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If we can now explain the formation of stars without supernatural intervention, on what grounds does the bible claim god created them?
Poor question. You're personifying the Bible. It can't make claims. The priestly writer has passed so he can't change what he wrote. The priestly writer also didn't write a scientific paper, he wrote a religious story. The writer doesn't claim his story is based on "science". The writer is not responsible for what people claim today.
Why do some people today still claim the stars were created by God when science has shown that no supernatural intervention is necessary for their formation?
I think the answer depends on the purpose, just like the priestly writer's story.
Scripture is like Newton’s third law of motionfor every action there is an equal and opposite reaction.
In other words, for every biblical directive that exists, there is another scriptural mandate challenging it.
-- Carlene Cross in The Bible and Newton’s Third Law of Motion
™ Version 4.2