Escape velocity

Definition

Escape velocity is the minimum speed an object must have to break free from a celestial body's gravitational influence without further propulsion. It depends on the mass and radius of the celestial body.

5 Must Know Facts For Your Next Test

1. 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.
2. Escape velocity does not depend on the mass or shape of the object attempting to escape.
3. For Earth, the escape velocity is approximately 11.2 km/s.
4. Escape velocity is derived by equating kinetic energy and gravitational potential energy.
5. If an object reaches escape velocity, it will move away from the celestial body indefinitely unless acted upon by another force.

Review Questions

• What factors determine a celestial body's escape velocity?
• Why does an object's shape not affect its escape velocity?
• What is Earth's escape velocity?

Related terms

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

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

Gravitational Constant (G): A fundamental constant denoted by $G$, approximately equal to $6.67430 \times 10^{-11} \text{m}^3 \text{kg}^{-1} \text{s}^{-2}$, which appears in Newton's law of gravitation.