Question

What is the escape speed (in km/s) from an Earth-like planet with mass 6.5e+24 kg and radius 70.0 x 109 m? Use the gravitational constant G = 6.67 x 10-1 måkg' s?

Answer 1

In order to calculate the escape speed, we can use the formula below:

$v=\sqrt[]{\frac{2GM}{d}}$

So, for G = 6.67 * 10^-11, M = 6.5 * 10^24 and d = 70 * 10^9, we have:

$\begin{gathered} v=\sqrt[]{\frac{2\cdot6.67\cdot10^{-11}\cdot6.5\cdot10^{24}}{70\cdot10^9}} \\ v=\sqrt[]{\frac{86.71\cdot10^{13}}{70\cdot10^9}} \\ v=\sqrt[]{1.2387\cdot10^4} \\ v=1.113\cdot10^2 \\ v=111.3\text{ m/s} \end{gathered}$