Well, I've been in a mine lift - basically a wire cage an a bloody long cable - looking up as it went down a 2,000m hole.
The sky rapidly becomes a blindingly bright circular dot as your eyes adapt to the darkness and I doubt you'd see any stars for this reason. After a few hundred metres the sky is so small it can't be seen at all as the lift shaft was maybe 3-4m diameter. Hard to say though is it went down/up so fast height was very hard to judge.
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