A satellite is launched into a circular orbit of radius ' $R$ ' around the earth. A second satellite

Question

A satellite is launched into a circular orbit of radius ' $R$ ' around the earth. A second satellite is launched into an orbit of radius $1.03 R$. The time period of revolution of the second satellite is larger than the first one approximately by\

Professor PC Thomas Classes · Answer

(b) : Radius of first satellite, $R_{1}=R$ Time period of first satellite, $T_{1}$\ Radius of second satellite, $R_{2}=1.03 R$\ $\because \quad T^{2} \propto R^{3}$\ or $\quad T \propto(R)^{3 / 2}$\ $	herefore \quad T_{1} \propto(R)^{3 / 2}$\ ∴ Time period of second satellite, $T_{2}=$\ $(1.03 R)^{3 / 2}$\ $	herefore \frac{T_{1}}{T_{2}}=\frac{(R)^{3 / 2}}{(1.03 R)^{3 / 2}}=\frac{1}{1.045}$\ or $\quad T_{2}=1.045 T_{1}$\ So, change in percentage = $$ \frac{\left(1.045 T_{1}-T_{1}ight)}{T_{1}} 	imes 100=4.5 \% $$