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The orbital velocity is inversely proportional to the square root of the radius of the orbit
Consider an astronomical body in which the mass is distributed spherically. Let M(r) be the amount of mass that is contained within a distance $\mathbf{r}$ of the center of the body.
For circular orbits the gravitational attraction for a mass $m$ has to balance the centrifugal force for that mass in the orbit. This means that
$\frac{\mathrm{GmM}}{\mathrm{r}^2}=m v^2 / \mathrm{r}$
where $\mathrm{G}$ is the gravitational constant and $\mathrm{v}$ is the orbital velocity. The mass $m$ cancels out and is irrelevant. Thus the orbital velocity is given by
$v^2=\frac{\mathrm{GM}}{\mathrm{r}} \Rightarrow v=\sqrt{\frac{\overline{\mathrm{GM}}}{\mathrm{r}}}$
For circular orbits the gravitational attraction for a mass $m$ has to balance the centrifugal force for that mass in the orbit. This means that
$\frac{\mathrm{GmM}}{\mathrm{r}^2}=m v^2 / \mathrm{r}$
where $\mathrm{G}$ is the gravitational constant and $\mathrm{v}$ is the orbital velocity. The mass $m$ cancels out and is irrelevant. Thus the orbital velocity is given by
$v^2=\frac{\mathrm{GM}}{\mathrm{r}} \Rightarrow v=\sqrt{\frac{\overline{\mathrm{GM}}}{\mathrm{r}}}$
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