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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