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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!

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  • $\begingroup$ 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? $\endgroup$
    – GiorgioP
    Oct 10 '20 at 16:56
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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.

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