What is the true weight of an object in a geostationary satellite that weighed exactly $10.0~N$ at t

Question

What is the true weight of an object in a geostationary satellite that weighed exactly $10.0~N$ at the north pole? (Given radius of earth is $6400~km$ and radius of geostationary orbit is approximately $42300~km$)

Professor PC Thomas Classes · Answer

True weight is the actual gravitational pull, $W' = \frac{GMm}{r^2}$. Since surface weight $W = \frac{GMm}{R^2} = 10~N$, we get $W' = W(\frac{R}{r})^2 = 10(\frac{6400}{42300})^2 \approx 0.23~N$.