A satellite of mass `m` is orbiting the earth in a circular orbit of radius `r`. It starts losing energy due to small air resistance at the rate of `C J//s`. Then the time teken for the satellite to reach the earth is...........

Answer

`t =(GMm)/(2C)((1)/(R_(e ))-(1)/(r ))`

Explanation

`E_(i) = -(GMm)/(2r) rArr E_(f) = -(GMm)/(2R_(e ))`
`Delta E =(GMm)/(2) [(1)/(R _(e ))-(1)/(r )]`
`t = (Delta E)/(C ) rArr t = (GMm)/(2C)[(1)/(R_(e ))-(1)/(r )]`