9) what would be the weight of a 59.1-kg astronaut on a planet with the same density as earth and having twice earth's radius?

The weight of the astronaut is given by

where m=59.1 kg is his mass and  is the gravitational acceleration on Earth. 

To solve the problem, we must find the value of g on the new planet. g is given by

where G is the gravitational constant, M the mass of the planet and r its radius. 
The mass of the planet can be written as

where d is the density and V the volume.
We can assume that the planet is a sphere, therefore the volume is proportional to :

and we can write the mass as

and then, g becomes

So, in the end g is proportional to the radius of the planet, r (because the density of the new planet d is the same as the Earth's one. If the radius of the new planet is twice the Earth's radius, g will be twice the value of g on Earth:

And since the mass of the astronaut is always the same, the weight on the new planet will be twice the weight on Earth: