Difference between revisions of "Talk:2908: Moon Armor Index"
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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.'' [[User:EebstertheGreat|EebstertheGreat]] ([[User talk: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.'' [[User:EebstertheGreat|EebstertheGreat]] ([[User talk:EebstertheGreat|talk]]) 03:17, 19 March 2024 (UTC) | ||
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+ | 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? |
Revision as of 03:33, 19 March 2024
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?