Escape velocity

Definition

Escape velocity is the minimum speed needed for an object to break free from the gravitational attraction of a massive body without further propulsion. It depends on the mass and radius of the body being escaped from.

5 Must Know Facts For Your Next Test

1. Escape velocity is derived from equating kinetic energy with gravitational potential energy: $\frac{1}{2} mv^2 = \frac{GMm}{r}$.
2. For Earth, the escape velocity is approximately 11.2 km/s.
3. 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.
4. Escape velocity does not depend on the mass or shape of the escaping object but only on the properties of the planet or star it’s escaping from.
5. If an object's speed reaches escape velocity, it will move away indefinitely unless acted upon by another force.

Review Questions

• What is the formula to calculate escape velocity?
• How does escape velocity relate to kinetic and potential energy?
• Why doesn't escape velocity depend on the mass of the escaping object?

Related terms

Gravitational Potential Energy: The energy possessed by an object due to its position in a gravitational field, given by $U = -\frac{GMm}{r}$.

Kinetic Energy: The energy possessed by an object due to its motion, calculated as $KE = \frac{1}{2}mv^2$.

$G$ (Gravitational Constant): $G$ is a proportionality constant used in Newton's law of universal gravitation, approximately equal to $6.67430 \times 10^{-11} \, m^3 kg^{-1} s^{-2}$.