Dot product between relative velocity and relative position in orbital mechanics

Question

Reading Curtis' book Orbital Mechanics I found this relation that confused me.

$$ \underline{r}\cdot\underline{\dot{r}}=r\dot{r} $$

What happens, say, for a circular orbit where $\underline{r}$ and $\dot{\underline{r}}$ are orthogonal? Shouldn't the scalar product be zero?

Thank you!

Answer 1

Yes, it should be, and it is. On the right side of the equation, $\dot r$ is zero for a circular orbit, because $r$ is constant.