Thank you all for the responses. I am in high school (AP physics) and its no wonder why I do not understand this if you're pointing me in the direction of graduate books.
So then why can r be replaced with a if the orbits are not circular? mv^2/r, as you stated, applies to a circular orbit. How then is it possible to simply replace "r" with "a" in the law of periods equation of Kepler's third law?
Kepler's third law states T^2=(4pi^2/GM) x r^3 for CIRCULAR orbits. My question is, in the derivation for this equation ma=GMm/r^2 why can centripetal acceleration be used to replace a at m(v^2/r)=GMm/r^2 yielding v^2/r=GM/r^2 when the orbit is not circular. Planets have elliptical orbits so why...