In a scale model in which the stars are ships, the average ship will be over a million miles from its nearest neighbour.
Why the writer not use THE before the adjective nearest?
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We use determiners before nouns, and determiners can be classified in five groups (Source):
Articles: a/an, the
Demonstratives: this, that, these, those
Possessives: my, your, his, her, its, our, their, x’s (possessive ’s)
Quantifiers: (a) few, fewer, (a) little, many, much, more, most, some, any, etc.
Numbers: one, two, three, etc.
I the sentence you quoted, the author wants to describe the vicinity of a ship and they chose a possessive determiner. Although I don't know what the writer tries to convey by "the average ship", perhaps average in size, he or she could simply say:
The distance between one (average?) ship to the other will be more than a million miles.
My side note: Personally, I haven't faced a sentence which had two determiners before a noun. So, apart from the fact that it could sound odd, I would think that is not grammatical to have two determiners in a row.However, I am not 100 percent sure myself.