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Revision as of 16:11, 20 August 2013

Welcome to the explain xkcd wiki!

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Moon Armor Index
Astronomers are a little unsure of the applicability of this index, but NASA's Planetary Protection Officer is all in favor.
Title text: Astronomers are a little unsure of the applicability of this index, but NASA's Planetary Protection Officer is all in favor.

Explanation

Ambox notice.png This explanation may be incomplete or incorrect: Created by a ROCK-LOVING MOON ARMOR SAMURAI BOT - Please change this comment when editing this page. Do NOT delete this tag too soon.

In this comic, Randall hypothesizes a situation in which each planet's moons were converted into protective armor to coat their respective planets. For example, the Moon would coat Earth in a 43 kilometer layer if it were molded into protective armor for the planet. It is unknown how the moons would be converted into armor, but with current technology, this would be highly impractical, if not impossible.[citation needed] It is also unclear how planets such as Jupiter, Saturn, Uranus, and Neptune, which are gas giants and thus have no solid surface, would sustain such a layer of armor, nor is it immediately evident what threat might necessitate such drastic measures. A 43km moon rock layer might in fact endanger life on Earth by blocking out the sun and impacting ecosystems, rather than protecting it.

Mars' moons Phobos and Deimos, being very small compared to Mars, would make a very thin layer over Mars. Huge Jupiter would be covered with almost 3km of "moon", which indicates just how much moon mass there is around Jupiter. This is, to a smaller degree, similar for Saturn, Uranus and Neptune.

Some trans-Neptunian dwarf planets and dwarf planet candidates are included, as well: Only Pluto, having a moon (Charon) of a comparable size to its planet, would have a layer thicker than Earth's. Salacia, Haumea, Quaoar, Gonggong and Eris are among the ten largest such objects.

The comic uses the ≈ sign to show that the formula is only an approximation: this is because it does not take account of the armor having a larger surface area as it gets thicker. This approximation would be perfect for a shield of thickness zero, but for the thickest shield (Pluto) the error is around 4% (52.5 km by approximation, but 50.4 km by calculation). If P, M and A are the Planet radius, Moon radius and Armour thickness respectively, we can use V(P+A) = V(P) + V(M) to get A^3 + (3P)A^2 + (3P^2)A - C^3 = 0 and then solve the cubic to make an accurate calculation. For multiple moons, this calculation can be used repeatedly to armor each moon with the previous moon, before using the final moon-conglomerate to armor the planet. Compression effects due to increased gravity at the planet's surface in comparison to the moon's surface, which could compress the moon mass into smaller volumes, are not taken into account either.

The title text states that astronomers are "unsure" about the applicability of protective armor made from moons, possibly because they are wary of moons and planets getting too close. It is dubious whether there would be an actual increase in planet safety due to the procedure. Moons as they are already serve a protective purpose by deflecting incoming asteroids, and by covering a small portion of sky.

The title text continues that NASA's Planetary Protection Officer, whose job it is indeed to protect planets, is purportedly in favor of the idea. However, they are in fact responsible for keeping other celestial bodies safe from Earth's contamination, not for shielding planets in armor, as the title text suggests. There is no known method of shielding other planets from contamination by physically armoring them. [citation needed]

Planet/
dwarf planet
Area (km²) Moons Volume (km³) Moon shield thickness
Earth 5.1007*10^8 1 2.196*10^10 43 km (27 mi)
Mars 1.4437*10^8 2 (5695±32)+(1033±19) 5 cm (2 in)
Jupiter 6.1469*10^10 95 1.7646*10^11 2.87 km (1.78 mi)
Saturn 4.27*10^10 146 7.651*10^10 1.79 km (1.11 mi)
Uranus 8.1156*10^9 28
Neptune 7.6187*10^9 16
Pluto 1.7744*10^7 5 (9.322×10^8)+(approx 87100+38800+900+200) 52.5 km (32.6 mi) (by XKCD)

50.4 km (31.3 mi) (by full calculation)

Salacia 2.27*10^6 1 1.41*10^7 6.21 km (3.85 mi)
Haumea 8.14*10^6 2 (17.2*10^6)+(2.57*10^6) 2.43 km (1.51 mi)
Quaoar 3.78*10^6 1 4.19*10^6 1.11 km (0.69 mi)
Gonggong 1
Eris (1.70±0.02)*10^7 1

Transcript

Ambox notice.png This transcript is incomplete. Please help editing it! Thanks.

[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
[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 Mt Everest. The zoom in to the Mars' bar has a thickness label of 2" and is compared to a rover wheel over it. Pluto's bar has a label named "(Mostly Charon)", with arrows pointing away from the label.]


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