[Arkcon]

The mines, if they've been launched from 2 planets owned by two empires, aren't orbiting each planet per se, but are all in one sector, so it all happens in one move. In that case, you'll need mine sweeping capability to get them all.

If your hopping between planets in two different sectors within one silmutaneous turn, then the minesweepers are availible to work on each sector individually.