I am aware that the dot product of the position and velocity vector, $(\vec{r}\cdot\vec{v})$, in circular motion under a central force, $F(r)=-\frac{k}{r^2}$, is equal to zero as the two vectors are always perpendicular to each other.

My questions are:

• Is this also the case for elliptical orbits?

• In what situation is the dot product no longer zero?

Thanks