Editing 2908: Moon Armor Index

{{comic
| number    = 2908
| date      = March 18, 2024
| title     = Moon Armor Index
| image     = moon_armor_index_2x.png
| imagesize = 740x390px
| noexpand  = true
| titletext = Astronomers are a little unsure of the applicability of this index, but NASA's Planetary Protection Officer is all in favor.
}}

==Explanation==
In this “What If?”-style comic, [[Randall]] hypothesizes an imaginative situation in which each planet's moon(s) become converted into protective armor (as a form of {{w|Overburden#Analogous uses|overburden}}) to coat the respective planet. For example, the {{w|Moon}} would coat {{w|Earth}} in a 43 kilometer layer if it were molded into protective armor, almost five times the height of {{w|Mount Everest}}. 

This visual index illustrates that the moons of both Earth and Pluto are unusually massive in comparison to their planet. The large relative size of Earth’s moon — and its protective role in deflecting asteroids — is one reason that’s been suggested by astronomers for why intelligent life successfully evolved on Earth.

Mars's moons {{w|Phobos (moon)|Phobos}} and {{w|Deimos (moon)|Deimos}} are small compared to Mars, so they would contribute a thin 2-inch layer of 'armor' around Mars, in contrast to the 20-inch (0.5&nbsp;m) diameter of a {{w|Mars rover}} wheel. Huge Jupiter would be covered with almost 3 km of "moon" matter, which indicates just how much moon mass orbits Jupiter, a situation mostly similar for Saturn, Uranus, and Neptune.

Six trans-Neptunian {{w|dwarf planet}}s and dwarf planet candidates are included, as well: Only Pluto, having a moon ({{w|Charon (moon)|Charon}}) of a comparable size to its planet, would have a layer thicker than Earth's. {{w|120347 Salacia|Salacia}}, {{w|Haumea}}, {{w|50000 Quaoar|Quaoar}}, {{w|225088 Gonggong|Gonggong}} and {{w|Eris (dwarf planet)|Eris}} are among the {{w|List of trans-Neptunian objects#List|ten largest such objects}}. (Two dwarf planets with moons — {{w|Makemake}} and {{w|90482 Orcus|Orcus}} — are not mentioned in the comic, but would be similarly depicted.)

The title text states that astronomers are "unsure" about the applicability of this index, a joking understatement that imagines this comic as being a serious contribution to astronomical academic knowledge. Astronomers might also point out additional issues:
* wariness of {{w|Giant-impact hypothesis|moons and planets getting too close}}.
* moons already serve a protective purpose by deflecting and even intercepting some incoming asteroids (with a ''slight'' chance of turning a future miss into a hit).
* the four gas giants — Jupiter, Saturn, Uranus, and Neptune — lack a solid surface to practically sustain a layer of armor without even ''more'' ambitious engineering than the already complicated process of somehow distributing soft-landed fragments of disassembled satellite evenly all across a planet.
* although the coating would provide some protection to the underlying surface on which it was placed, it would effectively become part of the planet, and raise the surface. The things we would normally care about protecting, such as any life forms that exist, would be forced to relocate to this new surface, and therefore not benefit from any protection, while suffering significant detrimental impact to habitats, etc.

The title text continues that NASA's [https://what-if.xkcd.com/117/ Planetary Protection Officer] is purportedly in favor of the idea. In reality, this officer is actually responsible for keeping other celestial bodies safe from Earth's contamination, not for shielding planets in armor. Theoretically, though, armoring other planets could indeed protect them from further Earth-sourced contamination, and armoring Earth would also theoretically protect other planets by burying the biosphere and all of Earth life not already sent into space — a potentially civilization-smothering action, though a surprisingly unapocalyptic result compared to many of Randall’s “What If?” scenarios.

{| class="wikitable"
|-
! Planet/<br>dwarf planet !! Surface area (km²) || Moons || Total volume (km³) || Moon shield thickness
|-
| {{w|Earth}} || 5.1007×10^8 || {{w|Moon|1}} || 2.196×10^10 || 43&nbsp;km (27&nbsp;mi) (4.86 × height of {{w|Mount Everest}})
|-
| {{w|Mars}} || 1.4437×10^8 || {{w|Moons of Mars|2}} || {{w|Phobos (moon)|(5695±32)}}+{{w|Deimos (moon)|(1033±19)}} || 5&nbsp;cm (2&nbsp;in)
|-
| {{w|Jupiter}} || 6.1469×10^10 || {{w|Moons of Jupiter|95}} || 1.7646×10^11 || 2.87&nbsp;km (1.78&nbsp;mi)
|-
| {{w|Saturn}} || 4.27×10^10 || {{w|Moons of Saturn|146}} || 7.651×10^10 || 1.79&nbsp;km (1.11&nbsp;mi)
|-
| {{w|Uranus}} || 8.1156×10^9 || {{w|Moons of Uranus|28}} || 5.61×10^9 || 0.69 km (0.43 mi)
|-
| {{w|Neptune}} || 7.6187×10^9 || {{w|Moons of Neptune|16}} || 1.04×10^10 || 1.36 km (0.84 mi)
|-
| {{w|Pluto}} || 1.7744×10^7 || {{w|Moons of Pluto|5}} || {{w|Charon (moon)|(9.322×10^8)}}+{{w|Moons of Pluto|(approx 87100+38800+900+200)}} || 52.5&nbsp;km (32.6&nbsp;mi) (by this comic's approximation)
50.4&nbsp;km (31.3&nbsp;mi) (by full calculation)
|-
| {{w|120347 Salacia|Salacia}} || 2.27×10^6 || {{w|Actaea (moon)|1}} || 1.41×10^7 || 6.21&nbsp;km (3.85&nbsp;mi)
|-
| {{w|Haumea}} || 8.14×10^6 || {{w|Moons of Haumea|2}} || {{w|Hiʻiaka (moon)|(17.2×10^6)}}+{{w|Namaka (moon)|(2.57×10^6)}} || 2.43&nbsp;km (1.51&nbsp;mi)
|-
| {{w|50000 Quaoar|Quaoar}} || 3.78×10^6 || {{w|Weywot|1}} || 4.19×10^6 || 1.11&nbsp;km (0.69&nbsp;mi)
|-
| {{w|225088 Gonggong|Gonggong}} || 4.75×10^6 || {{w|Xiangliu (moon)|1}} || 1.44×10^6 || 0.3 km (0.19 mi)
|-
| {{w|Eris (dwarf planet)|Eris}} || (1.70±0.02)×10^7 || {{w|Dysnomia (moon)|1}} || 1.61×10^8 || 9.47 km (5.88 mi)
|}

===Implications of choosing a volume-to-area ratio===
The usual means of comparing a moon to a planet might be to compare the volume of both. This comic compares moon volume (kilometers cubed) to planet surface area (kilometers squared); specifically, the index derives a ''linear'' indicator (the thickness of the new material) by dividing the ''area'' of the main body (proportional to the square of its uncounted radius) into the ''combined volume'' of all other bodies (proportioned cubes of their own radii), which gives an unusual dimensional analysis (dividing X kilometers-cubed by Y kilometers-squared gives a length, Z, in kilometers, not a simple dimensionless ratio).

This particular methodology makes the Pluto-Charon system (Charon being roughly half the diameter and one-eighth the volume of Pluto, before even adding that of the other moons) surprisingly similar to the Earth-Moon one (our sole Moon is around one-quarter Earth's diameter, and therefore less than 2% its volume; also in comparison, the Earth and Moon are respectively slightly more than 150 times and around 3 times the volume of Pluto), but leaves them ''both'' as still standing out significantly against all other planetary comparisons, even against comparably-sized 'planet's.

===The complexities of armor thickness calculations===
The comic uses the ≈ sign to show that the formula is only an approximation: it does not take account the increase in armor surface area as it gets thicker. This approximation would be perfect for a shield of thickness zero, but for the thickest shield (Pluto) around a small celestial body the error is around 4% (52.5&nbsp;km by this approximation, but 50.4&nbsp;km by more thorough calculation). To find the correct value, we can use the formula for the volume of a sphere, V = 4/3 * pi * r³ (where V is the volume and r is the radius). Using this formula, we can find and add together the volumes of each moon, as well as the volume of the planet, to get a total volume of the new shielded planet. Then we can find its radius using the formula r = (V / (4/3 * pi))^1/3, derived from the previous formula. Subtracting the radius of the previous planet from the radius of the new planet gives us the thickness of the armor.

This process described above assumes that all objects involved are completely spherical, which may not be the case. The act of tearing apart a solid moon, perhaps into rough gravel, might add microvoids to the new layering that bulk up the volume slightly. But neither are gravitational compression effects taken into account on an originally loose material; the planet's gravitational pull could settle some of the moon material into a slightly smaller volume than the one it occupied as lower-gravity moon.

The planet below could also be marginally affected by the change in its total planet-and-armor mass, for rocky planets mostly within any {{w|pedosphere}} or previously exposed outer {{w|lithosphere}}. The interaction with {{w|Titan (moon)#Lakes|surface liquids}} and atmospheres, especially in planets defined {{w|Gas giant|primarily by their gas layers}}, would depend much upon how impermeable and/or rigid the chosen layering method made the additional material. One could imagine a spherical shell of moon matter around Jupiter with such high structural strength as to resist crumbling into its gaseous maw. Alternatively, the moon material could be expected to sink towards the gaseous planet's center until it reaches a layer sufficiently dense and/or rigid to stop it sinking further. In this case the moon material would displace a volume of the planet's gas causing an increase in the planet's radius.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[Text above diagram:]
:Moon armor index:
:How thick the shells around various worlds would be if their moon(s) were converted into protective armor
:≈Total moon volume/Planet surface area

:[Above the diagram, there is a depiction of two moons orbiting a planet, an arrow pointing right, and the same planet with an additional layer around it without orbiting moons.]

:[The diagram consists of vertical bars showing "moon armor" thicknesses for the Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto, Salacia, Haumea, Quaoar, Gonggong and Eris. Earth's bar has a label named "43 km thick" and is compared to the height of a comparatively small Mt Everest, with randomly drawn features indicating a cross section of the additional layer's rocky material. Most of the other armor thickness bars are not very tall compared to Earth. Some bars, notably Jupiter's, are embellished with various strata-like lines that possibly correspond to different contributing moons. Most bars show some small dots and patterns. A circular viewport shows the zoomed in detail of the top of Mars's otherwise not visible bar that reveals a thin layer with the label of 2", and also the bottom of a Mars rover wheel on top of the new surface. Pluto's bar is slightly taller than Earth's and has a label "(Mostly Charon)" inside, with arrows pointing into the bar area, which looks similar to that of Earth's Moon.]

{{comic discussion}}

[[Category:Astronomy]]
[[Category:Bar charts]]
[[Category:Mars rovers]]