1389: Surface Area
Title text: This isn't an informational illustration; this is a thing I think we should do. First, we'll need a gigantic spool of thread. Next, we'll need some kind of... hmm, time to head to Seattle.
- A larger version of this image can be found by clicking the image at xkcd - which can be reached easily from here as always, by clicking on the comic number above.
- 1 Explanation
- 2 Transcript
- 3 Discussion
This map shows the total surface areas of all terrestrial planets, dwarf planets, moons, asteroids and minor planets that are larger than 100 m in the Solar System. They have all been represented as regions of a single massive landmass - a supercontinent like Pangaea - which is clearly surrounded by some kind of ocean.
Solid Surfaces Present in Comic
On the area that signifies Earth the continents are drawn using a map projection that keeps the scale of the continents correct. (This is something that Randall cares about as can be seen in 977: Map Projections). The parts of the surface of the Earth that are covered by oceans are also included in the surface area of the Earth (i.e. the map shows the Earth's crust). An extra layer of 3–4 km of water seems rather insignificant when comparing to the Earth's radius of 6,370 km.
The Moon has been inlaid in this map next to Antarctica which thus makes a great comparison of how small the Moon is compared to the Earth (there is room for more than 13 lunar surfaces on the Earth). Similarly, it is clear that the planet Venus is almost as big as the Earth.
This is also the general idea of the map - to give an idea about how big the Earth is and how small many of the other known planets etc. are; both compared to Earth and to each other. The map drawn on the Earth is probably there mainly as a guide to size, because none of the features that are known on some of the other objects, especially The Moon (i.e. craters and "seas") and on Mars (i.e. Olympus Mons), are included.
Other Moons, Asteroids, and Dwarf Planets
The objects mentioned by name on the map are all but one amongst those that have reached hydrostatic equilibrium and these are all included on this List of gravitationally rounded objects of the Solar System.
The one named object that is not on the above list is the asteroid Vesta, which is included because it is the second largest object in the Asteroid belt. It is placed right next to the largest object in this belt, the dwarf planet Ceres, which is no longer considered an asteroid. And next to these two are the rest of the asteroids in two areas (see below), which thus groups all asteroids together.
The only object from the above list, (that qualifies for having a solid surface in hydrostatic equilibrium), which is not included is the Saturn moon Mimas, which is also clearly the smallest object on the list.
This moon should have been located amongst the other five smaller moons of Saturn between the Earth and Titan (the largest of Saturn's moons). Mimas has a surface area of 490,000 km2 which is somewhat smaller than the smallest included Saturn moon Enceladus with a surface area of 799,000 km2.
Generally the moons that belong to a given planet (for those with more than one moon large enough to be included), have been clustered together. Apart from the six (not seven...) moons of Saturn to the right of Earth, the four Galilean moons moons of Jupiter are located above the Earth, the five included moons from Uranus is located to at the top to the far right.
The last planet to have many moons is Neptune, but only Triton is included. This is a fairly large moon, and the only of the 14 known moons of Neptune to be on the above list. However, there is one other moon, Proteus which is notable for being as large as a body of its density can be without being pulled into a spherical shape by its own gravity. It has a length of 424 km in the longest direction, and a mean radius of 210 km. A rough calculation of its surface area from this mean radius gives an area of 550,000 km2, making the surface area slightly larger than Mimas. As there is an unlabeled area located right next to the other Neptune moon Triton, it is most likely that this small area should represent Proteus, and that it is an error that it was not labeled.
As this is the smallest area, the cut-off of objects could have been at 500,000 km2, as Vesta is also larger than this, which would make room for Proteus, but explain the missing Mimas.
Two of the included objects also have moons that are large enough to be included: Earth, of course, and the dwarf planet Pluto with its moon Charon. In both cases these moons have been inlaid in the area of their mother planet.
Whereas the moons of the gas giants and the asteroids have been located above and to the right of the Earth, the planets and dwarf planets have been included below earth (along with the two moons mentioned above). Mercury, Mars and Venus all touching Earth, and then below them the four Trans-Neptunian dwarf planets - the Plutoids.
Not Included Dwarf Planets
On the list from above there are, however, also these 10 objects which have not been included with name on the map. These object are, however, only likely candidates for being dwarf planets (depending on whether they have reached hydrostatic equilibrium or not), and on the map they have thus been relegated to the sections without individual names. These object are thus probably grouped together (along with other relatively small objects like comets and smaller moons) in the area labeled Various small moons, comets, etc, which is located at the bottom of the map between Mercury and Mars. The surface area for all of these object, when the surface area have been estimated, are larger than 1 million square kilometer, and thus larger than several of the named objects. So it is not the size that is the reason why such objects as Sedna and Quaoar are not included with name, but probably the fact they are not investigated enough yet.
The remaining objects in the Solar System with a solid surface are the minor planets, which on the map has been labeled as asteroids even though these objects are grouped together in several other "belts" than the Asteroid belt. Here they have been assigned to two regions at the top of the map. Above the right part of the Earth area is the area Asteroids (1 km+) which include any object not already included larger than 1 km. (As these objects are no longer round it is the largest dimension, the length, that should be at least 1 km long). And finally the area Asteroids (100 m+) thus include any object not already included larger than 100 m.
Most of the rest of the objects that have been included in these three sections can likely be found on this List of Solar System objects by size.
Very Small Objects
Tiny objects smaller than 100 m down to space dust are excluded altogether as explained in the note below the headings. This is probably because their total surface area is impossible to estimate accurately, and also because any estimate would likely be too large to fit easily into the map.
Between Earth and Titan is a tiny speck noted all human skin, which is an interesting sort of solid surface. A rough estimate of the average body surface area and thus of the average area of all humans skin can be made from these average values and from population pyramids as this pyramid for 2015. Average adults have a skin area of around 1.7-1.8 m2, but as a large part of the human population are children (with skin area down to about 0.25 m2 for infants) the total average will be smaller. By extrapolating the given values an average area of about 1.6 m2 can be found. This would make the area 7.2 billion × 1.6 m2 ≈ 11,500 km2. This is 60 times smaller than the smallest of the labeled moons Miranda (of Uranus) with a surface area of 700,000 km2.
The title text jokingly claims that this comic is not actually for information, but rather is something Randall thinks we should really do – that is, to stitch all the solar system's solid surfaces together, as the sub-sub heading says. To do this, we would need a giant spool of thread and then something he has to go get in Seattle… which presumably must be the Space Needle, a needle-like tower in Seattle, which should then be used in this grand project.
This could also have been a reference to the Seattle seamstresses if it weren't for the fact that it's not.
Skinning Planets and Surface Areas
Since the land areas are on the surfaces of spheres, this would seem impossible as it would involve lots of deformation and be particularly challenging. It will also be very gruesome when he comes to the part of collecting (and stitching) all human skin together. The inclusion of this speck on the map is, however, also there to make it clear what the real intention is with the planets. Their surface is to be "skinned" of them, as you would have to do with the humans! Then it is all these "planet skins" that should be stitched together using the space needle. This also explains the ragged edges, and why the continents keep their correct size. It would make Randall into a planetary version of The Silence of the Lambs movies character Buffalo Bill, a serial killer who tried to make a suit out of the skin from the women he killed.
Randall would also need quite a lot of space for the very large ocean. However, the whole supercontinent is just somewhere between 3-4 times larger than the area of the Earth. And the area of the entire image is less than 9 times the area of the earth. As the formula for calculation surface areas for spheres (4*π*r2) goes with the radius (r) squared, the diameter of the planet needed for the experiment do not need to be larger than 3 times that of the earth. Although there are no objects in the Solar System with this particular size, it is still smaller than the gas giants, the smallest of these have a radius of almost 4 times that of the earth. Exoplanets with this range of diameters have certainly been found, however, already at 1.7 times the earth radius most planets size to be of the Super-Earth type and turns in to the gas dwarf type of planets. So an ocean of the size needed are not easy to come by.
As has been explained above the earth's surface is included disregarding surface water (oceans) and the same is valid for other objects with surface water, as the Saturn moon Titan which has great lakes (or even oceans) of liquid methane on the surface or the Jupiter moon Europa which is covered in a deep ocean with a thick cap of ice. (Interestingly this moon is placed on the map very near to the continent of Europe - maybe for easy comparison of these two areas).
The gas giants Jupiter, Saturn, Uranus, and Neptune have, however, not been included because they do not have any "solid surfaces"; even if they had a solid core (which is itself not clear), this would not comprise any "surface". The gas giants are believed to lack any well-defined surface at all, with the gases that make them up simply becoming thinner and thinner with increasing distance from the planets' centers, eventually becoming indistinguishable from the interplanetary medium. But if they were included via some sort of surface definition, the map of this comic would become a tiny speck amongst the map of the gas giants. Similarly, the surface of the Sun is also not considered a solid surface but hot plasma; if it were included it would reduce even a map of the gas giants to a tiny speck.
The map is drawn in a similar style to the two maps of the Internet that Randall has created in the past:
Below is a table listing the object roughly in the order they would be read of the map (the same order as in the transcript.) But they can be sorted by each of the columns.
The data is taken when possible from the following table: List of gravitationally rounded objects of the Solar System, and surface area is given with three significant digits.
For Vesta and Proteus (the most likely candidate for the unlabeled area next to Triton) the area is calculated from their mean radius (i.e. they are not spherical). See also above in the explanation, also for calculating the area of all human skin.
The surface for a given object is also given as a Fraction of Earth's surface, and from this the number of times the object could be placed on the Earth's surface is given as one divided by this fraction. For instance it can be seen that The Moon's surface can be placed more than 13 times on top of that of the Earth.
|Object||Type||Surface area (km2)||Fraction of Earth's||1/Fraction|
|Io||Moon of Jupiter||4.19×107||0.082||12.2|
|Callisto||Moon of Jupiter||7.30×107||0.143||7.00|
|Europa||Moon of Jupiter||3.09×107||0.061||16.4|
|Ganymede||Moon of Jupiter||8.70×107||0.171||5.80|
|Asteroids (1 km+)||Asteroid||N/A||N/A||N/A|
|Proteus (not labeled)||Moon of Neptune||5.50×105||0.00011||910|
|Triton||Moon of Neptune||2.30×107||0.045||22.2|
|Asteroids (100 m+)||Asteroid||N/A||N/A||N/A|
|Oberon||Moon of Uranus||7.29×106||0.014||71.4|
|Miranda||Moon of Uranus||7.00×105||0.0014||714|
|Ariel||Moon of Uranus||4.21×106||0.008||125|
|Umbriel||Moon of Uranus||4.30×106||0.008||125|
|Titania||Moon of Uranus||7.82×106||0.015||66.7|
|Tethys||Moon of Saturn||3.574×106||0.007||143|
|Enceladus||Moon of Saturn||7.99×105||0.0016||625|
|Dione||Moon of Saturn||3.97×106||0.0078||128|
|Iapetus||Moon of Saturn||6.70×106||0.0132||75.8|
|All humans skin||Human organ||1.15×104||0.000023||43400|
|Rhea||Moon of Saturn||7.34×106||0.0144||69.4|
|Titan||Moon of Saturn||8.30×107||0.163||6.14|
|The Moon||Moon of Earth||3.79×107||0.074||13.5|
|Various small moons, comets, etc.||N/A||N/A||N/A||N/A|
|Charon||Moon of Pluto||4.58×106||0.009||111|
- [At the top of a map is a heading, with two sub headings and a note in brackets:]
- Without the space
- The Solar System's solid surfaces stitched together
- (Excluding dust and small rocks)
- [Below the headings there is a map with several distinct areas. Each area is labelled with a name or a description. This label is noted inside the area, except for areas that are too small; here the label is written outside and a line indicates which area the label belongs to. Only exception is the largest area, on which the contours of the Earth's continents are drawn. Surrounding the map is wavy lines to indicate that this is either an island or one big super-continent placed in an even larger ocean.]
- [Here below are the labels given as they appear in "normal" reading order in as read from left to right in the three main rows as will be indicated:]
- [Row one, above the line defined by the general top of the Earth area:]
- Asteroids (1 km+)
- [Here – above the Asteroids area before the Triton area - is a small unlabelled area (the only other except Earth)]
- Asteroids (100 m+)
- [Row two, the unlabelled Earth area's row, but here only given those that are directly written to the right of this area:]
- All human skin
- [Row three, all the remaining items that are mainly below the Earth area:]
- The Moon
- Various small moons, comets, etc
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