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:
where m=59.1 kg is his mass and
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: