Question

if the mass of the planet is eight times of the earth and its radius is twice the radius of the earth what will be the escape velocity of that planet?​

Answer 1

Given in the question :-

Planet mass is 8 times that earth

Planet radius is twice then the radius of earth.

Let mass of the Earth = M

Radius of the Earth = R

Now, we know that The equation to get escape velocity  

v = √(2 g r)

 If the mass of planet is eight times then escape velocity = 2 √2 times. 

Escape velocity reduced to by 1/√2. If radius expands twice

Hence the net escape velocity will be increase.

2 √2 ×  (1/√2)= 2 times now.

Now it is clear that the escape velocity of that planet will be 2 times from the earth.

Escape velocity of the earth = 11.2 km/s

Escape velocity of that planet = 2 × 11.2 = 22.4 km/sec.

Hence the escape velocity of that planet will be 22.4 km/s