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...........

Explanation

`E=(-GMm)/(2r)rArr (dE)/(dt)=(GMm)/2 1/(r^(2))(dr)/(dt)=C`
`rArr dt=(GMm)/(2C) (dr)/(r^(2))`
`int_(0)^(t)dt=(GMm)/(2C)int_(r)^(R)1/(r^(2))drrArr t=(GMm)/(2C)[1/r-1/R]`