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Escape from a potential well
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A particle escapes if its energy is positive relative to infinity.
A particle with total energy E ≥ 0 relative to infinity escapes, since gravitational energy is −GMm/r. Setting ½mv² = GMm/R gives the escape speed √(2GM/R).
Earth: about 11.2 km/s.
Escape speed doesn't depend on the direction or mass of the object.
In more detail
An object trapped in a potential well needs enough energy to escape the well. The escape energy is the difference between its energy and the top of the potential barrier.
Real-world uses
- Rockets must provide enough energy to escape Earth's gravitational well.
- Electrons need enough energy to leave a metal surface in the photoelectric effect.
- A rocket must reach escape speed to leave Earth's gravitational well, which is set by the depth of the potential energy well.
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Frequently asked questions
What is escape energy?
The minimum energy needed to leave a bound state, such as a gravitational or electric well.
Why does a deeper well need more energy?
Because the potential energy at the bottom is lower, so more energy must be added to reach the top.
Is escape velocity the same from every planet?
No. It depends on the planet's mass and radius, so a larger or denser planet needs a higher speed to escape.
Related topics in Work, Energy & Power
Efficiency · Energy and power bills · Power of engines and climbers · Work in rotation · Rotational kinetic energy · Rolling without slipping energy