Skip to main content

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

Formula
Formula: Second Cosmic Velocity

Second cosmic velocity

Unit
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:\[ v ~=~ \sqrt{ 2 ~\cdot~ \frac{6.67 \cdot 10^{-11} \frac{\mathrm N \, \mathrm{m}^2}{\mathrm{kg}^2} ~\cdot~5.97 \cdot 10^{24}\,\mathrm{kg} }{6.38 \cdot 10^6 \,\mathrm{m}} } ~=~ 11.2 \, \frac{\mathrm{km}}{\mathrm s} \]

Radius of the celestial body

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

Mass

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

Gravitational constant

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