Two satellites `S_(1)` and `S_(2)` are revolving round a planet in coplanar and concentric circular orbit of radii `R_(1)` and `R_(2)` in te same direction respectively. Their respective periods of revolution are 1 hr and 8 hr. the radius of the orbit of satellite `S_(1)` is equal to `10^(4)`km. Find the relative speed in kmph when they are closest.

Explanation

By Kepler's `3^(rd)` law, `(T^(2))/(R^(3))="constant ":.(T_(1)^(2))/(R_(1)^(3))=(T_(2)^(2))/(R_(2)^(3))` or `(1)/((10^(4))^(3))=(64)/(R_(2)^(3))" or "R_(2)=4xx10^(4)" km"`
Distance travelled in one revolution, `S_(1)=2pi R_(1)`
`=2pi xx10^(4)" and "S_(2)=2piR_(2)=2pi Rxx4xx10^(4)`
`v_(1)=(S_(1))/(t_(1))=(2pi xx10^(4))/(1)=2pixx10^(4)" km"//"h"`
and `v_(2)=(S_(2))/(t_(2))=(2pi xx4xx10^(4))/(8)=pixx10^(4)" km"//"h"`
`:.` Relative velocity `= v_(1)-v_(2)=2pixx10^(4)-pixx10^(4)`
`=pixx10^(4)" km"//"h"`