Escape Velocity Calculator

Formula

The formula to calculate the escape velocity (ev) is:

\[ ev = \sqrt{\frac{2 M G}{R}} \]

Where:

\( ev \) is the Escape Velocity (m/s)
\( M \) is the Mass of the Planet (kg)
\( G \) is the Gravitational Constant (\(6.674 \times 10^{-11} \, \text{N} \, \text{m}^2 / \text{kg}^2\))
\( R \) is the Radius of the Planet (m)

What is Escape Velocity?

Escape velocity is the speed that an object needs to travel to escape the gravitational pull of a larger body. It is the minimum velocity required to leave the planet without further propulsion.

Example Calculation

Let's consider an example for Earth:

Mass of the Planet (M): \(5.972 \times 10^{24}\) kg
Radius of the Planet (R): \(6.371 \times 10^{6}\) m

Using the formula to calculate Escape Velocity:

\[ ev = \sqrt{\frac{2 \times 5.972 \times 10^{24} \times 6.674 \times 10^{-11}}{6.371 \times 10^{6}}} \approx 11186 \, \text{m/s} \]

This means that the escape velocity for Earth is approximately 11186 m/s.