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In one formula of orbital velocity for circular orbit it has inverse relation with radius $$v=\sqrt{\frac{GM}{r}}$$ while in critical velocity relation it has direct $$v=\sqrt{gr}$$ Why?

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    $\begingroup$ Hi, welcome to Physics SE. Please edit your question include the equations you're asking about. I assume one is $v=r\omega$, which you can insert by pasting v=r\omega between two dollar signs. $\endgroup$
    – J.G.
    Commented Aug 26, 2023 at 18:39
  • $\begingroup$ 1.$g=GM_E\over r_E^2$ escape velocity is the relation between kinttic energy and Potential difference rotation velocity is centripetalforce = gravitational force, so two different things. $\endgroup$
    – trula
    Commented Aug 27, 2023 at 12:58

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The two equations are the same, since $$g=\frac{GM}{r^2}$$

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