2906: Earth

Explain xkcd: It's 'cause you're dumb.
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Just think of all the countless petty squabbles and misunderstandings, of all the fervent hatreds, over so insignificant a thing as the direction and duration of a rocket engine firing.
Title text: Just think of all the countless petty squabbles and misunderstandings, of all the fervent hatreds, over so insignificant a thing as the direction and duration of a rocket engine firing.


The Pale Blue Dot image from Voyager 1. Earth is the "pale blue dot" halfway up the rightmost color band.

At first sight, this appears to be the famous Carl Sagan commentary, upon the Pale Blue Dot image of Earth, a picture taken by the Voyager 1 probe in 1990 (at that time 6 billion kilometers away) but having been transmitted back to Earth to be appreciated as one of the most iconic 'photos of Earth from space', along with Earthrise and The Blue Marble. Sagan's written, and later spoken, words evoke how the lives of all of us are somehow confined to barely more than a single pixel's-worth of existence upon an already zoomed-in view of space.

From the caption, however, it appears that 'Carl' is not looking at an image. Instead it is a spacecraft window. The minute apparent size of the Earth is as a result of the spacecraft being very far from Earth. This is an unintended consequence of an attempt to deorbit from low Earth orbit (i.e. not more than 2000 kilometers from the Earth's surface, from which the Earth should still mostly fill any view that points towards it). Rather than transitioning from LEO into a re-entry trajectory, somehow the vessel and crew have been sent into a much higher-reaching orbit, if not into a solar or extra-solar trajectory. And it is apparently Carl's fault. The speech is thus not an inward view of where we all are, but an outward look at somewhere that all the crew (unwillingly, and against all recent expectations) are not.

The title text continues with the traditional tone of the speech, only to become an implicit attempt to claim that it wasn't quite as drastic an error as it actually seems to have been.

The very same words (or as far as they go), but in the more traditional situation of an informative lecture, were previously used in 1246: Pale Blue Dot.

The scale of the error[edit]

The comic's distance from Earth is unlikely to be anywhere near that of Voyager 1, and would not be being seen portrayed by the same 1500mm high-resolution narrow-angle camera as took the alluded-to image. The apparent size of Earth, compared with Carl at his window, would depend a lot on the actual 'camera' geometry/position for the scene. For comparison, however, the Earth seen from the Moon is slightly under four times the diameter of the Moon as seen from the Earth, or perhaps nearly the size of a clenched fist, held at arm's length. This implies (unless the scene uses a particularly wide-angled lens, close to Carl and the window) that the vessel's position is now significantly beyond the orbit of the Moon.

The absence of a clearly visible Moon, which would have a near-identical phase to the illuminated Earth and could easily be the second brightest object in the scene, is therefore best explained by it being no more than a sub-pixel object, indistinguishable from the surrounding darkness of space, somewhere within thirty Earth diameters (and thus approximately, in this image, pixels) of the visible Earth. This could include being sufficiently in conjunction/opposition to Earth to blend in, or be obscured by it.

The general lack of other visible stars, etc, would be explained by the exposure being tuned to not wash out the illuminated internal view, and not being set up for useful astronomical shots, though may then set another range of useful limits on what magnitude of reflected sunlight must still arrive from Earth in order to remain visible.

The orbital speed in low-earth orbit is ~8 km/s. A typical de-orbiting maneuver requires slowing down by about 100 m/s (which according to the What If chapter "Orbital Submarine" could be accomplished with the 24 Trident missiles carried aboard an Ohio-class submarine.) However, escape speed is ~11 km/s, meaning the vessel must go faster by ~3 km/s. So Carl has indeed made quite an error if he fired the boosters thirtyfold too much and in the opposite direction (or 190fold in the correct direction, resulting in the spacecraft traveling in the opposite direction of previously).

The "pale blue" dot[edit]

Although it might initially look like a white dot, the comic truly has used a pale blue color for the dot that represents Earth, with the color used in the "2x" version of the image seeming to be 0xBDCFF4.

This can be interpreted as predominently a very light gray, with an extra hint of green and a bigger hint of blue. Or redefined as an HSV triplet of of 220.4 (a greenish-blue hue), 22.5% (relatively unsaturated) and 95.7% (very bright), all consistent with how the sunlit side of an Earthlike world would look with large oceans, vast swathes of terrestrial vegetation and atmospheric clouds, necessarily abstracted down to a very limited number of pixels.

Looking at an actual example of the 'original', seems to give a possible RGB of 0x95B39E (which gives: hue of 138, i.e. a 'bluish-green'; saturation level of 16.8%; brightness value of 70.2%), which is of course also consistent with the above assumptions about Earth. But all such images are of course ultimately derived as a composite of the data from eight separate 'filters', which don't neatly fit into the RGB color model, and always subject to various kinds of post-processing and image conversion techniques.


[Carl Sagan (drawn Cueball like but with flat hair) is standing in front of a black screen with a tiny pale blue dot in the middle. He indicates the screen by holding out his right hand palm up towards the screen. He is speaking to someone off-panel, who replies from a star burst on the right edge of the panel.]
Carl: Look again at that dot. That's home. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives...
Carl: On a mote of dust suspended in a sunbeam.
Off-panel voice: We know, Carl.
[Caption below the panel:]
Carl Sagan was not making us feel better about how badly he'd messed up the low Earth orbit reentry burn.

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I originally read the caption as "how badly we'd messed up", which... changes Sagan's tone somewhat. 08:02, 14 March 2024 (UTC)

At first I thought the joke was that the rocket firing had somehow gone so catastrophically badly that the entire Earth had literally been reduced to dust. Fabian42 (talk) 08:37, 14 March 2024 (UTC)

I also had this notion at first. That after the failed burn Earth had been destroyed... But I think not so anymore. So thx explain xkcd. ;-) --Kynde (talk) 12:43, 14 March 2024 (UTC)

So, according to explainxkcd, that’s a square “spacecraft window”?? Why have we never seen a square spacecraft window in any other context, ever? Did Randall screw up that badly in the original comic, or was it a previous explainxkcd editor who screwed up here? 08:58, 14 March 2024 (UTC)

I'm not sure what you're on about and why anyone has to have screwed up. Why can't it be a rectangular (we don't know it's square) spacecraft window? Bischoff (talk) 09:53, 14 March 2024 (UTC)
This is very clearly a triangle shaped window in a very elongated spaceship Whimsical (talk) 11:24, 14 March 2024 (UTC)
Maybe it is part of a huge spider-shaped window? (I home people here will remember that meta-reference to What If) 12:28, 14 March 2024 (UTC)
This picture from the Cupola module of the ISS has trapeze like windows. But the one behind the astronaut could easily have been a rectangle from what can be seen in the picture. So to argue that this window could not have been shot the same is just silly. Of course it was important to the joke that you did not realize it was a window until reading the caption. Also if this space craft has held up to go so far form Earth with living inhabitants it is obviously not a space ship in use today! --Kynde (talk) 12:43, 14 March 2024 (UTC)
There is precedent with the Space Shuttle (aft flight-deck window, others were round, the 'forward flight-deck' ones were of course the main flight/piloting ones with awkward quadrilateral shapes and pesky instrument panels where none are in the comic). The windows in the Shuttle were actually a weight issue (certainly, at first, they were plain (chunky!) glass, and added a lot of weight to the design.
Also look at Blue Origin's capsule for more current design that could end up eventually on an orbital/extra-orbital vessel. Although Crew Dragon is more conservative, and Orion's interior looks like it isn't so big (while Starship's eventual window configuration might eventually be vastly more conservative than the Dan Dare/Flash Gordon aesthetic of the concept imagery).
So... Possible, but depends upon the design needs for the craft (fully space-capable whilst intended to undergo re-entry, is all we really know). 16:13, 14 March 2024 (UTC)

In my mind is the scene in C.S. Lewis's religious novel Out of the Silent Planet, where an English philologist, Ransom, is abducted by criminals into outer space and meets aliens. In chapter fifteen, a wise sorn tries to figure out which planet Ransom is from. Probably Thulcandra, the garbage planet of the Solar System. Ransom doesn't like the sound of that, but the sorn gets out something that isn't a telescope and he shows Thulcandra to Ransom, and yup, that's us. Lewis writes it better. I don't know if Carl Sagan had read this. --Robert Carnegie [email protected] 13:12, 14 March 2024 (UTC)

Hoo boy, yep that book (and its sequel) are beyond even Narnia in their religious symbolism (though the later environmentalist movements could definitely find an allegory in them, too, not sure how intended that was, in CSL's time, some time before a practical Gaia Hypothesis/etc). I can imagine Randall knows of the book (though clearly more influenced by Sagan in a direct lineage). Not entirely sure Sagan will have taken interest in that genre, nor taken the above to heart. Probably no more than his genuine scientific and rhetoric interests, which may be sufficient genesis for his own coined meme. But that's just my gut feeling. i.e. Worthy of note, but not directly (or singly-indirectly) connected. 14:20, 14 March 2024 (UTC)
The Gaia Hypothesis is also religious, so it makes sense that it could be written into C. S. Lewis. Protecting the environment is important, but Mother Nature is basically a deity for misanthropes. (talk) 14:02, 15 March 2024 (please sign your comments with ~~~~)
It can be believed religiously, and is named after a goddess, but also can be used to describe the (long-term) self-regulating interactions of the various elements of biomes and atmos/geos-/pedospheres that interact, in a more scientific way. (Some people religiously believe in evolution as God's "fire and forget" Creationist act to get us from the very start of Genesis until Revelations, for example, but it doesn't stop a strictly agnostic scientific analysis of natural selection getting us here, with or without writings that describe everything in traditional concepts that may not necessarily' be entirely accurate - but sustained "God's chosen people" in ways that mattered... to put just one teleological spin on it.)
It can just be considered a more complex (and entirelg natural) global thermostat. Which might have difficulty dealing with people lighting unexpected fires in the middle of their bedrooms (e.g.), and can't stop them burning their own house down if they start a runaway effect that it has no power to stop, but normally it can counteract variations of temperature by eventually adjusting the heating/cooling elements. Or, I suppose, decides that a hotter/colder house is better, so long as there are still some pot-plants that will thrive under the new conditions (until nudged back by other effects).
...that's simplistic, as an analogy, and in key ways 'not really correct', but it starts to reflect the no-god-needed tenet of the general idea. (Not sure I have confidence in "it'll be alright", but I would say it has better chance than "we'll be alright", as we aren't vital to 'keep things going'. In fact, once we're gone then anything that remains will get its own chance to nudge conditions to a new equilibreum.) 15:23, 15 March 2024 (UTC)

The color for the blue dot seems to be around #B6C8EB. --1234231587678 (talk) 15:18, 14 March 2024 (UTC)

Zooming in, the central pixel is definitely #ABBBDC (a very easy color to hand type), with some artifacts around it of varying shades of grey. 20:58, 14 March 2024 (UTC)
I think we're discussing different versions of the two images. The single central pixel of the dot in the "regular-sized" image on the xkcd site, "earth.png" (364 x 472 pixels), is now #B5C6E9, while the six central pixels in the 2x image, "earth_2x.png" (728 x 945 pixels), are #BDCFF4. The "regular-sized" version here, "363px-earth_2x.png" (363 x 471 pixels) has a single central pixel, #ABBBDC, while the large image on *this* site, "545px-earth_2x.png" (545 x 707 pixels), has two central pixels, #BDCFF4. BunsenH (talk) 22:33, 14 March 2024 (UTC)

I'd say he nailed Sagan's hair... Inexplicable (talk) 19:11, 14 March 2024 (UTC)

Carl may *claim* to have messed up, but I find it hard to believe that he wouldn't aim the rocket for deep space, given half a chance.

Sounds about right. It's Carl Sagan... and besides, who wouldn't want the opportunity to venture into the final frontier? (Also, please remember to sign your post next time.) OmniDoom (talk) 23:40, 14 March 2024 (UTC)
Um. "Spend a little while in LEO then go home and live out the rest of your life" vs. "spend a little while much further out, in the company of a few people who really resent you, then die unpleasantly"? I'd go with the former. BunsenH (talk) 16:18, 15 March 2024 (UTC)

Does anybody know what is a typical reentry burn, for instance, when a capsule leaves the ISS? I wrote "some hundreds m/s" but it might be less than that. If the original orbit is very low, even a tiny reduction will lower the perigee enough to intersect the atmosphere. Rps (talk) 18:57, 18 March 2024 (UTC)

According to What If: Orbital Submarine, "A typical de-orbiting maneuver requires in the neighborhood of 100 m/s of delta-v, which means that the 24 Trident missiles carried by an Ohio-class submarine could be just enough to get it out of orbit." Take The A Train To Watertown (talk) 00:20, 20 March 2024 (UTC)
Most treatments I see of the respective Delta-V Budgets basically deal with having to overcome the atmospheric and gravity deficits upon launch to LEO, which don't easily apply/discount in reverse. Also the delta-v needed betwixt low-LEO and high-LEO (or roughly encompassing the difference between current space-stations and a Hubble servicing mission) is almost a full km/s (either way), so you might need to add that to the much smaller(?) final bit of atmosphere-hitting adjustment, whereupon you hopefully are now slowing down entirely passively. (Rather than bouncing off...)
If you can afford to wait, though, being at ISS heights will bring you down with zero (active) delta-v. There being tenuous atmosphere, already, that actually requires maintenance boosts every now and then to keep it up there. So maybe you need to consider it much as you do with a launch profile (over-powered rocket first-stage gets you over the atmospheric 'hump' quicker, and requires less total delta-v expendes for the same eventual mission). But the ultimate solution (entirely hand-brake your orbit, just fall straight down from space itself) is also not practical or necessary.
All in all, your "some hundreds m/s" is probably not far wrong.
Perhaps chase down the Crew Dragon operating manual, as a current example, if you want to put such actual figure(s) as used. Not sure how public that info is, but there are a lot of armchair experts out there that particularly reverse engineer vague SpaceX release-info into solid-looking figures that Musk then confirms "sound about right" if he responds to their assessments. If the usual suspects haven't crunched this number, then I'd be surprised. 05:24, 19 March 2024 (UTC)
I played around a bit with my DIY orbit calculator LITHOBREAK, to go from a 300x300 km orbit (calculated above the surface) to a 300x100km one, which puts your perigee inside the upper atmosphere, you need a Delta-V of 59m/s. To raise your apogee to about GEO, you need roughly 2400 m/s. I could be wrong (cobbled the tool togehther a long time ago), but it looks just about right. -- 06:06, 11 April 2024 (UTC)

My reading: The original plan for Voyager 1 was it, after LEO to complete its mission and to be destroyed by burning in the atmosphere. So, all the spectacular discoveries of Voyager 1, including the Pale Blue Dot, are unintentional results of Cara’s miscalculations. Contrary to popular opinion, the Carl’svcoworkers are deeply disappointed that Voyager didn’t burn. 12:43, 19 March 2024 (UTC)