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 depends only on the mass of the primary body and the radial distance from its center. It is independent of the mass of the escaping object. It is also independent of direction, provided no additional forces are present. For Earth, using standard accepted values for its mass and mean radius, the escape velocity at the surface is approximately \(11.2 \; km/s \). This value assumes no atmospheric drag and no rotational assistance. In practical aerospace applications, real launch systems require greater initial energy due to atmospheric losses, gravity losses during ascent, and trajectory constraints; however, these are engineering corrections to the ideal theoretical escape condition.
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.
