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)implies(dE)/(dt)=(GMm)/21/(r^(2))(dr)/(dt)=C`
`impliesdt=(GMm)/(2C)=(dr)/(r^(2))`
`int_(0)^(1)dt=(GMm)/(2C)int_(r)^(R)1/(r^(2))drimpliest=(GMm)/(2C)[1/r-1/R]`