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A sattelite is launched into a circular orbit of radius R around the earth while a second satellite is launched into an orbit of radius 1.02R the

percentage change in time periods of two sattelites is
plz anyone ans plz plz plz plz


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from\ kepler's\ law,\\T^2\ \alpha\ R^3\\ \Rightarrow T\ \alpha\ R^{ \frac{3}{2} }\\ \Rightarrow T=kR^{ \frac{3}{2} };\ k\ is\ some\ constant.\\ \\for\ radius=R,\\ T=kR^{ \frac{3}{2} }\\  \frac{dT}{dR}= \frac{3}{2}kR^{ \frac{1}{2}}\\ \\ when\ radius=1.02R;\ dR=1.02R-R=0.02R\\ \frac{dT}{dR}= \frac{3}{2}kR^{ \frac{1}{2}}\\ \Rightarrow dT=\frac{3}{2}kR^{ \frac{1}{2}} \times dR\\ \Rightarrow dT=1.5kR^{ \frac{1}{2}} \times 0.02R\\ \Rightarrow dT=0.03kR^{ \frac{3}{2}}=0.03T

% change= \frac{dT}{T} \times 100= \frac{0.03T}{T} \times 100=\boxed3
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