Escape Velocity

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

velocity escape

Escape velocity, abbreviated as \(v_e\), is the minimum velocity required to leave a planet or moon or the minimum velocity to overcome the pull of gravity.

 

Escape velocity formulas

\(\large{ v_e =  \sqrt { \frac{ 2 \; G \; m}{r} }  }\) 
\(\large{ v_e =  \sqrt { 2 \; g \; r }  }\) 
\(\large{ v_e =  g \; r^2  }\) 

Where:

 Units English Metric
\(\large{ v_e }\) = escape velocity \(\large{\frac{ft}{sec}}\) \(\large{\frac{m}{s}}\)
\(\large{ g }\) = gravitational acceleration \(\large{\frac{ft}{sec^2}}\) \(\large{\frac{rad}{s^2}}\)
\(\large{ m }\) = mass of the plamet or moon \(\large{ lbm }\) \(\large{ kg }\)
\(\large{ r }\) = radius from the center of mass (plamet or moon) to start point \(\large{ ft }\) \(\large{ m }\)
\(\large{ G }\) = universal gravitational constant \(\large{\frac{lbf-ft^2}{lbm^2}}\) \(\large{\frac{N - m^2}{kg^2}}\)

 

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Tags: Equations for Velocity