I would worry less about whether the credits will transfer and more about challenging him where he is. If he's bored and sullen in high school due to taking course work that he deems worthless and a waste of his time, he probably won't excel as he would have to to get into where he wants to go.
FWIW: I would not expect precalculus to transfer for credit to an elite university and an astronomy course may be dubious as well. Astronomy without a physics prerequisite is usually (not always) intended as a general education course rather than a course for science majors.
I would also note that even if they do not accept the courses as credit, they may very well grant course approval for them (this is one thing you should ask), so that he wouldn't need to retake, say, calculus, even if he didn't get credit for it. He could then take more advanced courses in his major instead, which would put him in an advantageous position for graduate school.