are about seven and a half billion 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 but back the mass of the atmosphere is about 2.5 percent less than what you would get by multiplying sea level pressure 14.7 pounds 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 lichen 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 planets 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 u.s. 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 degrees up about the height of a 30 meter 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 flatness score West Virginia was the least flat Kansa 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 atop 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 millimeter wide pancake procured from IHOP and analyzed its local release they found the difference between high and low points was on the order of about two millimeters if a typical pancake like this was the size of Kansas five million times larger two millimeter high Peaks would be ten kilometer high mountains in comparison Mount Everest is only about eight point eight kilometers tall and Earth's deepest scar the Marianas Trench is thought to be just under 11 kilometers deep so not only is Kansas about as smooth as a pancake 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 hands 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 one foot in diameter the volume of water contained in above and on it would only be about 14 milliliters that's this much water it's kind of hard to believe because at this scale spreading this much water across all of the oceans 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 stop 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's rules now according to them a ball must have a diameter of 2.25 inches plus or minus 5 thousandths of an inch now some writers have taken this to mean that pits and bumps of five thousandths of an inch are allowed proportionately on earth that would mean a mountain that was 28 kilometers 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 5,000th 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 thousandth of an inch or about half a micrometer deep and high scale down to the size of a billiard ball Earth's Marianas Trench would be 49 micrometer is 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 kilometers below you that's nearly the height of Everest and if they stood straight up they'd be tilted nearly two degrees relative to where you thought up was now here's an interesting coincidence generally speaking one mile from where you are earth curves down about eight inches one kilometer from where you stand it curves down about eight centimeters 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 six foot four inches tall can see up to five kilometers in any direction but Snooky at four foot eight can only see about four point three 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 peek into view hey what's that com factors all of this in now if earth was a smooth sphere the view from atop been nevus the highest mountain in the British Isles would end at the horizon 131 km/h with look like this but factoring in Earth's ups and downs here's a more precise boundary of what you can see locked rate Scottish Gaelic for Lake of death is only about 10 miles from the peak that's within an 80 mile 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 nevis 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 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 about a hundred and twenty degrees up and down and more than a hundred and eighty degrees 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 disk that's always the same distance from the observer this 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 altitude ok so standing on the surface looking straight down Earth will take up nearly a fall 180 degrees 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 kilometers up about where the ISS orbits 3% of the earth's surface is within your horizon but the earth will only take up about a hundred and forty degrees 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 ten degrees across at arm's 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 for more than twice this altitude 1,000 kilometers away earth is only a hundred and twenty degrees across that's one less fist-width each mrs. perfect that fits within our narrower vertical field of view so from a thousand kilometers up about six hundred and twenty miles 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 suomi npp look kind of weird I mean North America doesn't actually take up this much of the globe Earth's 120 degree width has been compressed to fit in an image much narrower compared Africa from its height to the famous blue marble picture taken from 45,000 kilometers away the latter looks more realistic like looking at a globe on your desk geosynchronous satellites are about thirty five thousand kilometres 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 degrees 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 two degrees across you could block it out with your outstretched 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 one thousandth 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 our Doradus 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 to them and ignore ball emptiness framing other stars the ones they marvel at while not knowing we're here or that there's anything here and as always thanks for watching [Music] if you don't follow me on Twitter or Instagram you are missing out on a treasure trove of premium content so check that out and know this I love you oh and this Vsauce shirt is only available to curiosity box subscribers this 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 out the curiosity box is good for all brains it comes to your door four times a year full of science gear and toys that I want you to have I want you to hold and learn from also a portion of the proceeds from every box goes to Alzheimer's 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 4 so one is connected to 4 2 is connected to 8 3 is connected to 12 and so on even past 40 you could keep imagining the numbers continuing for instance one can become 40 1 2 can become 42 and this emerges the Vsauce be many other shapes can be made by using different multipliers or different numbers around the circle math a logger has a fantastic video on this topic which you should check out if linked it down in the description thank you for being curious and as always thanks for watching

Channel: Vsauce

Views: 10,354,049

Rating: 4.8817735 out of 5

Keywords: earth, geology, mountains, outer space, math, science, vsauce, michael stevens, stars, vision, field of view, view, satellites, moon, Kansas, pancake, flat, topography, maps

Id: mxhxL1LzKww

Length: 26min 31sec (1591 seconds)

Published: Mon Jul 17 2017

Reddit Comments

[u/Baldemoto]

Holy shit about time.

[u/AkulBIG]

Lies. the Earth is pyramidal.

[u/fdebijl]

That ending was pretty depressing

[u/-bishpls-]

It was a very okay video. Definitely seems to skip over some of the more complex parts and focus more on middle school level science (for example, the little tangents about how small/large everything is, how many atoms there are in a drop of water, etc.). Other than the pancake/billiards ball tangent and maybe the fact that you can never see 50% of a sphere's surface I don't think there was much more to the video.

It's weird because Vsauce was, to me, going to become a very specialised channel talking about the intricacies of higher level maths or other sciences (see: Banach-Tarski, Supertasks) but after Brain Candy or Mind Field it seems to have taken a step back and focus more on approachable and understandable topics (Spinning, this video). But hey, it's supposed to be a two parter I think (?), so let's see whether it picks up.

[u/Wolham]

I'd like to disagree with the video. You do not have to move infinitely far away from earth in order to see 50% of it. That would only be true if you were only looking with one eye. However, we humans have two eyes,which means two points of perception, separated by a distance. Hence, in order to fit 50% of the earth's surface into our field of view, the earth would have to be as far away as to appear as big as the distance between our pupils. Which is, for 90% of caucasian people, 2.2-2.7 inches, or 55-68mm. For earth to appear 2.2 inches big, you would have to be 1 194 648 255 km away, which is approximately the distance from Earth to Saturn.

TL:DR; 95% of the caucasian population can see >50% of earths surface if they're hanging out on Saturn, due to the fact that we have two rather than one points of perfection (eyes).

[u/archaeopterex]

Wow, here i thought the channel's dead

[u/AStudyinBlueBoxes]

AT LAST

[u/sampathreddyv]

I don't understand the statement where he says if a giant human can hold earth in his/her hands "you and it(earth) would be torn apart by the immense tidal forces created by your gravities" How is it any different from a regular human holding a ball compared to a giant holding earth? Provided masses are in same ratios.

[u/parmesann]

did he say "I love you" at the end because he's seen us saying that we were angry about him not posting and he's sorry because he does still love us?