Formula: Third Cosmic Velocity (Escape the Solar System) Velocity Mass Planet radius Abstand Planet-Sonne
$$\class{red}{v_3} ~\approx~ \sqrt{ G \, \left( (\sqrt{2}-1)^2 \, \frac{ \class{brown}{M_{\text{s}}} }{ R } ~+~ 2\frac{ \class{brown}{M_{\text p}} }{ R_{\text p} } \right) }$$
$$\class{red}{v_3} ~\approx~ \sqrt{ G \, \left( (\sqrt{2}-1)^2 \, \frac{ \class{brown}{M_{\text{s}}} }{ R } ~+~ 2\frac{ \class{brown}{M_{\text p}} }{ R_{\text p} } \right) }$$
Third cosmic velocity
$$ \class{red}{v_3} $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$
Escape velocity necessary to escape the gravitational field of the solar system from the Earth without falling back into the solar system. Here, only the most dominant gravitational force is considered, namely that of the sun.
Solar mass
$$ \class{brown}{M_{\text{s}}} $$ Unit $$ \mathrm{kg} $$
The mass of our sun or another central star.
Planet mass
$$ \class{brown}{M_{\text p}} $$ Unit $$ \mathrm{kg} $$
Mass of the Earth or another planet from which the solar system is to be left.
Planet radius
$$ R_{\text p} $$ Unit $$ \mathrm{m} $$
Radius of the Earth or another planet from which the escape is started.
Abstand Planet-Sonne
$$ R $$ Unit $$ \mathrm{m} $$
Der mittlere Abstand der Erde (oder eines anderen Planeten) von der Sonne (oder einem anderen Zentralgestirn).