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A satellite of mass m is orbiting the ea...

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...........

Text Solution

Verified by Experts

The correct Answer is:
`[1/R-1/r]`
`E=-(GMm)/(2r)`
`(dE)/(dt)=(GMm)/2 1/(r^(2)) (dr)/(dt)`
`int_(0)^(t)dt=(GMm)/(2C)int_(r)^(R)(dr)/(r^(2))`
`t=(GMm)/(2C)[1/R-1/r]=(GMm)/(2C)[1/R=1/r]`
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