Escape Velocity: Definition, Formula and Derivation

In escape velocity class 11, students learn about the minimum speed required for an object to escape the gravitational pull of a planet. The escape velocity formula helps us calculate this speed given the planet’s mass and radius. One of the most important applications is finding the escape velocity of Earth, which is a frequently asked question in board exams and competitive exams. In this article, we will understand the derivation of escape velocity, the escape velocity of Earth formula, and solve numerical problems in a simple and clear way so that every student can understand the concept easily.

What is Escape Velocity?

It is the minimum velocity required by an object to escape from the gravitational field of a planet without coming back is known as escape velocity.

Formula of Escape Velocity

Where:
G = Universal Gravitational Constant
M = Mass of the planet
R = Radius of the planet

Derivation of Escape Velocity (Class 11)

Escape Velocity of Earth Formula

For Earth:

For Earth:

• $G = 6.67 \times 10^{-11} \, Nm^2/kg^2$
• $M = 5.98 \times 10^{24} \, kg$
• $R = 6.37 \times 10^6 \, m$

After substituting the values into the escape velocity formula, we get v_e​= 11.2 km/s.

Important Points

• Escape velocity does not depend on the mass of the object
• It depends only on the mass and radius of the planet
• It is √2 times orbital velocity
• The escape velocity of the Moon is less than that of Earth

Relation Between Escape Velocity and Orbital Velocity

Now compare both formulas:

Orbital velocity:$$v_o = \sqrt{\frac{GM}{R}}$$

Escape velocity: $$v_e = \sqrt{\frac{2GM}{R}}$$

Therefore:$$\boxed{v_e = \sqrt{2} \, v_o}$$