Question

You have been visiting a distant planet. Your measurements have
determined that the planet's mass is twice that of the earth but the
free fall acceleration at the surface of the planet is only one fourth
of that at the surface of the earth.
a) What is the planet's radius
b) To get back to earth you need to escape the planet. What minimum speed does your rocket need?

Answer 1

PART A:

The acceleration due to gravity is given by

Now, the acceleration due to gravity for the earth is

And the acceleration due to gravity for the other planet is

We have

and

Putting these values

The radius of the earth is

That gives us the radius of the planet is

So, the radius of the planet is 18040 km.

_________________________________________

PART B:

The escape velocity is given by

So, the escape velocity of the planet is

The mass of the earth is

Putting the values

So, the escape velocity is 9.4 km/s.