Question

if the mass of planet is eight times the mass of earth and its radius is twice of radius of earth what will escape velocity of that plannet.

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)

v = \frac{ \sqrt{2GM} }{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

Hope it Helps :-)