Definition:Escape Velocity

Definition

Let a body be propelled vertically upwards from the surface of a planet

Let the body keep travelling away from the planet indefinitely.

Let resistance from the atmosphere of the planet be considered as negligible.

The smallest initial speed at which this is possible is known as the escape velocity of the planet.

Examples

Earth

The escape velocity of Earth is approximately $11 \cdotp 2 \, \mathrm {km \, s}^{-1}$.

Also known as

Escape velocity is more properly known as escape speed, but the former is more usual.

Also see

• Escape Velocity of Projectile fired Upwards: this value is shown to be $\sqrt {2 g R}$.

• Results about escape velocity can be found here.

Sources

• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $1$: The Nature of Differential Equations: $\S 5$: Falling Bodies and Other Rate Problems: Problem $3$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): escape speed (escape velocity)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): escape speed (escape velocity)