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

## Second cosmic velocity

`$$ v_2 $$`Unit

`$$ \frac{\mathrm m}{\mathrm s} $$`

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

`$$ r $$`Unit

`$$ \mathrm{m} $$`

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

## Mass

`$$ M $$`Unit

`$$ \mathrm{kg} $$`

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

## Gravitational constant

`$$ G $$`Unit

`$$ \frac{\mathrm{N} \, \mathrm{m}^2}{\mathrm{kg}^2} = \frac{\mathrm{m}^3}{\mathrm{kg} \, \mathrm{s}^2} $$`

The gravitational constant is a physical constant that occurs in equations describing the interaction between masses. It has the following experimentally determined value:

`$$ G ~\approx~ 6.674 \, 30 ~\cdot~ 10^{-11} \, \frac{ \mathrm{m}^3 }{ \mathrm{kg} \, \mathrm{s}^2 } $$`