College Physics 2.10 – The tidal friction

Tidal friction is slowing the rotation of the Earth. As a result, the orbit of the Moon is increasing in radius at a rate of approximately 4 cm/year. Assuming this to be a constant rate, how many years will pass before the radius of the Moon’s orbit increases by 3.84×106 m(1%)?


\displaystyle \Delta \text{t}=\frac{3.84\times 10^6\:\text{m}}{4\:\text{cm/year}}\times \frac{100\:\text{cm}}{1\:\text{m}}=96\:000\:000\:\text{years}

\displaystyle \Delta \text{t}=9.60\times 10^7\:\text{years}

It will take about 96 million years.