Answer :
The gravitational force between two objects depends on their masses and the distance between them. The closest answer choice is 1160N.
The weight of an object can be calculated using the formula:
Weight = Mass × Gravity
Given:
The mass of an astronaut o Earth is [tex]m = 59.1 kg[/tex]
weight of an astronaut on Earth is [tex]W = mg[/tex]
where [tex]g = GM/r^2[/tex]
Here the density of the planet is the same as Earth and has twice Earth's radius:
[tex]density = m / V[/tex]
The volume of the planet:
[tex]V = (4/3) \pi (2r)^3[/tex]
[tex]= 8[/tex] (volume of the earth)
The mass of the planet:
[tex]m = 8 m_e[/tex]
The weight of astronauts on the planet is:
[tex]W = m (GM/(2r)^2)\\= m (8 GM/4r^2)\\= (59.1) (2) g\\= (59.1)(2)(9.8)\\= 1158.36 N \\=1160 N[/tex]
Therefore, the closest answer choice is 1160N.
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