Question

We have a planet with the same medium density as the earth but that has three times bigger radius. How big would the gravitational pull be on the surface of this planet if you compare it to the gravitational pull at earth at 9,82m/s^2. I need a thorough solution to this question please, and also, please explain each step of the solution thoroughly as I'm new to this subject and don't know so much.

Answer 1

Weigh of any object is given by

where m is the mass of the object and g is acceleration due to gravity.

Let's consider that the object is on the surface of the planet whose mass is M and radius is R, then according to Newton's law of gravitation, the gravitational force between the planet and the object is given by

but this force F is nothing but the weight of the object. So

(Acceleration due to gravity on earth)

(The radius of the planet is 3 times the radius of the earth.)

So the gravitational pull on the surface of the planet is one-ninth of the gravitational pull on the earth.