I understand that, do you understand that they're easier to derive with calculus?
I could just as easily Google the formulation of it, and copy and paste. I made this thread to teach, not to be tested about some introductory level math lol
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I didn't ask you to derive them from calculus, I asked you to derive them from first principles. Shouldn't be too hard for an astrophysicist.
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http://lmgtfy.com/?q=Kepler%27s+laws+of+motion And what difference would it make if I just copied what I could find here? Nothing. No, I don't feel like doing rudimentary functions concerning ellipses, when I can just as easily define these laws using a faster, more efficient method. Ask yourself, what kind of math would an astrophysicist do in 2016?