So I wanted to derive the total energy for an elliptical orbit, $E = -GmM/2a,$ and while I was doing it, I ran into this hurdle. So at the closest point to the focus, the orbiting object is at a distance of $a(1-e)$ from the focus, where a is the semi-major axis and e is the eccentricity. So if we were to take the centripetal force at this point we should get $$\frac{mv^2}{r} = \frac{GmM}{r^2}$$ and $r = a(1-e)$ so then we would get $$\frac{1}{2}mv^2 = \frac{GmM}{2a(1-e)}$$ which is the kinetic energy. If we were to add this to the potential energy $$U = -\frac{GmM}{a(1-e)},$$ we get the total energy as $$E = -\frac{GmM}{2a(1-e)}.$$ Isn't this wrong because the total energy of an ellipse is $E = -GmM/2a$? Why did I end up with a total energy not equal to that?