Question

What is the escape speed (in km/s) from an Earth-like planet with mass 4.9e+24 kg and radius 70.0 × 105 m? Use the gravitational constant G = 6.67 × 10-11 m3 kg-1 s-2.

Answer 1

Answer:

The escape velocity = 9.66 km/s

Explanation:

The mass of the planet is represented by m

$m=4.9\times10^{24}\operatorname{kg}$

The radius is represented by r

$r=70.0\times10^5m$

The gravitational constant is represented by G

$G=6.67\times10^{-11}m^3kg^{-1}s^{-2}$

The escape velocity (v) is given by the formula:

$\begin{gathered} v=\sqrt[]{\frac{2GM}{r}} \\ v=\sqrt[]{\frac{2\times6.67\times10^{-11}\times4.9\times10^{24}}{70\times10^5}} \\ v=\sqrt[]{\frac{65.366\times10^{13}}{70\times10^5}} \\ v=\sqrt[]{0.9338\times10^8} \\ v=\sqrt[]{93380000} \\ v=9663.33\text{ m/s} \\ v=9.66\text{ km/s} \end{gathered}$

The escape velocity = 9.66 km/s