Question

An astronaut goes out for a space-walk at a distance above the earth equal to the radius of the earth. What is her acceleration due to gravity at that point?

Answer 1

Answer:$\frac{g}{4}$

Explanation:

Let m be the mass of Astronaut

M=mass of earth

G=Gravitational constant

R=radius of Earth

Force Exerted by Earth on Astronaut

$F=\frac{GmM}{R^2}$

acceleration due to gravity is $=\frac{F}{m}=g$

$g=\frac{GM}{R^2}$

When it is at $r=2R$

$g'=\frac{GM}{(2R)^2}$

$g'=\frac{GM}{4R^2}=\frac{g}{4}$