Question

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?

Answer 1

`(W)/(9)`

Step-by-step 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

`W=F_1=(GmM)/(RE^2)`

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

`(F_1)/(F_2)=((RE+2RE)^2)/(RE^2)\\\Rightarrow (W)/(F_2)=9\\\Rightarrow W=9F_2\\\Rightarrow F_2=(W)/(9)`

The weight above the surface of the Earth is
`(W)/(9)`