A satellite of time period 24 h is orbiting the earth at a height 6R above the surface of earth, where R is radius of earth. What will be the time period of another satellite at a height 2.5 R from the surface of earth ?

Explanation

As `T^(2) prop R^(3) " " ` … (By Kepler. third law )
` :. " " (T_(1)^(2))/(T_(2)^(2) ) = (R_(1)^(3))/(R_(1))`
` or ((T_(2))/T_(1))^(2) = ((R_(2))/(R_(1)))^(3)`
` rArr T_(2)^(2) = T_(1)^(2) [ (3.5R)/(7R)] ^(3)`
`rArr T_(2)^(2) = (T_(1)^(2))/8 `
`rArr T_(2) = (T_(1))/(2sqrt(2))`
`T_(2) = 24/(2sqrt(2)) " " ....( :. T_(1) = 24 "hours ")`
` :. T_(2) = 6sqrt(2) ` hours