Assume the earth to be a nonrotating sphere with mass ME and radius RE. If an astronaut weights W on the ground, what is his weight when he is 2RE above the surface of the earth?

Respuesta :

Answer:

[tex]\dfrac{W}{9}[/tex]

Explanation:

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

m = Mass of person

M = Mass of Earth

RE = Radius of Earth

Force is given by

[tex]W=F_1=\dfrac{GmM}{RE^2}[/tex]

It can be seen that force or weight is inversely proportional to Radius of Earth

[tex]\dfrac{F_1}{F_2}=\dfrac{(RE+2RE)^2}{RE^2}\\\Rightarrow \dfrac{W}{F_2}=9\\\Rightarrow W=9F_2\\\Rightarrow F_2=\dfrac{W}{9}[/tex]

The weight above the surface of the Earth is [tex]\dfrac{W}{9}[/tex]