# Escape Velocity: How to Escape the Gravitational Field?

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Newton's law of gravity

F_{\text g} ~=~ G \, \frac{\class{brown}{M} }{r^2} \, \class{brown}{m}

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Gravitational force and centripetal force equated

G \, \frac{\class{brown}{M} }{r^2} \, \class{brown}{m} ~=~ \frac{\class{brown}{m} \, \class{blue}{v}^2 }{r}

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Gravitational acceleration and centripetal acceleration equated

G \, \frac{\class{brown}{M} }{r^2} ~=~ \frac{\class{blue}{v}^2 }{r}

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Gravitational acceleration and centripetal acceleration equated and radius canceled

G \, \frac{\class{brown}{M} }{r} ~=~ \class{blue}{v}^2

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Necessary orbital velocity for a stable orbit

\class{blue}{v} ~=~ \sqrt{ G \, \frac{\class{brown}{M} }{r} }

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