We're developing teleportation and another planet seems like a safe distance from a bunch of these shenanigans.If you can explain why the number and names of planets are relevant to the gameplay, we can provide you with count/names.
If you're asking about mineral deposits it's a difficult comparison, with a chain of volcanic islands for Japan versus a large and ordinary-seeming landmass for the ENs, but we know it was rich in gold and silver. The 12th century was when Sado Island started mining gold, and in the 17th century it was one of the world's largest producers of gold. It was known for significant surface deposits of native gold and argentite in quartz during the Heian period. If you're asking about mining techniques, let me see what I can do. This page suggests panning native gold dust/nuggets was initially the main (or only) method. It suggests that mining gold ore to refine didn't become widespread until the 16th century, but this seems to have been because of political pressure amidst feuding daimyo leading them to increase the production of precious metals for funding, rather than the lack of capacity. Given the differences in the EN, I suspect mining gold ore may have become common earlier.Let us throw the question back: which types of mines are historically plausible to have existed in 12th century Japan?
This page lists a variety of Japanese mines. It's largely modern but includes the opening dates, and sorting through reveals some historical mines that'd have been open around then. The Toi gold mine was opened by the Sumitomo group in 1370 to exploit hydrothermal gold ore deposits, which is close but insufficient. Researching the Taishu (est 699, initially hydrothermal silver deposits, later kaolinite) and Ikuno (est 807, information scanty but plausibly gold, silver, and/or copper) mines might be a try since they're old enough to qualify but apparently not notable enough to have articles like the Toi gold mine does.
EDIT: I found an additional source here. Going through it for details. The short version seems to be that it claims that gold, silver, lead, copper, and sulfur were the main substances of interest in the requested time period, and that the sort of extensive mining operation we would consider a "mine" were rare if not nonexistent before 1596. This is odd given how early Sado Island began producing gold, but I suspect that the paper is considering surface mining techniques such as placer mining or open pits as distinct from underground mining.
So for a TL;DR: My understanding is that 12th century Japan was mostly using surface mining techniques like placer mining (panning and digging in stream beds) or open pits (just dig a big hole, no tunnels or shafts) for the usual suspects of gold, silver, copper, lead, and sulfur, along with whatever misc gemstones can be discovered alongside those.
EDIT 2 ELECTRIC BOOGALOO: I didn't mention iron, but I think people are more generally aware of Japan's historical difficulties sourcing quality iron ore and how/why the Elemental Nations have already been established to differ in that regard.
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