Understanding Kepler's Laws: Unraveling the Mathematical Derivations

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I have to write a paper about the derivation of Kepler's laws, but I don't understand how the derivations work. If anyone could help explain to me how they work.
 
on Phys.org
What will you derive the laws from?
There are some possibilities in the Wikipedia article on Kepler's Laws.
You will get help here if you make a start - even a false one.
 

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