Escape velocity is the minimum speed an object must reach to break free from a celestial body's gravitational pull without further propulsion. It depends on the mass and radius of the celestial body.
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The formula for escape velocity is $v_{e} = \sqrt{\frac{2GM}{r}}$, where $G$ is the gravitational constant, $M$ is the mass of the celestial body, and $r$ is its radius.
Escape velocity does not depend on the mass or shape of the escaping object.
For Earth, the escape velocity is approximately 11.2 km/s.
In general relativity, escape velocity can be interpreted in terms of geodesics in spacetime.
Black holes have an escape velocity greater than the speed of light, which is why nothing can escape from within their event horizons.
Review Questions
What factors influence the value of escape velocity for a given celestial body?
Why does an object need to reach escape velocity to leave a planet's gravitational field?
How does general relativity provide a different perspective on escape velocity compared to classical mechanics?
A fundamental constant ($G$) that appears in Newton's law of gravitation, representing the strength of gravity; approximately equal to $6.674 \times 10^{-11} \, \text{N m}^{2} \text{kg}^{-2}$.