Question

The escape velocity at the surface of Earth is approximately 11 km/s. What is the mass, in units of ME (the mass of the Earth), of a planet with three times the radius of Earth for which the escape speed is three times that for Earth?

Answer 1

Answer:11 km/s

Explanation:

Given

Escape velocity at the surface of earth is 11 km/s

Escape velocity is given by

$V_e=\sqrt{\frac{2GM}{R}}$

Escape velocity at the surface of earth

$11=\sqrt{\frac{2GM}{R}}$--------------------1

If Escape velocity is three times and the radius is also the three times

$V_e_2=\sqrt{\frac{2G(3M)}{3R}}$

$V_e_2=\sqrt{\frac{2GM}{R}}=V_e$

i.e. $V_e_2=11 km/s$