Escape Velocity

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

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

Where:

\(\large{ v_e }\) = escape velocity

\(\large{ g }\) = gravitational acceleration

\(\large{ m }\) = mass of the plamet or moon

\(\large{ r }\) = radius from the center of mass (plamet or moon) to start point

\(\large{ G }\) = universal gravitational constant

Solve For:

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