Elliptic orbits and why sun located at focal point acts like at the center of the ellipse?

In the book "Classical Mechanics Point particles and relativity by Greiner"

We calculate Forces in the motion on an ellipse as follows

we first parametrizate the ellipse $$vec r(t)=<acos(omega t),bsin(omega t)>$$and take second derivative and found $$vec F=mvec a(t)=-momega^2 vec r(t)$$

Which points the center of the ellipse

But then he follows "The planets also move around the sun along elliptic orbits. The sun as the center of attraction located in one of the focal points of the ellipse…"

with formula $$vec F_G=-gamma dfrac{mM}{r^2}dfrac{vec r}{r}$$

Question: If the force required to hold the particle in elliptic orbit points center and the sun is at the focal point so what is the extra force which make the logic complete?