The skill, knowledge, or state of being an artillery soldier; the practice and expertise required in operating artillery weapons.
From artillery plus -ship (a suffix meaning 'state or condition of'). This follows the pattern of creating abstract nouns from professions, like horsemanship or statesmanship.
The -ship suffix is ancient and incredibly productive in English—you can add it to almost any noun to mean 'the state or practice of being that thing,' which is why we have everything from friendship to craftsmanship to artilleryship.
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