2761: 1-to-1 Scale

Explain xkcd: It's 'cause you're dumb.
(Redirected from 2761)
Jump to: navigation, search
1-to-1 Scale
There's a version that shows the planets with no cropping, but it's hard to find a display that supports it.
Title text: There's a version that shows the planets with no cropping, but it's hard to find a display that supports it.

Explanation[edit]

Scaled representation of the full diagram. The comic corresponds to a tiny rectangle at the intersection of all the planets.

This comic is implied to be a part of a huge diagram that shows each of the eight planets at real size (as seen by the ant on Earth's surface). Each planet is represented by a circle thousands of kilometers in diameter. However, the planets have been awkwardly placed in an extremely tight circle, so that all eight planets touch (or nearly touch) a tiny central area of "space" a few inches large. This comic shows a fraction of this diagram, cropped so that we see this area of "space" and a little of the edge of each planet intentionally arranged next to it.

The joke of this comic appears to be that when planets are indeed displayed at a 1:1 scale, it is almost impossible to tell their relative sizes, even when the image technically shows (part of) each of the planets

The reason why each planet's circular border appears straight is because it's such a small area of each planet: you're only seeing a couple of square inches of the surface of each of the planets, and even though they are all round, the curvature would be imperceptible on this scale. The four gas giants are completely smooth, whereas the four rocky planets display features, most notably on Earth where grass and an ant are visible.

That it cannot have been an image of the real planets aligning is clear, as Mercury can be shown to be in front of Jupiter (implying that the latter is in the part of its orbit on the far side of the Sun from the viewer), yet Jupiter obscures Earth (which necessitates that it be in the arc of orbit nearest any given observer). In other words, there is no possible real alignment of the planets in which Jupiter passes between Mercury and Earth. In the title text it is made clear that this is just a small part of a larger drawing, so this is not an image taken from far away – they are only placed this way for scale.

The title text remarks that it is hard to find a display that supports a version of the image without cropping. This is because a true 1:1 scale image showing all of the planets would be at least as big as the largest one, Jupiter – far larger than any monitor or display currently available[citation needed] – or perhaps even big enough to hold Saturn's rings, in whatever orientation they lie. Furthermore, the amount of video memory that a graphics card would need to have in order to output at anywhere near the same DPI to such a display, even as a 1-bit-per-pixel-image (i.e., all pixels are either black or white), is well beyond the capabilities of any graphic card that existed at the time of publication.[citation needed]

Transcript[edit]

[A frame with a central area of black 'space', bounded at various intersecting angles by eight 'straight lines' representing planetary surfaces, originating from various out-of-frame angles of 'down' and the white of some bodies obscuring some part of the others.]
[There are labels indicating which line represents each planet.]
[The four gas-giants' lines are simply drawn, near straight and featureless.]
[The lines for the rocky inner-planets have variations to them, stereotypical of some part of their surface.]
[The "Earth" line ('down' being out the top of the frame) has a profile indicating various small-scale vegetation and also features the white silhouette of an ant that may be of a realistic size for your display.]
[Caption below the panel:]
The solar system's planets at 1:1 scale


comment.png add a comment! ⋅ comment.png add a topic (use sparingly)! ⋅ Icons-mini-action refresh blue.gif refresh comments!

Discussion

Really want an explanation for this one. Melomaniac (talk) 03:23, 11 April 2023 (UTC)

My comment got deleted by a bot!!! 2659: Unreliable Connection (talk) 03:23, 11 April 2023 (UTC)

RIP... Melomaniac (talk) 03:25, 11 April 2023 (UTC)
No, UC, it just got overwritten by the 'bot, when it did its job and (re)created the whole initial state of the various pages to depict the new comic coming out. (Noting that you'd not set them all up fully/correctly.)
That you had spotted it already and had just gotten in ahead of the 'bot clearly isn't something it was prepared to handle. But as someone spotting it can usually wait a short while for the 'bot to catch up, I don't think it's a problem. In fact, you could have just copied your old contributions into the now receptive page(s), with nary any comment. Too late now. 172.70.90.101 03:44, 11 April 2023 (UTC)
This may have broken the next link on the previous page. --172.71.160.36 06:41, 11 April 2023 (UTC)

The lines represent the surfaces of the planets I think, so it's basically all the planets overlaid on top of each other. 172.71.142.35 03:28, 11 April 2023 (UTC)

Yup, I think it's what he meant - but I find it unlikely that the gas giants would have this clear cutoff of a "surface". 162.158.189.241 03:34, 11 April 2023 (UTC)
If there is a gas - liquid phase transition (and I think at least the gas giants have them): Why not? OK, you could see "rain" as blurring a clear cutoff, but wouldn't that also apply to Earth, then?Tier666 (talk) 08:04, 11 April 2023 (UTC)
Gas giants' diameters are frequently defined at the average radius at which the atmosphere has a pressure of 1 bar (approximately equal to the pressure at sea level on Earth). There's not a physical edge there, like the boundary between the ground and the atmosphere on a rocky planet, but it is a reasonably well-defined (or, at least, define-able) measurement. FWIW, the pressure gradient is pretty high, and Jupiter's atmospheric pressure increases from 1 bar to 10 bar over about 100 km, which is about 0.1% of the radius, so it's fairly insensitive to the pressure you choose.162.158.158.139 16:20, 13 April 2023 (UTC)

I’d think the same citation as stands for ridiculously large would also cover larger than currently exists on earth, and his that citation is not in fact needed? 162.158.174.186 06:53, 11 April 2023 (UTC)

It seems like the gas-covered worlds are explicitly those with clearly cutoff "surfaces," so maybe in those cases the cutoff is some specific gas density -- which occurs at a consistent radius throughout the planet, thus creating a flat surface. While for rocky worlds (except Venus, which is treated like a gas planet here), a density cutoff can lead to bumpiness due to terrain. Trimeta (talk) 03:57, 11 April 2023 (UTC)
Correct re: gas giants. Typically 1 bar, which is approximately Earth's atmospheric pressure at sea level.162.158.158.139 16:20, 13 April 2023 (UTC)
just to be very clear (this being a explanation site!) that Venus is "treated like a gas giant" because of it's thick atmosphere. It would be just as correct to say "All the gas giants are treated like Venus" After all, ordinary telescopes couldn't take a picture that sees through any atmospheres, except Earth, where you'd see clouds but often surface where clouds don't appear. Sorry if that's an overexplanation Cuvtixo (talk) 19:10, 11 April 2023 (UTC)

On Twitter there seems to be concern that all planets are depicted flat. This may make this a contribution/mockery of the ongoing Flat Earth discussions in some corners of the internet. --198.41.242.132 06:49, 11 April 2023 (UTC)

You can't see the curvature of the Earth when standing on it; doesn't mean it's flat. Since we're looking at the planets at a 1:1 scale, we're literally only seeing a couple of inches of each of their edges (notwithstanding the whole gas-giants-don't-have-a-sharp-edge issue). 162.158.239.20 12:06, 11 April 2023 (UTC)
actually you can see it, standing on the shore of any large lake on a calm day looking at a shore that's ~6.5 miles (10.5km) away. You'll lose ~8ft (2.5m) below the horizon - 162.158.186.213 13:55, 11 April 2023 (UTC)

The display for an uncropped version of the image would not only be larger than any display on earth. It would be larger than earth. 162.158.86.243 06:59, 11 April 2023 (UTC)

By necessity, at least as large as Jupiter. Maybe slightly above two Jupiters (max dimension squared compared to display height*width of any common aspect ratio) if you wanted to not overlay any of the others at all. And make the lower limit a packing-problem, then add a buffer so there isn't the actual need for any to touch. 172.70.90.253 10:02, 11 April 2023 (UTC)
I'm going to add that. Someone was confused enough to put Template:cite needed there, which may be a joke onto itself?, I can't tell. I've removed the cite needed, but I guess it needs to be more clear why it's totally nonsensical and doesn't need a citation? Cuvtixo (talk) 19:16, 11 April 2023 (UTC)
The four inner planets are small enough to fit the upper left corner of any display big enough for Jupiter. As Uranus and Neptune are smaller than the latter one, they cannot extend past its top, bottom or right edge in the constellation shown, so they will not need additonal screen space either. Only Saturn is shifted so far to the left that he will require more width than Jupiter itself, but will still fit within the same height. Knowing Randall, the shown angles are not random, but were calculated to match a commercial available display ratio with Saturn placed touching the left edge and Jupiter touching the top, bottom and right edges. 16:9 or 16:10 at 142 km hight would be a fair guess, so I would not rule out 4:3 resulting in total width significantly smaller than two Jupiters. Of course Randall might also be playing hardcore nerd: The outer diameter of Saturns F ring, which is almost always included in representations, has almost exactly a ratio of 32:9 to Jupiters polar diameter, making a picture showing the former in front of the latter a perfect match for those new fancy double wide monitors. 162.158.111.77 00:22, 12 April 2023 (UTC)
Just use a projector, obviously. Boffy b (talk) 21:33, 19 April 2023 (UTC)


What can we use as a citation for the graphics card? I couldn't find a single unified source for that concept, but stitched together some information to cover this:
The world's largest digital display is the Fremont Street Experience, at 457m by 27m, which is about 12,000 sq meters. It has 16.4 megapixels. https://en.wikipedia.org/wiki/List_of_largest_video_screens
The mean radius of Jupiter is about 70x10^6 m, so its area is roughly 1.5x10^16 sq meters.https://en.wikipedia.org/wiki/Jupiter
That means the world's largest digital display would only provide a 7.8x10^-13 fraction of the area of Jupiter.
Going with NVIDIA's Titan V, which has Total Video Memory of 12288 MB, that would mean it could handle about 98x10^9 black-and-white (1 bit) pixels.
Using the pixel density of the world's largest digital display (16.4 megapixels), scaling it up by its 12000 sq meters to the area of Jupiter (1.5x10^6 sq meters), that comes out to 2.1x10^19 1-bit pixels. So, we would somehow need about 2.1x10^8 of those graphics cards working together to handle our Jupiter-sized display.
That display wouldn't even be at HD resolution, let alone 4K. Then again, if we use Apple's "Retina" designation that is dependent on reasonable viewing distance, that might be acceptable. DanShock (talk) 20:22, 14 April 2023 (UTC)

1-to-1 scale means 'assume all planets are the same size,' right? I see Earth's grass is shown to be as large as Martian rocks, because Earth is a third again as large. (At the scale where grass is visible, Earth looks flat.) At first I thought the point was that altitude variation in cloud-tops varied so little that a gas giant shrunk down to Earth size would be featureless and have a distinct edge, but that's wrong. Ground isn't cloud-tops. Do gas giants have any solid ground? We've seen Jupiter eat comets, and it makes sense they would've collected at least some minerals and metals. According to [Astronomy], gas giants have Earth-sized solid cores. I'm guessing gas giants' immense gravity compresses their cores into featureless spheres, which, if scaled to Earth-size and viewed at the scale where one could see grass, would look flat. Yes? EllenNB (talk) 10:14, 11 April 2023 (UTC)

Gravity itself won't compress (and 'flatten') the cores. "Shell theory" shows that gravitational force only counts from the proportion of the body that is within the radius of the bit you're concerned with. But there'll also be the external pressure (from being at the bottom of a thick atmosphere that ultimately is above far more of the planetary mass) and possibly a degree of compression density to make any Earth-sized core slightly heavier than if it was just a bare core of the same size but shorn of outer layers.
As to flatness, I can take you to very flat stretches of Earth and very lumpy bits (depends which direction I go, from where I am now), all within 30 minutes' drive. We can'teven know how representative a sample of planetary cross-sections we are seeing (once we get over the issues of gas/space boundaries for gas-giants), but I bet there are bits that resemble the diagram... If you really want it to be so real. 172.71.242.87 11:05, 11 April 2023 (UTC)
No, 1-to-1 means that they are actual size, not the same size. SDSpivey (talk) 13:37, 11 April 2023 (UTC)


There are several pieces of information here that are featured but don't make sense to me. What's the function of the dark polygon in the center? Why are the lines showing each surface going in random directions? Why is the surface of each planet so flat at a full scale rendition? When I look out my window at full sized Earth, it's not flat. It's quite bumpy, actually. But perhaps he doesn't mean these are full size, he might be saying that they're all shrunk, but the same amount, so 1:1:1:1:1... but even then, I'm totally lost.

"What's the function of the dark polygon in the center?" I think it is a view of the dark sky, "above" the surface of the Earth, Mars, etc. Rps (talk) 11:43, 11 April 2023 (UTC)

I think the "polygon" is a grassy Earth itself, with the white above it sky. Earth is the rearmost planet pictured. Then in front of Earth, on all sides except the top, are the overlays of the various planets, what little of each one as can fit. But then maybe the polygon is night starry sky, and Earth is the white area above it. -boB (talk) 14:35, 11 April 2023 (UTC)
No, the polygon is the sky. Zoom in and you see the Milky Way and stars and other space stuff. And the ant on the Earth has its legs pointing upwards (in the reference frame of the image). 162.158.239.26 03:09, 12 April 2023 (UTC)
Agreed. -boB (talk) 13:43, 12 April 2023 (UTC)
"...you see the Milky Way and stars and other space stuff" - I thought that was grime on my monitor until I zoomed in and the 'grime' got scaled up with the rest of the image! 172.68.146.52 21:47, 21 April 2023 (UTC)

Is this an ant on earth, over the letters "EA" ? On my monitor, set for my less-than-perfect vision, it is 15mm long, which (at a 1:1 scale) makes it a cow ant, or a large african ant. I guess people with normal vision get fire and carpenter ants instead? And those on smartphones get pavement ants?172.68.50.73 11:00, 11 April 2023 (UTC)

I do believe it is! It's 6 mm on my desktop monitor and 3 mm on my phone. We also don't know what side of the Earth we're looking at, so I suppose it could really be any ant, including the one in your local area. I like to think it's a black garden ant (Lasius niger), since I'm most familiar with those :) 162.158.239.25 12:16, 11 April 2023 (UTC)
The image metadata suggests 80dpi for the image. The ant is around 20px long, so the ant is 6.35 mm long. Quantum7 (talk) 23:21, 17 April 2023 (UTC)

It took me a good while to figure out this one; I don't normally need to come here, but this one stumped me at first. (The comments as of right now weren't too illuminating either.) I think the lack of color was an issue; I first thought the black polygon in the center was the earth, and then interpreted the various lines as a really weird diagram type I'd never seen before, like a phase diagram or something; I also considered one-dimensional planets. I colored in the planets to aid me. The way I now interpret this one is thus: imagine an observer sitting a tremendous distance away from the solar system, and they have a camera with an extremely supremely highly zooming telephoto lens. Then a lining-up of all eight planets happens – I believe this is impossible IRL (because of resonances or something), but just go with it. The observer manages to snap this incredible image of a teeny tiny spot of the sky, which simultaneously manages to include the very very edges of all the planets as well as some of the sky behind them all. The sky is the black polygon: it has nebulae and stars. Neptune is in front of Uranus, and that as well as Mercury are in front of Saturn, which is in front of both Jupiter and Mars; Venus is between Mercury, Mars and the Earth, and the Earth is also behind Jupiter. The reason why these are all so smooth is because it's such a small area: we're literally only seeing a couple of square inches of the surface of each of the rocky planets. (See, you can see an individual ant on the Earth. Go to the most rugged mountain range you can find and observe a couple of square inches; it'll be locally flat.) The lack of atmospheres on the rocky planets as well as the hard edges of the gas giants are artistic license. This one is a member of the genre of "true yet unhelpful diagrams"; I'm surprised that isn't a category on this wiki. – 162.158.238.4 12:58, 11 April 2023 (UTC)

((Written whilst 162.158.238.4 was editing, above, and I got an edit conflict on that. The editor concerned touches on this ordering business, but I'm pasting my original in unaltered, not rejigged as a more focused reply.)) I was wondering abut the "overlap order" for a while, until I twigged it. May not be worth officially documenting, but my analysis, showing that (perhaps depending upon specific orbital positions, during a given range of times, which can of course be checked) it's probably based upon distance away from Earth.

  • Earth is bottom-most. Could be 1st/2nd, shared with Mars, as their overlap isn't shown.
  • Mars is our nearest neighbour. (As above, could be 1st or 2nd on stack.)
  • Venus next. Although it could be 7th (only obscured by Mercury) or anywhere else down to 3rd.
  • Jupiter as 4th from bottom. (Could be 3rd..5th, though.)
  • Saturn takes 5th-up position. (4th..6th)
  • Mercury as 6th. (Or all the way to topmost, but I made an assumption about its relationship to the last two.)
  • Uranus as 7th. (6th/7th a possibility, depends on Mercury)
  • Neptune as 8th. (7th/8th possible, Mercury again.)

...or at least that's what my mental notes tell me. Not helped by starting off counting from near to far and possibly messing up my numbers when I realised it made sense to flip them. It could also be "delta-V needed to reach the planet concerned" (either without or including flyby slingshot momentum borrowing/burning), but that's something I'd also need to check. I doubt it really needs tying down/Explaining, and when I edited the Transcript I decided not to record every nuance of the "variously orientated surfaces", as I think it adds nothing so long as the description gives the general idea. 141.101.98.121 13:06, 11 April 2023 (UTC)

So no one is going to mention that for the clarity depicted you'd need to literally place the planets inside of each other, or have some sort of focal length from zero to infinity? I'm not sure if that bothers me more or less than the missed trick of making the length of ground shown relate to some comparative parameter (albedo might have been a fun one) - 162.158.186.213 13:55, 11 April 2023 (UTC)

To be fair, you're also going to have to choose a "flat" few inches of surface that stands proud of the local geography (such that anything higher is below the curvature of the Earth for its proximity), and deal with an impossible resolution of an impossibly zoomed telephoto shot from a viewpoint unimaginably distant (whilst a near-enough non-Solar conjunction/asterism is happening, or at least was, when the light passed each body), without significant atmospheric distortion (which is a relatively minor issue, compared with the scarcity of photons that reach the camera anyway).
Can we perhaps instead assume that these are just individual 1:1-scale cross-sectional diagrams (or even carefully curated local photos) drawn together into a hybrid image to accurately retain the scaling verisimilitude, and individual contexts, but happily faking the relative positions? 172.70.85.56 15:00, 11 April 2023 (UTC)

It would take some work to check, but I'm wondering if the angle of the horizons of the various planets are perpendicular to the line made between the earth and the planet in question 162.158.154.141 15:36, 11 April 2023 (UTC)

This is how I interpret this image: I didn't want to make the black dot as small as in the picture so dimensions are insanely larger 172.69.194.80 20:35, 11 April 2023 (UTC)

that is a very clarifying picture, thank you! Shall we include it on the explanation page? It belongs there IMO Flekkie (talk) 22:19, 11 April 2023 (UTC)
You may by me. The original picture is from NASA https://solarsystem.nasa.gov/resources/686/solar-system-sizes/ and they have no restrictive copyright either. I view this picture as 2D planets stacked and not real planets viewed in space since this is clearly impossible orientation and you couldn't see half the planets, let alone ant on Earth's surface, from behind Neptunes orbit 162.158.239.26 10:43, 12 April 2023 (UTC)
I calculated the positions of the planets based off the same idea and created a similar figure mathematically (source code). 172.69.194.80's version differs very slightly: the "window" is exaggerated a bit (all planets should meet at this scale) and Mars is visible rather than being behind Venus/Satern. However as it is much prettier with the NASA images I suggest we include 172.69.194.80's in the main explaination. Quantum7 (talk) 23:34, 17 April 2023 (UTC)
Is this right though? Based off the image Mercury is in front of Saturn. For this to happen, Mercury has to be closer distance wise, so Saturn has to be on the opposite side of the sun. But that can't be true if Saturn is in front of Jupiter and behind Uranus/Neptune?

I don't like the current explanation, since the planets never line up like this. --162.158.203.40 07:11, 12 April 2023 (UTC)

This is truly one of the comics of all time. AzureArmageddon 08:48, 12 April 2023 (UTC)

We have a 1::1 bird book, where each page has a photo of the bird (or a portion of the bird, in case of flamingos) at 1::1 scale. This comic is a play on those books. -- Bob Jenkins 172.71.150.174 15:25, 12 April 2023 (UTC)

Regarding the flamingo, and anything else bigger than the book, what a waste of an opportunity for a fold-out section..! 172.70.91.152 18:58, 12 April 2023 (UTC)

This image is only going to be 1:1 scale on a really large display too; The grass on Earth is around a centimeter in length when the image is full-screen on my 27" (68.58 cm) monitor, while it's clear from the way it is depicted that it is supposed to be long grass, at least 50 centimeters in length. That means that the display which would make this truly 1:1 is about 50 times larger than mine, or in other words has a diagonal of about 34 m. This is bigger than a typical cinema screen, but I suppose not that much bigger and there ought to be cinemas in which one can display this image such that it is truly 1:1. 162.158.87.66 06:27, 13 April 2023 (UTC)

The ant is 'about right' for a possible ant even on my display (8"/20cm). If that would be 0.5m long grass, the ant would be truly huge, nothing like the typical ones around here. Which I think are actually smaller (certainly more svelte) than the image, if I wandered down the garden path to find an actual ant or three in the 'wild'.
So I don't think that's long grass of the kind you're assuming. But it does resemble the kind of 'pre-grass' (one step up from mosses) or microscrub (effectively bonzaied grass due to local growing conditions) to be found on a bit of semi-fresh dusty hardcore/well-worn footpath, as also shown by the loose stoney debris also present. 172.70.91.151 09:50, 13 April 2023 (UTC)