Asterite is a resource in Warframe that can only be found during Railjack missions. Asterite is used to upgrade your Railjack with new weapons, ordnance, and components. The costs of these items can be pretty high, so prepare to farm quite a bit of Asterite to level up your Railjack fully.
Where to find farm Asterite
While Asterite can be found in any mission, a great place to farm it is at the Phanghoul Satellites node, on Earth Proxima. This is a straightforward and easy mission that involves taking out 30 Fighters and two Crewships. You can finish it quickly, then get down to the real reason you loaded in, Asterite farming.
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Asterite can spawn from asteroids, the red barrels that float around the level, and the metal scrap you can find near wrecks and terrain. Because this level is so large, it is filled with clusters of these objects. When you finish the mission, stay in the level and move from asteroid belt to asteroid belt, farming all the objects. Pick up the drops, and a substantial amount of them should be Asterite.
Because they are in mission drops, Asterite drops will be affected by resource boosters, so if you want to get a 3-day booster from the market and farm for a weekend, this will double the amount that you will gather. To make the process quicker, the crew can all leave the Railjack and search different parts of the level on their Archwings, then go when they have farmed everything they can find.