Question

What is the true weight of an oboject in a geostationary satellite that eighed exactly 10.0 N at the north pole?

Answer 1

For geostationary satellite,
$r=4.2\times {10}^4$ km
$h=3.6\times {10}^{4}km$
Given, mg = 10 N
$mgh=mg-\frac{R^2}{(R+h{)}^2}=10\frac{(6400\times {10}^3{)}^2}{(6400\times {10}^3+3600\times {10}^3)}=\left[\frac{{(64\times {10}^5)}^5}{(6.4\times {10}^6+36\times {10}^5)}\right]=10\left[\frac{4096\times {10}^{10}}{(42.4{)}^2\times {10}^{12}}\right]=\frac{4096}{17980}=0.227N$