Tidal effects of the moon on the earth have caused the earth's rotation rate to slow, thus reducing the spin angular momentum of the earth leading to an increase in earth's day by \(0.1 \mathrm{~s}\) in the past 3800 years. This reduction has been made up for by an increase in the orbital angular momentum of the moon around the earth. Therefore how much farther is the moon now from the earth than it was 3800 years ago? (Note that the moment of inertia of the earth about its axis is \(I=0.33 M R^{2}\) and that the mean earth-moon distance is \(3.8 \times 10^{5} \mathrm{~km}\).)