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

Step-by-step explanation:

The mass of the planet is represented by m

The radius is represented by r

`r=70.0*10^5m`

The gravitational constant is represented by G

`G=6.67*10^(-11)m^3kg^(-1)s^(-2)`

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

`\begin{gathered} v=\sqrt[]{(2GM)/(r)} \\ v=\sqrt[]{(2*6.67*10^(-11)*4.9*10^(24))/(70*10^5)} \\ v=\sqrt[]{(65.366*10^(13))/(70*10^5)} \\ v=\sqrt[]{0.9338*10^8} \\ v=\sqrt[]{93380000} \\ v=9663.33\text{ m/s} \\ v=9.66\text{ km/s} \end{gathered}`

The escape velocity = 9.66 km/s