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Why we have two formulas for Standard Gravitational Parameter: $$\mu=GM \ \,{\rm and}\, \mu = rv^2 \ .$$

I don't see any direct connection between the two formulas. How can we derive the second from the first? Is it somehow connected with this formula, $$v_e = \sqrt{\frac{2GM}{r}}.$$

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The first definition of $\mu=GM$ is the standard definition of the SGP. The second one comes from the velocity of a circular orbit. If you have an object in a circular orbit of radius $r$ and velocity $v$ around a body of mass $M$, then the velocity is given by $$v=\sqrt{\frac{GM}{r}}$$

From this you can see that $rv^2=GM$ for circularly orbiting objects. Thus the two definitions are equivalent

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