Talk:2908: Moon Armor Index

Can someone hurry up/w the explanation?162.158.159.162 22:43, 18 March 2024 (UTC)

Did it :) --1234231587678 (talk) 00:16, 19 March 2024 (UTC)

According to https://sl.bing.net/kR6wrqrekg0 it would be 43.1 meters. 172.70.174.117 23:17, 18 March 2024 (UTC)

Bing was wrong, it screwed up the units 172.70.38.181 23:39, 18 March 2024 (UTC)!

Anyone figure out if this takes the recently-discovered moons into account? I'd expect as much but it would make a good addition to the explanation. 172.70.131.155 01:39, 19 March 2024 (UTC)

The new moon around Uranus is 8 km in diameter, and the moons around Neptune are 23 km and 14 km in diameter. The inventory of outer moons is believed to be complete down to 2 km for Jupiter, 3 km for Saturn, 8 km for Uranus, and 14 km for Neptune. And the total combined mass of smaller moons (e.g. in Saturn's rings) is also constrained.

All these moons are round, and thus approximately ball-shaped. The volume of a 3-ball with radius r₀ is 4⁄3 πr₀³. Uranus and Neptune are also approximately ball-shaped with radii of 25,559 km and 15,299 km, respectively. (I don't know exactly how these radii are defined, but I assume optically. Uranus and Neptune don't have solid surfaces.) The volume of a spherical shell is just the difference of the outer and inner spheres, so 4⁄3 π(R³−r³) if the outer radius is R and the inner radius is r. These volumes are equal if the whole moon is converted into a spherical shell. So for Uranus, we have 4⁄3 πr₀³ = 4⁄3 π(R³−r³), where r₀ is the radius of the moon, r is the radius of Uranus, and R−r is the thickness of the shell. Solving gives R−r = ³√(r₀³+r³)−r. Plugging in r₀ = 8 km and r = 25,559 km gives R−r = 0.26 mm. If we laid it on top of the other moons instead of the "surface" of Uranus itself, it would make practically no difference. Doing the same calculation for each newly-discovered moon of Neptune gives thicknesses of 17 mm and 3.9 mm (for a total of 21 mm).

In other words, they are tiny rounding errors. EebstertheGreat (talk) 03:17, 19 March 2024 (UTC)

I like that turning the Moon into a spherical shell coating the Earth is not definitely stated to be impossible with current technology. There's so much hedging going on I feel like I'm trapped in a maze in The Shining. EebstertheGreat (talk) 03:17, 19 March 2024 (UTC)

The formula used seems to give the instantaneous technical distance, but in reality, there would be a rate of change of the surface area of the planet as each layer of thickness x was added. Does anyone know if this is significant with the distances we are talking, or does it just turn out to be a rounding error?