Question

Calculate the height of the communication satellite. $[GivenG=6.67\times {10}^{-11}N{m}^2/k{g}^2,M=6\times {10}^{24}kg,R=6400km]$

Answer 1

given :- $G=6.67\times {10}^{-11}N/m^2/k{g}^2$

$M=6\times {10}^{24}kg$

$R=6400km$

w.k.t; $T=2\pi \sqrt{\frac{r^3}{GM}}$

$T^2=\left(\frac{4{\pi }^2}{GM}\right)r^3{r}^3=T^2\frac{GM}{4{\pi }^2}$

$\therefore (R+h{)}^3=\frac{T^{2}GM}{4{\pi }^2}$ $[\because$ because $(r{)}^3=(R+h{)}^3]$

putting the values will get :

$R+h=3\sqrt{75.74\times {10}^{21}}$

$R+h=4.231\times {10}^{6}m$

$h=4.231\times {10}^{6}m-R$

$h=4.231\times {10}^{6}m-6.4\times {10}^6[\because R=6.4\times {10}^6]$

$h=35.9\times {10}^{6}m$ or $35910km$