# Dot product between relative velocity and relative position in orbital mechanics

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!

• Welcome to Physics SE. Please, take into account that questions line "check my calculations" or 'hot to go from ea. "X" to eq. "y"' are considered homework-like questions and are at risk of been closed. Just as a hint, what would be $\dot r$ in the case of a uniform circular motion? Oct 10 '20 at 16:56

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.