Escape velocity is the minimum initial speed required for a body to move away from a massive object and reach an infinite separation distance with zero residual velocity, under the influence of gravitational attraction alone and in the absence of non-conservative forces such as aerodynamic drag or propulsion after launch. It is derived directly from conservation of mechanical energy as formulated in classical mechanics by Isaac Newton.
Escape Velocity Formula |
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\( v_e \;=\; \sqrt { \dfrac{ 2 \cdot G \cdot m }{ r } }\) (Escape Velocity) \( G \;=\; \dfrac{ v_e^2 \cdot r }{ 2 \cdot m }\) \( m \;=\; \dfrac{ v_e^2 \cdot r }{ 2 \cdot G }\) \( r \;=\; \dfrac{ 2 \cdot G \cdot m }{ v_e^2 }\) |
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| Symbol | English | Metric |
| \( v_e \) = Escape Velocity | \(ft\;/\;sec\) | \(m\;/\;s\) |
| \( m \) = Mass of the Planet or Moon | \( lbm \) | \( kg \) |
| \( r \) = Radius from the Center of Mass (Planet or Moon) to Start Point | \( ft \) | \( m \) |
| \( G \) = Universal Gravitational Constant | \(lbf-ft^2\;/\;lbm^2\) | \(N - m^2\;/\;kg^2\) |
Escape velocity is a direct consequence of gravitational potential energy and conservation of energy in classical mechanics. It is not a propulsion requirement to maintain that speed continuously, rather, it is the minimum initial speed required so that gravitational deceleration asymptotically reduces velocity to zero at infinite separation.
