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I'm currently working on an essay regarding astrophysics. The level of this essay is of high school standards but I do like math and physics so advanced calculations doesn't frighten me.

Anyway so the essay's is about the astrophysics behind our search for extraterrestrial planets and I'm keen to conclude this. However, I seem to get stuck at the math part since I don't know what kind of formulas I should use for this. For instance the transit method or the Doppler method and more. To get this essay as complete as possible, I would like to demonstrate my own examples in this by having mathematical formulas and calculations for my "own solar system"

Are there any persons here who are familiar with the very physics behind extraterrestrial methods? Not the literal part but the mathematical part. If you know any about anything then you're the best!