Formula: Second Cosmic Velocity Second cosmic velocity    Radius of the celestial body    Mass    Gravitational constant

Formula: Second Cosmic Velocity
Escape Velocity of a Rocket to Leave the Gravitational Field of the Earth

Second cosmic velocity

Second cosmic velocity is the velocity necessary to escape without propulsion from the gravitational field of a celestial body.

For a rocket to escape the Earth's gravitational field, it must have the following minimum velocity: \[ \class{purple}{v_2} ~=~ \sqrt{ 2 ~\cdot~ \frac{6.67 \cdot 10^{-11} \frac{\mathrm N \, \mathrm{m}^2}{\mathrm{kg}^2} ~\cdot~5.97 \cdot 10^{24}\,\mathrm{kg} }{6.38 \cdot 10^6 \,\mathrm{m}} } ~=~ 11.2 \, \frac{\mathrm{km}}{\mathrm s} \]

Radius of the celestial body

Radius of the celestial body you are trying to escape. For example, radius of the Earth.


Mass of the celestial body. In the case of the Earth, the mass is: \( 5.972 \cdot 10^{24} \, \mathrm{kg} \).

Gravitational constant

The gravitational constant is a physical constant that occurs in equations describing the interaction between masses. It has the following experimentally determined value: $$ G ~\approx~ 6.674 \, 30 ~\cdot~ 10^{-11} \, \frac{ \mathrm{m}^3 }{ \mathrm{kg} \, \mathrm{s}^2 } $$

+ Perfect for high school and undergraduate physics students
+ Contains over 500 illustrated formulas on just 140 pages
+ Contains tables with examples and measured constants
+ Easy for everyone because without vectors and integrals

Learn more